THE UNIVERSIT Y OF MICHIGAN COLLEGE OF LITERATURE, SCIENCE, AND THE ARTS Department of Astronomy Final Report SOLAR SOFT X-RADIATION Roger J. Thomas ORA Project 05567 under contract with: NATIONAL AERONAUTICS AND SPACE ADMINISTRATION GODDARD SPACE FLIGHT CENTER CONTRACT NO. NAS5-3176 GREENBELT, MARYLAND administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR April 1970

This report was also a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan, 1970.

TABLE OF CONTENTS Page LIST OF TABLES v LIST OF FIGURES vii ABSTRACT ix CHAPTER Io INTRODUCTION 1 II. THE SOLAR SOFT X-RAY EXPERIMENT 10 1. Introduction 10 2. General Characteristics 10 3. Correction for the Background Signal 12 4. The Effective Bandpass 13 5. The Solar Aspect Correction 15 6. Time Resolution, Accuracy, and Coverage 17 7o The Dynamic Range and Sensitivity 18 8. Instrumental Stability 19 9. Conversion of Detector Response to X-ray Flux 21 10o Accuracy of the X-Ray Flux Values 26 III, THE X-RAY SLOWLY VARYING COMPONENT 44 1. Determination of the Daily E(8,12) Base-Level 44 2. Comparison with Ca+ Plage Indices 45 35 Comparison with X-Rays of Other Wavelengths 51 IV. THE X-RAY BURST COMPONENT: STATISTICAL STUDIES 59 1o Selection of Ha Flare Events 59 2, The List of Ha Flares Having X-Ray Coverage 61 3. Characteristics of the Ha Flares in Catalog II 79 4. Characteristics of the Soft X-Ray Bursts in Catalog II 81 a. Occurrence of the bursts 83 bo General time-profile properties 84 c. Mean burst durations 89 d. Accuracy of source position and burst amplitude 90 5. Time-Relations Between Ha Flares and Soft X-Ray Bursts 91 ao Starting times 92 b. The X-ray precursor 94 iii

TABLE OF CONTENTS (Concluded) CHAPTER Page c. Maximum and ending times 100 6. Comparison of Soft X-Ray Burst Amplitudes with Other Phenomena 103 ao Ha flare importance 103 bo Time of occurrence 109 c. Location on the disk 110 d. General solar-activity level 114 e. Characteristics of the associated plage 116 f. Characteristics of the associated radio bursts 122 7. Total X-Ray Burst Energies 126 V. THE X-RAY BURST COMPONENT: STUDIES OF INDIVIDUAL EVENTS 131 1. Selection of Events 132 2. Ha Isophotometry 137 3. General Comparison of the Soft X-Ray and Ha Events 143 4. Comparison with the Results of Chapter IV 151 5. Observations at Other Wavelengths 155 VI. SUMMARY 158 1. The Slowly Varying Component 158 2. The Burst Component 160 REFERENCES 166 APPENDIX. TWO METHODS FOR THE DETERMINATION OF FLARE EMISSION IN Ha 179 1. General Formulation 179 2. Method A: "Typical" Total Area and Peak Intensity 186 3. Method B: Isophotometry 188 iv

LIST OF TABLES Table Page 2.1. Dynamic Characteristics of the Michigan Instrument 19 2.2. Temperature Determinations of Solar Active Regions 30 2. 3. University of Michigan Solar X-Ray Experiment Aboard OSO-III 43 3.1. Correlation of E (8,12) with Ca+ Plage Indices 46 3.2. Relationship Between Arbitrary Ca Plage Intensity Scale and Photometric Measurements of Ca Plages 47 5 3. Characteristics of Compared Experiments 53 4. 1. Ha Flares with X-Ray Coverage (Catalog II) 62 4.2. Classification of Flare Area 76 4.3. Frequency Distribution with Flare Importance 79 4.4. Frequency Distribution with Hemisphere of Occurrence 80 4.5. Mean Differences Between Ha and Soft X-Ray Starting Times 93 4.6. Mean Differences Between Ha and Soft X-Ray Maximum and Ending Times 101 4.7. Mean E(8,12) Amplitudes for Flare-Associated Bursts 104 4.8. Mean Emission-Rate Enhancements for Ha and Soft X-Ray Events 106 4.9. Mean El (8,12) Amplitude Versus Universal Time 110 4.10. Mean E (8,12) Amplitude Versus Location on the Disk 111 4.11. Mean Eln(8,12) Amplitude Versus Disk-Center Distance 112 4.12. Mean E (8,12) Amplitude Versus Initial Detector Mode 114 4.13. Correlation of AEl (8,12) with Solar-Activity Indices 115 4.14. Mean E n(8,12) Amplitude Versus Plage Characteristics 118 v

LIST OF TABLES (Concluded) Table Page 4.15. Soft X-Ray Events Associated with Type IV Radio Bursts 123 4.16. Mean E(8,12) Amplitude Versus Spectral Class of Radio Burst 125 4.17. Total 8-12 A Emission During Ha Flares 128 4. 18. Reported Values of Total Flare Emission 128 5.1. Ha Data for the Analyzed Flares 133 5.2. E(8,12) Data for the Analyzed Flares 133 5.3. Data for the Reduction of the Analyzed Flares 141 5 4. Photometric Times of Maximum 152 5.5. Peak Enhancements in Emission Rates 153 5.6. Total Flare Emission in Ha and 8-12 A 155 5.7. Total Energy Emission During the 24 March 1968 Flare 156 6.1. "in" X-Ray Emission Measures Due to Thermal Bremsstrahlung 161 A. lo "Typical" Areas and Peak Intensities for Ha Flares 188 vi

LIST OF FIGURES Figure page 2-1. Spectral efficiency of the Michigan ion chamber. 14 2-2. Time-profile of the soft X-ray burst on 6 May 19670 25 2-3. Correction for any error due to the adopted gray-body temperature of 2 x 106 K. 28 2-4. Relation of the conversion factor y to the Michigan experiment's effective bandpass as defined by X2- 32 2-5. High resolution X-ray spectra between 7 and 20 A obtained by the Goddard Space Flight Center's crystal spectrometer aboard OSO-III. 34 2-6. Spectrum of a major X-ray burst on 22 March 1967 plotted in absolute units. 36 2-7. Spectral response of the Michigan ion chamber to a major X-ray burst on 22 March 1967. 37 2-8. Comparison of the daily base-levels of E(8,12) and E(1,8) from 1 August 1967 to 31 March 1968. 39 2-9. Comparison of the peak rates of E(8,12) and E(2,12) for X-ray bursts associated with major Ha flares. 41 3-1. Relation between the daily values of Eb(8,12) and the calcium plage index Z Ax I for the period 10 March to 1 June 1967. 50 3-2. Composite average spectra of the slowly varying component between 1/2 - 60 A for two dates. 52 3-3. Comparison of Eb(8,12) with (a) Eb(1/2,3) and (b) Eb(8,20) for the interval 1 August 1967 to 31 March 19680 56 4-1. Frequency distribution of Catalog II flares with Universal Time. 82 4-2. Frequency distributions of Catalog II bursts with (a) rise-time and (b) mean rate of E(8,12) rise. 85 vii

LIST OF FIGURES (Concluded) Figure Page 4-3. Scatter diagram of X-ray burst amplitude AE(8,12) versus 87 rise-time for events of Catalog II. 4-4. Time-profile of the soft X-ray burst on 11 April 1967. 88 4-5. Time-profile of the soft X-ray burst on 17 June 1967 95 (Catalog #76). 4-6. Frequency distribution of E(8,12) background fluctuations as a function of duration. 99 4-7. Relation between AS(8,12) and estimated AS(Ha) for various flare importance classes. 107 4-8. Frequency distribution of plages having a given number of events in Catalog II. 117 4-9. Scatter diagram of AE(8,12) versus total area of the related sunspot group. 121 5-1. Ha filtroheliogram of lb flare on 26 March 1967. 134 5-2. Ha filtroheliogram of lb flare on 24 March 1968. 135 5-5. Ha filtroheliogram of lb flare on 25 March 1968. 136 5-4. Representative Ha isophotes of the lb flare on 25 March 1968. 139 5-5. Comparison of the 8-12 A emission rate (top), Ha emission rate (middle), and Ha intensity (bottom) during the lb flare on 24 March 1968. 144 5-6. Comparison of the 8-12 A emission rate (top), Ha emission rate (middle), and Ha intensity (bottom) during the lb flare on 25 March 1968. 146 5-7. Comparison of the 8-12 A emission rate (top), Ha emission rate (middle), and Ha intensity (bottom) during the lb flare on 26 March 1967. 149 5-8. Comparison of the Ha and 8-12 A emission rates for the lb flares on 26 March 1967 (top), 24 March 1968 (middle), and 25 March 1968 (bottom). 150 viii

ABSTRACT Data from The University of Michigan's ion chamber photometer aboard the earth-orbiting satellite OSO-III are used to investigate relationships between solar soft X-radiation and phenomena observed at other wavelengths. The Michigan 8-12 K X-ray data are exceptionally well suited for such studies because they cover an interval of more than a year on a nearly continuous basis with excellent time resolution, sensitivity, dynamic range, and stability. X-ray fluxes are determined using the assumption of a 2 x 106 K gray-body spectrum which remains constant with timeo Uncertainties in derived fluxes that are caused by this assumption are shown to be small even during X-ray bursts. We find that the slowly varying component of solar soft X-radiation is + closely related to both the area and intensity of the Ca emission of chromospheric plages. The X-radiation associated with each plage apparently origirates from a condensation which is significantly above the chromosphere and whose thickness does not depend strongly on its area. There is some evidence that these condensations are not isothermal and that their temperatures and/or densities decrease with ageo In addition, the data suggest that the temperature of the X-ray emitting source is influenced by variations in the general level of solar activity, The burst component of solar soft X-radiation is examined for 283 events that are associated with well verified Hca flares of importance > 1. Of these flares, 282 are accompanied by a significant enhancement in X-radiationo The peak amplitude of this X-ray enhancement correlates with the area and intensity ix

of the Ha flare. For a flare of a given area and intensity, the peak amplitude of the associated X-ray burst is found to be a function of its distance from the solar limb, an effect attributed to the Ha observations. The peak amplitude also depends on the general level of solar activity at the time of the burst and on the age and "flare-richness" of the associated plage. The latter effects are most likely due to density variations in the X-ray emitting region itself. The properties of the general time-profiles for flare-associated bursts, as well as their frequency of occurrence from center to limb, imply that such bursts are predominantly thermal in nature. It is shown that thermal bremsstrahlung radiation is negligible at 8-12 A for these bursts, so that the dominant mechanisms are recombination and line emission. However, some cases are observed of a relatively weak, impulsive component in 8-12 A bursts which may be due to nonthermal processes. We find that the start of the soft X-ray burst typically, but not always, precedes the onset of the Ha enhancement by a few minutes. In general, the Ha i.rtenLsity of the flare's brightest point and the associated soft X-ray flux have roughly similar time-profiles. Isophotometry of three selected flares shows that in two cases the similarity is even more striking when the X-ray flux curve is compared to that of the flare's total Ha flux. This suggests that the time variation of each emission process is governed by the energy source term rather than the decay term as is usually assumed. In addition, we find that the peak enhancements in the soft X-ray and Ha emission rates are nearly identical for these flares. Furthermore, it is shown that the total energies emitted by these flares in the forms of 8-12 A X-radia x

tion and Ha emission are the same within observational errors. Finally, it is estimated that energy radiated between 8-12 A may account for almost one-tenth of a flare's total electromagnetic emission. xi

CHAPTER I INTRODUCTION The University of Michigan's ion chamber photometer aboard the National Aeronautics and Space Administration satellite OSO-III was one of the first to monitor the soft X-radiation of the sun for more than a year on a nearly continuous basis. The data it provided are exceptionally well suited for the investigation of many aspects of various solar phenomena. The present study takes advantage of these fine observations to examine the properties of the solar X-ray "slowly varying" and "burst" components, as well as to infer some of the physical characteristics of those regions in the solar atmosphere which are responsible for this radiation, The first suggestion that the sun might emit X-radiation was made independently by Hulburt (1938) and Vegard (1938) as a possible mechanism for the maintenance of the earth's ionosphere. The fact that sudden ionospheric disturbances (SID's) seemed to be closely related to solar flares (Martyn et alo, 1957; Newton and Barton, 1937) then implied that the sun's "ionizing radiation" was appreciably enhanced during these chromospheric eruptions and that this enhanced emission originated from the same general region as the optical flare (Giovanelli, 1938)o Therefore, the ionosphere can be considered as being a very broad-band detector of short wavelength solar radiation, and by monitoring distant radio signals using certain standard techniques (see for example Aarons edo, 1963), data can be easily obtained for the study of XUV solar radiation (roughly 1-1500 A). 1

2 Until recently, this technique had provided a major source of information about the "slowly varying" and "burst" components of radiation in this spectral region (e.g., Kundu, 1965). These ionospheric studies are continuing (e.g., Donnelly, 1968a, 1969a; Reid, 1969), and have even advanced to the point where emitting region sizes can be estimated from observations during a solar eclipse (Meisel, 1968), Unfortunately, the interpretation of ionospheric disturbances in terms of the incident solar radiation is quite uncertain, requiring detailed knowledge of the temperature, density, and composition of the earth's upper atmosphere, as well as the appropriate dissociation and recombination rates, among other parameters. In addition, some early investigators naturally assumed that most of the enhanced ionizing radiation during a solar flare was due to hydrogen Lyman-alpha emission (C. S. Warwick, 1963), an assumption which is now known to be incorrect (Hallam, 1964). Furthermore, it appears that hard Xradiation (<1 A) does not contribute to SID's (Donnelly, 1968a) or to the maintenance of the ionosphere (Allen, 1965), so that ionospheric studies provide no direct information about this spectral region. For these reasons and because many X-ray bursts of only moderate amplitude do not produce any observable ionospheric effects (Dickerman and Thornton, 1966), data from groundbased detectors are insufficient to support a complete and quantitative investigation of solar X-radiation. Direct observations made above the earth's atmosphere are essential for this program, The U. S. Naval Research Laboratory pioneered in obtaining such observations, the first of which utilized a captured V-2 rocket to carry a photographic plate shielded by a thin beryllium filter to an altitude greater than

3 100 km on 6 August 1948. Upon recovery, the plate was found to be darkened, thus providing the first direct evidence for solar soft X-radiation (Burnight, 1949). This observation was followed by a series of flights which allowed the NRL group to develop and refine their instrumentation in order to expand the spectral region covered, improve spectral resolution, and put the measurements on a quantitative basis. Friedman (1962, 1963a) reviews the work of the NRL solar X-ray group from 1948 to 1961, a period when they were virtually the only observational researchers in the entire field. By 1961, these rocket-borne X-ray detectors were providing data of sufficient quality to reveal the main characteristics of solar X-radiation and to allow a better determination of the ionospheric parameters mentioned earlier. However, a major limitation of this technique is the fact that the detector is above the earth's atmosphere for only a few minutes of the flight. Although such brief observations do not seriously compromise studies of the quiet sun, they are inadequate to follow the total development of X-ray bursts, since these may last more than an hour. Furthermore, the occurrence of a burst is unpredictable (at least at this time) so that there is very little chance for a rocket flight to bracket the initial rise of an event, which in many respects is the most interesting phase of the entire burst. These difficulties may be overcome to some extent by means of detectors aboard a very high altitude balloon. On 20 March 1958, the first complete profile of a directly observed X-ray burst was recorded with this technique (Peterson and Winckler, 1958). Many such balloon observations were made by the University of Minnesota group, and their work through 1962 has been summarized by

Winckler (1964). Unfortunately these studies also have severe limitations in that only the most energetic X-rays can penetrate the earth's atmosphere to balloon altitudes. In addition, a relatively large and somewhat uncertain correction must still be applied to account for the atmospheric absorption above the balloon (Peterson and Winckler, 1959). Therefore, even this method is not completely satisfactory. Since ionospheric observations and suborbital and balloon flights are relatively inexpensive and simple, much valuable information about solar Xradiation has been and will be obtained by these means. But some other observing technique is obviously required in order to conduct an "ideal" X-ray experimento In addition to high stability, accurate absolute calibration, and high signal-to-noise ratio, the characteristics of such an ideal experiment should include: 1o Time resolution better than 1 second, Unlike the slowly varying background component which changes on a time scale of several hours, the time scale of solar X-ray bursts is less than a minute and in some cases is as small as a second (e.g., Kane, 1969). 2, Spectral resolution (X/A\) better than 1000 at 10 A. Since X-ray emission lines have widths of about 0.1 A, a spectral resolution better than 1000 at 10 A will be necessary to observe these line profiles properly (J. W. Evans et al., 1969). 35 Spatial resolution better than 1 arc-second, Several lines of evidence, including direct photographs (e.g., Vaiana

5 et al., 1968), all suggest that X-ray emitting regions have significant structure at 1 arc-second, and that perhaps 0.1 arc-second resolution is necessary to resolve them adequately (J. W. Evans et al., 1969). 4. High dynamic sensitivity. The initial, very gradual rise often associated with soft X-ray bursts can normally be observed only with a detector which has a high dynamic sensitivity (Teske and Thomas, 1969). 5. Adequate absolute sensitivity. Longward of 2 A, a sensitivity of 10-8 erg/(cm2 sec A) is sufficient even during solar minimum. For shorter wavelengths, only upper limits to the minimum solar flux are known, so that the necessary absolute sensitivity levels in this interval cannot yet be established. However, an unambiguous observation of quiet sun hard X-radiation and gamma radiation is of extreme importance in determining to what extent nonthermal electromagnetic or nuclear processes occur in the nonactive solar atmosphere (Neupert, 1969). 6. Dynamic range better than 4 orders of magnitude. Soft X-ray flux variations of nearly 3 orders of magnitude have been observed (Van Allen, 1968), while in the hard X-ray region, the variations may be greater than 4 orders of magnitude (Kane and Winckler, 1969). Therefore, a dynamic range at least this large is needed to avoid detector saturation. 7. Coverage of the entire X-ray spectrum. An X-ray emitting region cannot be characterized by a single temperature

6 and density (Blake et al., 1963a; Mandel'shtam, 1965a; Cline et al., 1968). Therefore, each interval of the X-ray spectrum gives information about a different portion of the emitting region, so that the entire spectrum must be observed in order to develop a realistic emission model, 8. Continuous operation for more than 10 years. Investigations into possible variations of X-ray emission characteristics during the entire solar cycle require observations over at least a 10-year period. However, in order to include the unpredictable starting phase of the X-ray burst component, these observations must be of a continuous monitoring type. Although present technology is not sufficiently advanced to conceive of a single instrument combining all these characteristics, all but the last can be approached by observing the sun with several instruments simultaneously, each of which provides some part of the total desired properties. However, the longterm, continuous monitoring capability can only be achieved by detectors aboard space satellites (short of building at least three observatories on the surface of Mercury or the Moon). With the advent of such X-ray instrumented satellites, the amount of information concerning the sun's X-radiation has increased at a tremendous rate. After Vanguard 3 and Explorer 7 failed to return useful data, the first successful solar X-ray satellite, Solar Radiation I, was launched in June 1960, and once again it was the U. S. Naval Research Laboratory that pioneered this new field (Kreplin et al., 1962). Following this initial success, a great num

7 ber of satellites with solar X-ray detectors were put into orbit by Great Britain and the Soviet Union, as well as the United States. Although the vast majority of these X-ray satellites orbit the earth, there are some which are orbiting the moon (Explorer 35) or the sun (Mariner 5). The great amount of effort being expended in this field can be seen by noting that in the interval March 1967 to March 1968, the period of special concern to this dissertation, at least 12 different satellites were monitoring the sun's X-radiation (Cosmos 166, Explorers 30, 33, 35, and 37, Mariner 5, OGO's 4 and 5, OSO's 3 and 4, and Velas 7 and 8), some of which had several solar X-ray experiments aboard' These satellite experiments were in addition to rocket and balloon flights during this period, along with the continuing indirect studies using ionospheric effects. The question naturally arises: why is there so very much effort over a mere 100 A spectral band from a single, ordinary star? Of course, the reasons usually cited for studying the sun are appropriate here: (a) since the sun is about 250,000 times closer than the next nearest star, requirements on instrumental absolute sensitivity are less stringent by a factor of more than 1010; (b) also because of its proximity, the sun is the only star whose surface features can presently be resolved; (c) the fact that the sun is near the middle of the Hertzsprung-Russell main sequence means that knowledge about the sun may be extrapolated to the greatest number of other stars with a minimum amount of uncertainty;

8 (d) since the sun's particle and radiation emission affects every object in the solar system to some extent, knowledge of solar emissions is essential to a complete understanding of these objects; (e) and naturally, such a study is intrinsically interesting, The X-radiation of the sun is of particular importance for other reasons as well: (a) X-ray emitting regions in the corona can be observed during their entire disk passage, while these coronal condensations can be seen in visible light only at the limb; (b) since these regions consist of very hot plasma confined by a magnetic field and since bursts seem to be related to instabilities in this field, solar X-ray observations touch on several problems associated with controlled thermonuclear fusion; (c) solar X-radiation gives information about plasma under conditions unobtainable in the laboratory; (d) some hard X-ray bursts seem to be caused by very energetic nonthermal acceleration processes and thus may provide information in this area of great current interest; (e) knowledge of the sun's X-ray flux and its variations is essential for a proper understanding of the earth's ionosphere; (f) such knowledge is also necessary to assess correctly the possibility of X-ray induced changes in the structural characteristics of materials considered for space applications; (g) through its effect on the ionosphere, solar X-radiation strongly in

9 fluences the quality of long-distance radio communication, which can be completely disrupted during a large X-ray burst; (h) X-ray bursts are usually associated with solar flares and so give additional information on these complex phenomena; (i) there is evidence that a soft X-ray enhancement is the very first manifestation of a solar flare, a possibility of obvious consequence for a flare early-warning system; (j) since high-altitude nuclear explosions produce large bursts of Xradiation, it is important for national defense to be able to distinguish them from solar X-ray bursts; (k) in addition, it may be possible to utilize solar bursts to estimate the effects of nuclear explosion X-radiation on defense systems such as anti-missile tracking, guidance, and communications. Clearly, the X-ray region of the solar spectrum is exceptionally rich in information content and well worth intensive investigation, even though it accounts for only one-millionth of one percent of the sun's total luminosity! Many excellent reviews of previous solar X-ray studies are already available and so will not be duplicated here. In addition to references cited earlier, these reviews include, in chronological order, Friedman (1963b), Kundu (1963), Lindsay et al. (1965), Mandel'shtam (1965a, 1967), Goldberg (1967), Underwood (1968), and most recently Neupert (1969). However, a summary of present ideas concerning solar X-radiation, including those derived from this study, will be given in Chapter VI.

CHAPTER II THE SOLAR SOFT X-RAY EXPERIMENT 1. INTRODUCTION On 8 March 1967, NASA's Third Orbiting Solar Observatory (OSO-III) was launched from Cape Kennedy, Florida, and successfully attained earth orbit. A brief description of this satellite and the seven scientific experiments aboard is given by Brandt (1969). The present study is primarily concerned with The University of Michigan's soft X-ray ion chamber photometer which is located in the rotating wheel section of OSO-III. The original design of this ion chamber was due to Dr. Robert W. Kreplin of NRL. The associated electronics were developed by the Consolidated Systems Corporation of Monrovia, California, which also constructed the entire instrument. The designs of both the electronics subsystem and the ion chamber were modified somewhat for this experiment by The University of Michigan Space Physics Research Laboratory, which was also responsible for the final testing and calibration of the complete system. Dr. Richard Go Teske heads The University of Michigan's solar X-ray project and is the principal investigator in this OSOIII experiment. 2o GENERAL CHARACTERISTICS Basically, an ion chamber photometer is a gas-filled container with a window made of some very thin material. Incident photons, which pass through this window and are absorbed in the filler gas, produce free electrons by the process 10

11 of photoionization. The energy of each photo-ejected electron is quickly converted into secondary ionizations of the gas, producing many more free electrons. These are collected by a low-voltage anode in the chamber and the resulting current is then measured by an electrometer. Such measurements can be treated quantitatively because of the following properties of X-ray photoionization (Hinteregger, 1965): (a) the average number of ion-electron pairs formed per unit number of photons absorbed in a gas is directly proportional to the photon energy; (b) the value of this proportionality factor, called the gas ionization efficiency, is known reliably from numerous experiments; (c) the fractional number of photon absorption events not leading to any ion formation is practically negligible. Since the operating voltage across the chamber is low, no electron multiplication occurs in the filler gas. Therefore, only those free electrons produced by the radiation entering the detector are collected. Because the number of these electrons is proportional to the energy of the absorbed photons, an ion chamber photometer functions as a total energy detector. With this type of detector some spectral information is obtained in the sense that it responds effectively only to radiation in certain wavelength intervals. These intervals are determined by the transmission properties of the window material, the window's thickness, the absorption characteristics of the filler gas, the gas pressure, and the effective length of the chamber. By an appropriate combination of these parameters, the detector's response can be re

12 stricted to a particular spectral band of only a few Angstroms. This procedure is limited, however, by the relatively small number of suitable filler gases and window materials. A more complete discussion of X-ray detector instrumentation in general and the ion chamber photometer in particular can be found in the excellent review articles by Boyd (1965) and Giacconi et al. (1968). 3. CORRECTION FOR THE BACKGROUND SIGNAL The above description of an ion chamber's operation refers to an ideal observing situation. In reality, the orbiting satellite is passing continuously and at a high relative velocity through a medium of charged particles which exists at this altitude. Some of these charged particles penetrate into the detector and cause ionizations in the filler gas. Because the resulting free electrons are in addition to those caused by solar X-radiation, this background signal must be subtracted from the total response in order to obtain a value which is due solely to the sun. Since the Michigan experiment is located in the rotating wheel section of OSO-III, the background signal is measured directly during those intervals when the detector is pointed away from the sun. The encoded voltage of the ion chamber's electrometer is recorded every 0.64 second, while the satellite's wheel section rotates with a period of 1.7 seconds. Therefore, each wheel rotation results in roughly one word of solar soft X-ray data and two words of particle background data. It is easy to distinguish between them since the total response is always larger than the background alone. However, as a check, a sun-sensing

13 photocell mounted next to the ion chamber puts a "tag" on each solar word to insure its proper identification. In the remainder of this paper, the term "ion chamber response" will refer to only that part which is due to the sun's X-radiation. 4. THE EFFECTIVE BANDPASS -4 The Michigan experiment has an aluminum window 5 x 10 cm thick and a nitrogen gas filling at about one atmosphere pressure. This combination gives rise to the spectral efficiency response, e(X), shown in Figure 2-1. Here spectral efficiency is defined as the ratio of the radiation flux absorbed within the filling gas to that incident upon the detector window. It can be shown (e. g., Acton, 1964a) that this ratio is given by the expression: -(4 mPx)G -( mPx)W (\) = [1 - e ]e (2.1) where j is the mass absorption coefficient, p the density, x the thickness of m the material in question, and the subscripts G and W refer to the gas filling and window material, respectively. The relation shown in Figure 2-1 was first calculated from this expression using parameters appropriate for the Michigan detector and then checked by illuminating the instrument with a calibrated iron55 source in airo Clearly, the definition of an effective bandpass is somewhat arbitrary for a detector with such a spectral efficiency response. One possibility is to choose those wavelength intervals in which the ion chamber has at least 10% of its maximum response efficiency. By this definition, the effective bandpass of

14 (X) =[-e-(Lm PX)N2 e-(PX)AI (px)A, = 3.27 mg-cm-2 1.0 - (px) = 3.18 mg-cm-2 0.01,< 0 5 10 15 20 X (Angstroms) Figure 2-1. Spectral efficiency of the Michigan ion chamber. The mass absorption coefficients as a function of wavelength were taken from Victoreen (1949) and Cooke et al. (1962). The nitrogen surface density of the instrument actually flown was 0.00331 gm/cm2. This change alters the above curve by less than 5%.

15 the Michigan instrument is 8.0 to 12.1 A and 2. 0 to 4.0 A. However, it would be more convenient to consider a bandpass which consists of a single wavelength interval, Therefore, one may choose that spectral band in which the detector efficiency is always larger than the peak of the short wavelength lobe. This definition results in an effective bandpass of 8.0 to 11. 5 A. Moreover, it seems justifiable to ignore the short wavelength lobe since solar radiation is always observed to be at least a factor of five stronger at 10 A than at 3 a (for example, see the flare spectra published by Culhane et al., 1969; Pounds, 1970). This means that radiation in the interval 2-4 A contributes less than 2% of the Michigan detector's response. Yet another method is to select that interval which minimizes the effect on the detector's response due to changes in the spectral distribution of the incident radiation. This procedure was first described by Van Allen (1967a) and further developed by Wende (1969). It is described in more detail in Section II-9 of this chapter. For The University of Michigan instrument, this method implies a bandpass of 8.0 to 11.9 A. Since all three methods give approximately the same result, the response function shown in Figure 2-1 can be adequately characterized by an effective bandpass of 8 to 12 A, and measurements made by the Michigan ion chamber photometer will be considered as referring only to this wavelength interval. THE SOLAR ASPECT CORRECTION Actually, the spectral efficiency relation shown in Figure 2-1 is correct only when the sun is in the direction normal to the detector window. In the

16 general case where the sun is at some angle l to this direction, the surface densities px of the window material and filler gas become larger than the values indicated in Figure 2-1 by a factor of sec P. The detector response is further altered by the fact that the ion chamber's effective aperture is proportional to cos P. However, this aspect effect is negligible for the Michigan experiment because of two characteristics of the OSO-III system. First, the ion chamber is designed to telemeter the value of the highest response which occurred during the 0.64-second interval since the previous transmission. This means that one of the three data words recorded in each wheel rotation will always refer to a measurement made at the smallest aspect angle attained during that rotation. Second, the attitude of the satellite is maintained so that the angle between the wheel section's rotation plane and the direction to the sun never exceeds 2-1/2~, which is therefore the largest possible angle for a recorded solar measurement. Since the change in Michigan's ion chamber response at a 2-1/2~ aspect angle amounts to less than 0. 2%, a correction for this effect has not been applied. It should also be noted that because the ion chamber window is recessed in a physical collimator, it is fully illuminated only when the sun is within 9~ of the normal direction. Therefore, the 2-1/2~ limit on the angle of the rotation plane with respect to the sun is completely adequate to insure that the sun does pass through the "view cone" of the Michigan detector. However, since the sun's diameter is just 1/2~, this 9~ view cone does not allow any resolution of the solar disk, so that all measurements refer to the total X-ray flux

17 emitted by the sun's entire visible hemisphere. 6. TIME RESOLUTION, ACCURACY, AND COVERAGE Since a measurement is made each time the sun passes through the detector's cone of view, the time resolution of the original data is 1.7 seconds, i.e., the rotation period of the satellite. However, for economy of presentation, the final output was determined by averaging sets of four consecutive data points, so that the effective time resolution is actually 6.8 seconds. There appears to be no significant loss of information due to this reduction procedure (Teske, 1969a). The absolute time at which a measurement was made can be assigned within 1 second of the correct value in all cases, although the timing usually is much more accurate than this. The differences in accuracy are caused by a peculiarity of the satellite's internal timing system, but are of little concern to the present study. The Michigan experiment began returning data on 9 March 1967 with an expected lifetime of only six months; but it continued to transmit useful information until 17 August 1969, when the experiment was finally terminated by ground command. This remarkable longevity of nearly 2-1/2 years speaks well indeed for the design and construction quality of this sturdy device. Unfortunately, the second of the two tape recorders aboard OSO-III failed on 28 June 1968. After that date, only real-time data could be acquired during the ten-minute intervals when the satellite passed over a tracking station, thus severely limiting the utility of these observations.

However, even while the satellite's tape recorders were operating properly, the data coverage is not continuous. The major loss occurs during "satellite night" when the satellite's orbit carries it into the earth's shadow. In the case of OSO-III, there is approximately one hour of solar observation for every thirty minutes of satellite night. But this coverage is further interrupted by two other causes. One of these is due to the fact that nothing can be recorded while the satellite's tape recorder is "playing back" previously made observations to a ground station, a procedure which normally takes about five minutes. The other type of interruption occurs whenever the satellite passes through the enhanced density of charged particles in the region called the South Atlantic Anomaly. The background response caused by these particles becomes so large that it is not possible to determine accurately the component due to solar Xradiation. Therefore, all time intervals with high background rates have been carefully identified and eliminated from the following analysis. 7. THE DYNAMIC RANGE AND SENSITIVITY The length of the data word which describes the response of the Michigan instrument is limited to seven bits by the OSO-III telemetry system. Therefore, just 128 different values of the ion chamber current can be distinguished. This means that any attempt to increase the experiment's dynamic range can be accomplished only by degrading its dynamic resolution, or sensitivity. In order to overcome this difficulty to some degree, the Michigan ion chamber's response can be encoded according to one of two operating modes, whose characteristics are listed in Table 21l.

19 TABLE 2o 1 DYNAMIC CHARACTERISTICS OF THE MICHIGAN INSTRUMENT ~~_Mode E(8,12) erg/cm2sec Mode Range Resolution High sensitivity 0 - 0.0044 0.000035 Low sensitivity 0 - 0.12 0. 00095 The flux values in this table were derived from the ion chamber's response by a method described in Section II-9. Note that the high sensitivity mode has excellent flux resolution but covers only a rather small dynamic range. On the other hand, the low sensitivity mode has a much larger dynamic range but with poorer flux resolution. The instrument is designed to switch automatically between these two modes depending on whether the inferred 8-12 A solar flux is above or below the value of 0.0044 erg/cm2sec. This permits a total range (0.12 erg/cm2sec) which is adequate for all but the very largest X-ray bursts, and yet allows the detection of subtle changes (0.000035 erg/cm2sec) in the quiet sun level. Unfortunately, it was not possible to take full advantage of this strategy, since the quiet sun level exceeded 0.0044 erg/cm2sec more than one-half of the time, thus causing the ion chamber to operate in its low sensitivity mode even during the majority of nonburst periods. On the other hand, although the available high sensitivity coverage is somewhat limited, it is of great importance to many of the investigations described in Chapters III and IV. 8. INSTRUMENTAL STABILITY There are several possible sources for both short-term and long-term varia

20 tions in the operation of the Michigan ion chamber photometer. In the first place, the response of the instrument is partially a function of its temperature. This is due to the temperature-dependent values of the resistors, across which the electrometer measures its voltageo The temperature of these resistors varies during a given orbit, since the satellite is heated while exposed to the sun and cools when in the earth's shadow. However, this effect is negligible because the range in temperature which is encountered, 18 to 32~C, gives rise to only a 1% difference in the detector's output. Therefore, a constant temperature (20~C) is assumed for the instrument in the actual data reduction procedure. Another possibility is a deterioration of the experiment's electronic subsystem which amplifies, encodes, and then transmits the reading of the ion chambero In order to check for this, a known current is applied to the electrometer's input terminals about every six minutes. This calibration technique shows that the electronics have remained stable within around 1% during the experiment' s lifetime. However, there is no internal calibration system to monitor the nitrogen gas pressure in the ion chambero Gas leakage is a particularly worrisome problem with this type of instrument because an ultra-thin foil window accounts for a large portion of the chamber wall. Any significant loss of filler gas would alter the spectral efficiency curve of Figure 2-1 in such a way as to lower the detector's response to a given flux of solar X-radiation, The permeability of the foil window in the Michigan experiment was measured by a helium leak detector before launcho This measurement implied that the cham

21 ber would retain its filler gas for more than six months, but only if the foil window did not become punctured. Careful fabrication and handling might protect against such an accident on the ground, but once the instrument is in orbit the foil window is completely exposed to the possibility of micrometeoroid impacts. An attempt to estimate the frequency of impact by particles energetic enough to damage the foil led to contradictory results (Teske, personal communication). Depending on which observation of micrometeoroid density was considered, the expected lifetime of Michigan's aluminum window ranged from 23 days to well over a year. Fortunately, there is an external calibration source which can be used to overcome this difficulty: the sun itself. The excellent relation between the daily 2800 MHz solar flux and the soft X-ray base-level is well known (e.g., W. A. White, 1964; Pounds, 1965a; Teske, 1969a; Wende, 1969). The fact that all the E(8,12) values obtained between March 1967 and March 1968 followed very nearly the identical relation with the 2800 MHz flux (Teske, 1969b) is a strong indication that the entire Michigan experiment, including the nitrogen gas filling, remained highly stable during this period. 9. CONVERSION OF DETECTOR RESPONSE TO X-RAY FLUX The ion chamber photometer has a relatively restricted bandpass of effective response, as described in Section 11-4, but it cannot give any information whatsoever concerning the spectral distribution of the radiation within that bandpass. The response to a large number of low energy X-ray photons is identical to that caused by a smaller flux of higher energy radiation. There

22 fore, the incident X-ray spectrum first must be known in order to convert the measured ion chamber current into the proper energy flux of that radiation. Since the spectrum is in fact not generally known, the results of X-ray studies which use ion chamber detectors have been subject to a great deal of uncertainty. Thus, it is necessary to examine in some detail both the extent of this uncertainty and, in particular, the degree to which the flux values derived from the Michigan experiment can be considered as valid. Following Kreplin (1961), the ion chamber current as a function of time can be expressed as: i(t) = AGe * [ e(X)F(k,t)dX (2.2) where A is the detector's effective aperture, G is the ionization efficiency of the filler gas, e is the electronic charge, e(X) is the detector's spectral efficiency given by equation (2.1), and F is the specific flux of the incident radiation. For the Michigan instrument, the total window aperture is 3.88 cm2; but the thin window foil is supported by a wire grid which has a transmission of 83% as determined by optical calibration. Therefore, the effective aperture 2 -19 is actually 3.22 cm. Then, with e given as 1.60 x 10 coul and G taken to be 1.73 x 100~ ion pairs/erg for nitrogen gas, the Michigan ion chamber is characterized by: AGe = 8.91 x 10 coul cm2/erg (2.3) In order to approximate the incident specific flux, previous investigators

25 have always assumed that F can be separated into two components, one of which is just a function of wavelength and another of which varies only with time. That is: F(k,t) = B(X) * D(t) (2.4) However, the quantity of interest the integrated flux between 8 and E(8,12;t) _ f12 8 The time dependence of this value that this quantity will be called imply that E(8,12) can be written in the case of the Michigan experiment is 12 A as a function of time: F(k,t)dX = D(t) * f12 B(%)dX 8 (2.5) will be implicitly understood hereafter, so simply E(8,12). The above expressions then in the following form: E(8,12) = y * i(t) erg/cm2sec (2.6) where: f12 B(X)dX 8 7 = 00 AGe f c(X) B(X)d\'0 erg/(cm2sec amp) (2.7) Note that, for a given detector, this conversion factor y depends on both the effective bandpass (here 8 to 12 A) and the assumed form of the spectral distribution B(X). The most common procedure for the reduction of ion chamber measurements

24 is to assume that B has the same wavelength dependence as the Planck black-body function: B(X) (2.8) 5 hc/XkT 1) Xs(e'-1) This is often termed the gray-body approximation, since the complete expression for the specific flux (2. 4) includes the time-varying "dilution" factor D(t). A great many investigators have used this approximation with a gray-body temperature T of 2 x 106 K for observations near 10 A (see the reviews by Friedman, 1963a; and Mandel'shtam, 1965a). Therefore, the same procedure was followed for the Michigan experiment in order to compare the present results directly with those already observed. Furthermore, when the Michigan project began, very little was known about the true nature of the solar spectrum at Xray wavelengths, so the gray-body approximation seemed the best possible choice at that time. With T = 2 x 106 K, equations (2.1), (2.3), (2.7), and (2.8) can be used to calculate the conversion factor y of equation (2.6). Under the assumptions just described, the conversion factor for the Michigan experiment is: 7 = 7.71 x 108 erg/(cm2sec amp) (2.9) This constant will be used throughout the present study to determine E(8,12). Values of E(8,12) derived by the above procedure are presented graphically as a function of Universal Time (UT) by a computer-controlled plotter. Figure 2-2 shows examples of two such consecutive plots which display many of the

E(8, 2) erg/cm2 sec.005rT.125.001 MAY 6, 1967 MAY 6, 1967 0614 Oi__ "___a —-n-dnse0458 - -e "sunset mark the ^0418 Satellite " high sensitivit 6Ma 1967' ^ erating mode e o455 fX ay burst betchesetn 2-2. TimTe-profile of the soft X-ray detecto 6 at ei433 unL e an FiFgure 2 n end of each record. Thejchigan et raiti pn beginning 7%7 of o (flux scale on leftof record s and0 T. The secondecord shows hih and 50 T

26 features mentioned earlier for this experiment. "Sunrise" and "sunset" mark the beginning and end of these two records, which are separated by about half an hour of satellite "night." An X-ray burst begins at 0422 UT, when the detector is in its operating mode of high sensitivity. (The flux values are given by the scale on the left side of the ordinate axis.) The detector automatically switches to its low sensitivity mode as the burst exceeds.0044 erg/ 2 cm sec, and then becomes saturated for about six minutes during the peak of the burst. (Now the flux scale on the right side of the axis applies.) At the start of the second record, the detector is back in its high sensitivity mode with the X-ray flux gradually decaying to its pre-burst level. Studies to be presented in the remainder of this paper were all based upon measurements made from plots similar to those just described. 10. ACCURACY OF THE X-RAY FLUX VALUES How closely do the E(8,12) values derived by the above method approximate the actual integrated fluxes incident on the detector window E (8,12)? A relation between them can be written in the form: E = aEb (2.10) where b is, in general, not constant. The factor a is a measure of the absolute error in the reduction procedure and depends in part upon instrumental calibration inaccuracies. The absolute calibration of the Michigan instrument itself is believed to be within 6% of correct (Teske, 1969a). This type of error is relatively harmless in the sense that all final results can be corrected easily

27 by applying a single constant factor. Furthermore, any statistical relationships derived from such measurements remain qualitatively valid. On the other hand, the relative error in the data reduction, represented by the exponent b, is a much more serious problem. This error results from the fact that the solar X-ray spectrum does not actually correspond to a two million degree gray body and, more importantly, that the spectrum changes significantly with time. If b differs much from unity and especially if b is not a monotonic function of E, ion chamber measurements would be extremely difficult to interpret and any conclusions drawn from them would be highly questionable. After a careful study of this problem, Acton (1964) concluded that observations from an aluminum window ion chamber and reduced by assuming a constant two million degree gray-body spectrum are probably correct within a factor of four. But many investigators claim that this type of error can exceed an order of magnitude (Pounds and Willmore, 1963; Lindsay et al., 1965; Mandel'shtam, 1965a), while Neupert (1969) points out that the difficulty is enhanced for a detector such as the Michigan instrument, which has a very large dynamic range. One way to measure this error is to determine the effect on the calculated E(8,12) values due to expected changes in the solar X-ray spectrum. Figure 2-3 shows the result of one such study made by Teske (1969a). If the true spectrum is that of a gray body at a temperature T, this graph gives the correction factor which must be applied to E(8,12). It can be seen that this correction exceeds an order of magnitude whenever the corresponding gray-body temperature is greater than about twenty million degrees.

=2x106deg.) 1.0 ro 108 Multiply gray-body T (deg. K) 6 1 of 2 x 106 K Figure 2-3. Correction for any error due to -the adopted gray-body temperature of 2 x ec K. 12) by he ctogin 2r in or ader to obtain the correct flux for a spectra lope of temperature T. (Figure from Teske, 1969a.)

29 Now it is necessary to discover what range of T is to be expected. In principle, the appropriate gray-body temperature for a given set of observations can be estimated from measurements made by the ion chamber during satellite "sunrise" and "sunset." At these times, the earth's atmosphere differentially extinguishes the solar X-radiation and thus acts as a broad-band spectral analyzer. Such a technique has been used for observations made by moderate altitude rockets (Chubb et al., 1957; Mandel'shtam et al., 1962) and by an orbiting satellite with simultaneous measurements from three detectors of different wavelength intervals (Landini, 1967). The analysis is much more complex in the latter case, since the solar radiation passes into and then out of the earth's atmosphere at a large slant angle. This method therefore appears to be impractical for a single detector experiment, such as Michigan's, because of the great uncertainty due to errors in the atmospheric parameters which must be used (Mount, personal communication). It is interesting to note that this technique is now being inverted in order to determine more accurately these atmospheric parameters using high resolution observations of the solar X-ray spectrum (Rugge, personal communication). Although individual temperatures cannot be derived from the Michigan experiment itself, it is possible to estimate the expected range of T from values quoted by other investigators. Table 2.2 summarizes many such temperatures determined by a number of techniques which are appropriate for the spectral region 0 around 10 A. Some caution is necessary in using these values, however, because in general they refer to the electron temperature of the emitting plasma rather than its gray-body temperature, which is needed for expression (2.8). Moreover,

50 TABLE 2.2 TEMPERATURE DETERMINATIONS OF SOLAR ACTIVE REGIONS / 6 \ Wavelength Solar T (106 K) Wavelength Solar Method* Reference _Interval (A) Activity 1. 0-1.5 1.5-1.9 1.5-2.1 1.6-2.6 1.7 1.7-2.2 1.8 1.8 1.9-6.4 2 2 -5 2. 2 2.3 2.4-2.9 <2.5 2.7 2.8-3.0 5 -4 3 5 -8 5 -10 <4 -5 4** 4 -5 4.5 <5 < 6 6 10 < 10 20 8-20 20 8-11 8-12 7- 9 8-20 2-18 8-20 < 10 8-15 "soft X-rays" 2-18 2-18 7- 9 < 10 11-22 > 11 8-20 2-14 "soft X-rays" < 14 8-12 < 10 < 10 > 8 2-12 "soft X-rays" 8-20 nonflare nonflare nonflare nonflare nonflare nonflare nonflare nonflare flare nonflare nonflare nonflare nonflare nonflare nonflare flare nonflare nonflare nonflare subflare flare flare flare flare flare nonflare nonflare flare flare 2+ flare 1 2 3 2 3 3 3 3 3 2 5 3 3 3 2 3 3 5 6 3 7 4 6 5 5 Mandel'shtam et al., 1961 Zhitnik et al., 1967 Reidy et al., 1968 Jones et al., 1968 Pounds and Sanford, 1963 Culhane et al., 1963 Bowen et al., 1964 Reidy and Vaiana, 1966 Mandel'shtam, 1965a Negus and Glencross, 1968 Mandel'shtam, 1965b Blake et al., 1965a Billings, 1959 Tindo and Surygin, 1965 Mandel'shtam, 1965a Bowen et al., 1964 W. A. White, 1963 Evans and Pounds, 1965 Pounds et al., 1968 Landini et al., 1965 Beigman et al., 1969 DeJager, 1965a Acton, 1968 Pounds, 1965b Mandel'shtam et al., 1961 Mandel'shtam et al., 1962 Culhane et al., 1968 Wende, 1969 Kawabata, 1966a Elwert, 1964:i iet hods: 1 Ionospheric effects 2 Ratio of emission line intensities Ratio of broad-band responses 4Proportional counter 5 Visible coronal condensation 6 Theoretical model 7 Differential atmospheric extinction **Temperature revised by Acton (1968).

31 since the solar atmosphere is optically thin to X-radiation (Allen, 1969), the X-ray spectrum in reality cannot possibly be that of a gray body. Fortunately, this is not a serious problem because Acton (1964) points out that the spectral slopes given by both temperatures are very similar over a limited wavelength interval. According to the conversion scheme given by Mandel'shtam (1965a), the electron temperature extremes of 1 and 10 million degrees shown in Table 2.2 correspond to a gray-body temperature range of roughly 0.7 to 5 million degrees. With these limits, Figure 2-3 then implies that the relative error in E(8,12) is always less than 300%, assuming there is no line emission. A more comprehensive estimate of this error can be obtained by means of the Van Allen-Wende method mentioned in Section 11-4. In this procedure, expression (2.7) is used to calculate 7 as a function of effective bandpass for a variety of assumed spectra. Since the short wavelength limit of the Michigan detector's bandpass is clearly the aluminum K-edge at 8 A, only variations in the long wavelength limit X2 are considered here. Figure 2-4 shows the results of such calculations for gray-body and free-free (thermal bremsstrahlung) spectra as well as spectra which are softer than free-free by a factor of X2. Furthermore, a curve for each of these spectral types is plotted using temperatures of one, two, four, six, and ten million degrees (except for a gray-body spectrum at ten million degrees, which is unrealistic, as shown above). The set of curves in Figure 2-4 forms a "bow-tie" and so the combination of y and X2 which defines the narrowest part of this distribution will result in flux values which have the smallest possible relative errors. For example, the optimum point in this plot is:

32 10,~ )y erg /cm2 sec. amp. 108 9 10 II 12 13 14 15 X2 Figure 2-4. Relation of the conversion factor y to the Michigan experiment's effective bandpass as defined by \2. Curves are shown for three types of spectra at five different temperatures between 1 - 10 x 106 K. The values of 7 and X2 adopted for this study are indicated by o.

33 y = 5.9 x 108 erg/(cm2 sec amp), \2 = 11.9 A where variations in y due to changes in the X-ray spectrum lead to relative errors of less than 27%. This is only slightly better than the results obtained by the conversion factors actually used in the Michigan data reduction procedure: y = 7.71 x 10s erg/(cm2 sec amp), ~2 = 12 o Although the E(8,12) values calculated by these factors are too large by about 20% in general, the relative error is less than 350 for the wide range of possible spectra considered in Figure 2-4. In all of the discussion to this point, it has been tacitly assumed that the solar X-ray spectrum near 10 A, whatever its slope, is predominantly a continuum. This assumption is probably incorrect, at least during major X-ray bursts. With the exception of Fritz et al. (1967), and Meekins et al. (1968), all investigators who have observed solar X-radiation with high spectral resolution find that line emission strongly dominates the continuum around 10 A (e.g., Blake et al., 1965a, 1965b; Rugge and Walker, 1967; Walker et al., 1967; Evans and Pounds, 1968). The great enhancement of this line emission during an X-ray burst is clearly seen in Figure 2-5 (taken from Neupert et al., 1969). The figure shows a spectrum observed while an importance 2b flare was in progress, as well as one observed prior to the flare. These observations led Underwood (1968) to remark: "It appears necessary to reevaluate much of the earlier work done with broad-band photometers in terms of a spectrum dominated by line radiation. "

34 FLARE SPECTRUM 00:38 UT. 22 MARCH 1967 400 - 5 350250 \ /PRE-FLARE SPECTRUM (E11:30 UT. 21 MARCH 1967 50 - UV RADIATION 0 7 8 9 10 II 12 13 14 15 16 17 18 19 20 ANGSTROMS Figure 2-5. High resolution X-ray spectra between 7 and 20 A obtained by the Goddard Space Flight Center's crystal spectrometer aboard OSO-III. The measured values must be corrected for scattered UV radiation as shown. (Figure from Neupert et al., 1969.)

35 Such a "reevaluation" was made for the Michigan experiment using the flare spectrum of Figure 2-5. With an instrumental efficiency curve kindly supplied by Dr. Neupert, this spectrum was converted into absolute units, as shown in Figure 2-6, and then planimetered to obtain the "true" flux between 8 and 12 A: E (8,12) = 0.0137 erg/cm2sec (2.11) Next, the spectrum of Figure 2-6 was "folded" into the efficiency curve for Michigan's detector to give Figure 2-7. Planimetry of this curve then leads to the value of the ion chamber current which would be measured for such an incident spectrum: -11 i = 1.70 x 10 amp (2.12) Finally, this current was multiplied by the conversion factor of expression (2.9) to give the equivalent two million degree gray-body flux: E(8,12) = 0.0131 erg/cm2sec (2.13) It may be just coincidental that this value, derived by means of such a poor approximation to the actual X-ray spectrum, should be so close to the "true" solar flux shown in expression (2.11); but it does make those who worried about relative errors greater than an order of magnitude appear overly pessimistic. However, a good deal of care must still be exercised when interpreting the E(8,12) values measured by the Michigan ion chamber photometer. For example, Figure 2-7 shows that over 20o of the instrument's response is due to the single

F (X) ergs / cm2 sec. A 16 x 103 X-Ray Burst Spectrum 0038 UT, 22 March 1967 12 8 4 0....1. 1 -: L' I A, I,., A 8 9 10 II IZ 13 14 15 x Figure 2-6. Spectrum of a major X-ray burst on 22 March 1967 plotted in absolute units.

F (X)- (X)ergs /cm2 sec. 20 x 10-4 15 10 5 0 8 9 10 II 12 13 14 15 Figure 2-7. Spectral response of the Michigan ion chamber to a major X-ray burst on 22 Marcn 1967. The dashed curve is an estimated extrapolation of the emission line profile for the feature at 8.5 A.

38 emission line at 8.5 A. This feature has been identified as a resonance line of Mg XII by Garcia, and Mack (1965), Rugge and Walker (1967), and Beigman and Vainshtein (1969). Therefore, the Michigan experiment can be considered a combination broad-band flux detector and Mg XII line monitor. In addition, it should be noted that the Michigan detector was observing the sun at the time the spectrum of Figure 2-6 was made. At that time, the ion chamber was saturated, which means that the implied value of E(8,12) was greater than 0.12 erg/cm2sec. This value is, of course, much larger than the one ir expression (2. 13), which, according to Neupert's observations, should have resulted. But this discrepancy merely points out the uncertainties in the absolute calibration of these two instruments. For instance, Neupert (personal communication) warned that the calibration of his experiment may be in error by more than a factor of three. Hle.lso noted another possible explanation for this discrepancy: the scattered UV ra-diation in his observations might not have been taken properly into account. But whatever the cause of this difficulty, the above analysis shows that relative ion chamber results derived by means of the gray-body approximation may still be valid even during a large X-ray burst when the actual spectrum is as complex as the one in Figure 2-6. This can be shown in yet another way. II' the results of broad-band photometeris dco depend strongly on the actual shape of the solar X-ray spectrum, one would not expect a simple relation between the measurements made by two detectors with different spectral efficiency characteristics, since this would require the relative errors of -the two instruments to match perfectly at a11 times. Figure 2-8 shows the relation between E(8,12) and the 1-8 A flux measured by a NRL ion

E(8, 12) ICT2= erg /cm2 sec. 0 & ~,=e4w *9. t_^.w&G 4 S S~~~ ~~ Os rr~,c4.0 0 0 0 0. 0 10N 3 I I I I I I _- 1 - — I. —-* ----. —-* - - -- - — * — **, _ I 10-2 E (I, 8) erg /cm2 sec. Figure 2-8. Comparison of the daily base-levels of E(8,12) and E(1,8) from 1 August 1967 to 31 March 1968. The E(1,8) values were derived from NRL observations by means of the 2 x 106 K gray-body approximation.

0 chamber photometer aboard OGO-4. (The 1-8 A measurements were supplied by D. M. Horan of the NRL.) Specifically, the daily X-ray base-levels for both experiments on each day between 1 August 1967 and 31 March 1968 are plotted in this figure. The correlation between these two sets of data is clearly very good and the relation is almost linear. This relation will be discussed further in the next chapter, which will also define the "base-level" values used here. The X-ray spectrum is relatively simple during quiet sun conditions as in the above study, however. A much more stringent test would involve data from X-ray bursts where the spectrum is extremely complex and changing rapidly. Figure 2-9 shows such a comparison between E(8,12) and the 2-12 A flux observed by a University of Iowa detector (Drake, personal communication) and reduced on the assumption of a constant spectrum. The values plotted are the respective peak fluxes for every burst in Catalog II (described in Chapter IV) which was observed by both experiments. Again the correlation is excellent, in this case over a range of nearly two orders of magnitude. All six of the points which do not lie directly on the nominal relation were marked as uncertain by one or both investigators. It therefore seems safe to conclude that order of magnitude relative errors do not occur in properly reduced broad-band observations, even during large Xray bursts. The actual relative error for the Michigan experiment is perhaps less than 30o However, the absolute error may be much greater. For example, note that the E(8,12) values in Figure 2-9 are larger than the corresponding E(2,12) values from the Iowa observations, a situation which cannot possibly be correct.

41 E(8,12) erg /cm2 sec. 10' r 0 * * 0. * 0.0 00 0 0 * * 0.0 0 0..* \;'s **~ 0. ~-^ 0 *y *0 10-2 00*0 0 I 0 0 0. I I I I I I I I I I I l I 10-3 Figure bursts from a 10-2 I0 10I0 E(2,12) erg/cm2 sec. 2-9. Comparison of the peak rates of E(8,12) and E(2,12) for X-ray associated with major Ha flares. The values of E(2,12) were derived University of Iowa experiment aboard Explorer 35.

42 According to the many comparisons just described, it appears probable that the absolute values of the E(8,12) measurements which will be used in the remainder of this study are systematically too high, perhaps by as much as a factor of two or three. But the excellent time resolution, dynamic range, sensitivity, stability, and relative accuracy of the Michigan experiment, as well as its notable longevity, make the data obtained from this instrument extremely valuable for the study of solar soft X-radiation. In summary, the various characteristics of the Michigan ion chamber experiment discussed in this chapter are compiled in Table 2 3.

TABLE 2.3 UNIVERSITY OF MICHIGAN SOLAR X-RAY EXPERIMENT ABOARD OSO-III (All data refer to normal incidence) Physical characteristics Window: Metal foil Surface density Effective area Filler: Gas Pressure Surface density Ionization efficiency General: Chamber depth Collimation cone Satellite rotation period Instrumental calibration Stability Al (99.45c10 pure) 0. 00327 gm/cm2 3.22 cm2 99% N2 + 1% He N 1 atmosphere 0. 00331 gm/cm2 36. 0 ev/ion-pair 2.58 cm 250 square degrees (window fully illuminated) 1.7 sec ~ 6% ~ 1% Data characteristics Effective bandpass Conversion factor Effective time resolution Time accuracy Extensive coverage Limited coverage Flux absolute error 8-12 A 7.71 x 108 erg/(cm2 sec amp) 6.4 sec better than 1 sec 10 March 1967 - 28 June 1968 28 June 1968 - 17 August 1969 factor of 2-3 (?) (flux values probably high) ~ 300% Flux relative error

CHAPTER III THE X-RAY SLOWLY VARYING COMPONENT Solar radio emission is often divided into a slowly varying component with a time scale of 27 days and a burst component which shows significant variations within minutes. The same scheme of classification can be applied to the X-ray region of the spectrum (e.g., Kundu, 1963, 1965; Friedman, 1963a; Mandel'shtam, 1965a). This chapter will. describe some investigations of the slowly varying component of solar X-radiation; Chapters IV and V will consider its burst component. 1. DETERMINATION OF THE DAILY E(8,12) BASE-LEVEL A great deal of care must be exercised to identify the correct value of the nonburst X-ray flux for a study of the slowly varying component. During the period observed by the Michigan experiment aboard OSO-III, the sun was near its level of maximum activity and X-ray bursts occurred frequently. Long intervals exist in which the E(8,12) record is continuously disturbed, with bursts often overlapping one another. This is especially bothersome since X-ray bursts normally have greater durations than their optical or radio counterparts (as shown in Chapter IV). Moreover, the Michigan detector observes the entire solar disk, so that the true X-ray base-level can be attained only when no optical or radio event has occurred anywhere on the visible hemisphere for some period of time. But even this condition is not adequate because many X-ray bursts are not associated with a reported optical or radio event (e.g., Yefremov et al., 1962; Acton et al., 1963; Conner et al., 1964; Teske, 1969a). A final 44

45 difficulty is that the base-level flux is usually just a fraction of the flux during a burst. Therefore, any mistake in identifying the nonburst intervals can lead to substantial errors in the base-level values derived. To avoid some of these problems, no attempt was made to select those specific intervals which were thought to be devoid of burst activity. Rather, the baselevel for a given day was defined as the lowest flux value observed between 04002000 UT on that day (except that anomalously low measurements of short duration were discarded as spurious). While the above procedure is not ideal, we believe that it is more useful than presuming to identify the day's "nonburst" observations as is done for many other studies (e.g., Pounds, 1965a; Michard and Ribes, 1968; Wende, 1969). It definitely gives base-level values that are less misleading than those obtained from real-time observations, which include only 4 or 5 ten-minute intervals each day (Chitnis and Kale, 1966). The daily E(8,12) base-level fluxes, as defined here, are thus taken to measure the slowly varying component of solar X-radiation. These values will be used in the following investigations and will be referred to as Eb(8,12). 2. COMPARISON WITH Ca PLAGE INDICES Essentially all of the quiet-sun X-radiation (< 50 A) originates from coronal enhancements which overlie active regions roughly delineated by chromospheric calcium plages. This had been suggested indirectly by some early studies (e.g., Waldmeier, 1947; Elwert, 1956); but it is shown directly by observations of individual regions using pin-hole cameras (Blake et al., 1963b; Broadfoot, 1967; Pounds et al., 1968), slit-telescopes (Blake et al., 1963a),

46 Fresnel zone-plate optics (Elwert, 1968), grazing-incidence telescopes (Lindsay, 1965; Underwood and Muney, 1967; Vaiana et al., 1968), and raster-scanning devices (Negus and Glencross, 1968; Paolini et al., 1968; Beigman et al., 1969), as well as measurements during a solar eclipse (Kreplin, 1961). However, to study this relation by means of the OSO-III data, the sum of all Ca plages on the disk must be considered, since Michigan's experiment has no spatial resolution of solar features. Therefore, the Eb(8,12) fluxes were compared with the Ca plage indices EA, ZAxI, and ZA /2xI for the corresponding dates, obtained from measurements of the daily calcium spectroheliograms made at the McMath-Hulbert Observatory. Only the reports which were rated at least fair in quality between 10 March 1967 and 1 June 1967 were used here. The resulting correlation coefficients are shown in Table 3.1. TABLE 3.1 CORRELATION OF Eb(8,12) WITH Ca+ PLAGE INDICES Ca+ Plage Index Correlation Coefficient LA 0.64 ZAxI 0.70 EA3/2xI 0.69 The value ZA represents the total area of the visible plages, the individual plage areas having been corrected for foreshortening. The strong correlation of this index with Eb(8,12) indicates again the close relation between the plage regions and the source of soft X-radiation. Moreover, the size of the region seems to be a measure of its associated X-ray emission, which confirms the results

47 of several image-forming experiments (e.g., Underwood and Muney, 1967; Negus and Glencross, 1968). But the correlation of Eb(8,12) is even stronger with ZAxI, a rough indicator of the total Ca K excess flux due to the visible plages. The intensity values for this index are derived by estimating the rank of the brightest part of each plage on a scale of 1 to 5, which is then converted into the appropriate excess intensity I by means of Table 3.2. (This table is courtesy of the McMathHulbert Observatory.) Such a result implies that the conditions which determine the chromospheric plage brightness (that is, the level of the enhanced temperature, density, and magnetic field strength) extend into the overlying, X-ray emitting region. TABLE 3.2 RELATIONSHIP BETWEEN ARBITRARY Ca PLAGE INTENSITY SCALE AND PHOTOMETRIC MEASUREMENTS OF Ca PLAGES Intensity in Units of Excess _Scale _Ca,+ Background Intensity 1 153 -3 1.5 1-5.5 2 1.7.7 2.5 1.85.85 3 2.0 1.0 3.5 2.15 1.15 4 2.3 1.3 5? > 2.3 > 1.3

48 Teske (1969b) has continued this comparison through 30 April 1968 using the Michigan data and finds a correlation coefficient of 0.73 between Eb(8,12) and ZAxI for this period. Therefore, the time interval considered in the present study does not seem to be atypical. The fact that others (e.g., Michard and Ribes, 1968) find a much weaker correlation shows the advantage of the Eb(8,12) definition used here. Direct observations of individual X-ray regions indicate also that the X-ray emission is related to the area and intensity of the associated Ca+ plage (Blake et al,, 1963b; Pounds and Russell, 1966; Reidy et al., 1968), On the other hand, the X-ray emitting region is known to have an extensive three-dimensional structure (Vaiana et al., 1968; many others) so that it clearly must be treated as a volume source. It would be interesting to determine how this volume depends on the area of the underlying chromospheric plage. W. A. White (1964) finds that it is much better to assume that the thickness of the X-ray source is directly related to the mean plage diameter rather than to assume a constant thickness. Therefore, he sets the X-ray emitting volume 5/2 proportional to A. Unfortunately, his analysis is based on an incorrect interpretation of the intensity index for the Ca+ plage as estimated by the McMath-Hulbert Observatory. Probably for that reason, the present study does not substantiate White's result. Table 3.1 shows that the correlation of E (8,12) with A3/2 xI is no better than that with ZAxI. It follows that the major part of the soft X-ray emission originates from a volume whose thickness does not strongly depend on the size of the underlying plage. This would be the case if, for example, the

X-ray emitting region consisted of many small volume elements, each associated with the filamentary structure of the chromospheric plage. As the plage area grew by the addition of more such elements, there would not necessarily be any concurrent increase in the thickness of the X-ray emitting source. Although the correlation between Eb(8,12) and ZAxI is quite good in general, the relation appears much weaker when examined in detail. This can be seen in Figure 3-1, which plots the daily values used to find the correlation coefficient discussed above. By following the time development of this relation, two intervals were identified whose daily values fell in totally different regions of the figure. Eb(8,12) was higher than would be predicted from ZAxI for the period 15-17 April 1967, and at that time the largest plage on the disk was a region near the limb (McMath #8776) which was in its first rotation. (Unfortunately, there were no adequate Ca+ observations by McMath-Hulbert for 13-14 April when this region was directly on the limb.) In contrast, the major feature of the disk between 22-28 April was a very large, but fragmented plage near the central meridian (McMath #8778) which was four rotations old. During the latter interval, Eb(8,12) was noticeably low relative to ZAxI. Although McMath-Hulbert's spectroheliograph was readjusted between the two intervals considered here, an examination of data during the two-month period bracketing the readjustment shows that this had no systematic effect on the relation of Eb(8,12) to ZAxI. One interpretation of the above result is that a region's X-ray emission gradually decays over a period of several solar rotations. This would be consistent with the observations of Neupert (1967, 1968), who finds that both the

ZAXI 4 xl04 3 2 0 I 0 0 0 0. 0 0 0 x 0 x x x 0 0 0 0 0.. X X 0. 3 0 0 0. J1 0 0.0 @0 0 0 0 0 0 * 0 0 * 0 0 0 * 0 0 0. I I I I I I I I.002.004.006.008.010 Eb (8,12) erg/cm2 sec. Figure 3-1. Relation between the daily values of Eb(8,12) and the calcium plage index Z A x I for the period 10 March to 1 June 1967. The units for A are millionths of the solar hemisphere; I is in units of the Ca+ background intensity. Points for the dates 15-17 April are marked as o; those for 22-28 April as x.

51 temperature and density of a coronal condensation decrease as the associated active region ages. Another possibility is that X-ray sources display a "limbbrightening" effect. Such an effect has been suggested by Teske's (1969a) study, which shows that Eb(8,12) is high relative to other solar activity indices during both limb passages of a major active center. The observed "limb-brightening" is undoubtedly due to the height at which soft X-radiation is emitted. X-ray sources overlying plages at the limb are typically reported to have heights of roughly 100,000 km (e.g., Negus and Glencross, 1968; Paolini et al., 1968; Vaiana et al., 1968; Beigman et al., 1969). Thus a region's X-ray emission can be observed even if its chromospheric plage is just beyond the limb. 3. COMPARISON WITH X-RAYS OF OTHER WAVELENGTHS It is not possible to derive any information about the shape of the X-ray spectral distribution from measurements by a single ion chamber, as discussed in Chapter II. However, a rough estimate of the average spectral slope can be obtained from a, comparison of equivalent observations made by two or more dissimilar broad-band detectorso Figure 3-2 shows such "composite" spectra of the slowly varying component between 1/2-60 A for two different dates. The spectra are based on data from four NRL experiments (all carried by the satellite OGO-4) as well as from The University of Michigan's experiment. Table 3.3 gives the bandpass of each experiment and the gray-body temperature that was used in the reduction of each detector's response. For clarity of presentation, the spectra have been plotted on an arbitrary flux scale with a convenient separation between the data for

52 F (X) 107 0 M ichigon- ~ O) - 10 /19 August 1967 o I / O 0 0._) 10 0 |- / / 22 September 1967 103 " / I10 / / / 10 I I I I I 2 5 10 20 50 Figure 3-2. Composite average spectra of the slowly varying component between 1/2 - 60 A for two dates. The spectra are plotted on an arbitrary ordinate with a convenient separation. The spectral slopes of individual segments reflect the gray-body distribution assumed for each measurement. 19 August and 22 September 1967 represent dates of high and low base-level flux, respectively.

53 these two dates. The spectral slopes of the individual segments shown have been derived from the gray-body distribution assumed for each experiment. TABLE 3.3 CHARACTERISTICS OF COMPARED EXPERIMENTS Assumed Bandpass Gray-Body (, Investigator (A) Temperature (106 K) 1/2 - 3 10 NRL 1 -8 2 NRL 8 - 12 2 Michigan 8 - 20 2 NRL 44 - 60 0.5 NRL This figure shows, first of all, how well the Michigan results agree with those of NRL, the largest difference at 8 A being about 30%. Secondly, the rough spectral slope around 10 A seems to be quite close to the 2 x 10 K gray-body slope assumed in the reduction procedure for E(8,12). Both of these findings offer further support for the analysis of the Michigan experiment's reliability as discussed in Chapter II. Finally, it is obvious that the entire spectrum between 1/2 - 60 A cannot be represented correctly by a single temperature, a result which also agrees with observations made by other techniques (e.g., Pounds and Sanford, 1965; Bowen et al., 1964; Mandel'shtam, 1965a). Therefore, the X-ray emitting source is not isothermal, but apparently consists of a small, very hot nucleus suridrounded by more extensive regions of cooler and cooler material (although still hotter than the ambient corona). Such a model has been proposed by Blake et al. (1963a), and Evans and Pounds

54 (1968), and is consistent with the results of image-forming experiments which show that the size of a coronal X-ray source decreases as the wavelength of the observation becomes smaller (Blake et al., 1965a; Underwood and Muney, 1967). Since all of the experiments which were used to derive Figure 3-2 observed the sum of the X-ray emission from the entire solar disk, another interpretation of this figure is conceivable. Namely, each X-ray source on the sun is isothermal itself, but different temperatures apply to the various regions on the disk at any given time. However, this explanation is not tenable for the following reason. The dates for the spectra shown in Figure 3-2 were chosen because they represented the highest (19 August 1967) and the lowest (22 September 1967) daily base-level fluxes encountered in the time period studied. The Ca plages seen on the disk differed greatly in number, intensity, and total area on those two dates, Thus, the X-ray emitting regions associated with these plages also should have very different characteristics, according to the results discussed in the previous section. Yet Figure 3-2 indicates that the overall spectral shape has changed very little between the dates in question, although each spectrum represents the contributions from a completely different set of emission sources. This would be highly unlikely if the "isothermal hypothesis" just described were correct. Striking changes in theaverage spectral slope of the slowly varying component have never been observed, but a subtle hardening of the spectrum as the daily base-level increases can be detected by a statistical study of many days' observations. For this purpose, data from the NRL 1/2 - 3 A, 1-8 A, and 8-20 A detectors aboard OGO-4 were again used. Lists of hourly averages of the

55 "nonburst" measurements made by these detectors between 1 August 1967 and 31 March 1968 were searched to find the daily base-level fluxes in a manner identical to that described in Section III-1. Hereafter, these values will be referred to as Eb(l/2,5), Eb(1,8), and Eb(8,20). Unfortunately, the 44-60 A experiment aboard OGO-4 failed very early in November 1967 and so could not be used in this study. The resulting relation between Eb(8,12) and Eb(1/2,3) is given in Figure 3-3, along with that between Eb(8,12) and Eb(8,20). The comparison between Eb(8,12) and Eb(1,8) has been presented already as Figure 2-8 of Chapter II. Note that the poorest correlation is with Eb(1/2,3), which represents the emission of a coronal region's hottest portions. One possible explanation is that only certain regions have such a high-temperature component. This hypothesis therefore implies that the "quality" of the X-ray emitting sources is the most important criterion for Eb(1/2,3), rather than their "quantity" which is so important for Eb(8,12). An interesting problem for future investigation is to attempt an identification of any special characteristics which might exist for the chromospheric plages observed on days with anomalous Eb(1/2,3): Eb(8,12) ratios. This would be a valuable test of the hypothesis just described. Although the correlation between Eb(1/2,3) and Eb(8,12) is relatively weak, a straight line can be fitted to the points in Figure 3-3(a). An eyeestimate of this fit gives: Eb(l/2,3) = 2.2 x 10 E(8,12)12 (51)

Eb (8,12) erg/cm2 sec.. *0 10-2 * 0 * *00 4 _ *:.s *.. t 0 0~ 0 * *: * O I0..0 0 * * * 00 0 ~ ~ 0* — 0 * * * **J - 0 * * 0 0409*96 0 0 0 * *0 *8'0* 09 0 *0 4*" 0 0 00 0~ 00 10 b~ 0% 0r"?0 r On O\ 0 0 0 (a) (b) I I I 10-6 -ffr I I I I C1-2 Eb (, 3) erg/cm2 sec. Figure 3-3. Comparison of Eb(8,12) with (a) Eb(1/2,3) and (b) Eb(8,20) 31 March 1968. 10-' Eb (8,20) erg/cm2 sec. for the interval 1 August 1967 to

57 Since the exponent in this expression is greater than unity, Eb(1/2,3) becomes larger relative to Eb(8,12) on the average as the base-level flux increases, thus giving rise to the spectral hardening mentioned above. This hardening of the X-ray spectrum is seen much more convincingly in Figure 2-8, because the relation of Eb(8,12) with Eb(1,8) is clearly much better than with Eb(1/2,3). An eye-estimate of the best straight line fit to Figure 2-8 gives: Eb(1,8) = 1.04 Eb(8,12)12 (3.2) implying again that the shorter wavelength emission increases relative to Eb(8,12) on the average during periods of higher base-level flux. As might be expected, the "tightest" relation is between Eb(8,12) and Eb(8,20) shown in Figure 3-3(b). However, there is a very pronounced break 2 in the relation at about E (8,12) = o.oo38 erg/cm sec. This is probably unrelated to the Michigan experiment because it does not appear in any other comparison with Eb(8,12). It is more likely to be caused by an improper alignment of the flux scales for the high and low sensitivity modes of the NRL instrument. (Note that the break occurs well below the point where the Michigan detector changes its sensitivity.) By shifting each part of the curve horizontally toward the other an equal amount, the relation becomes approximately: Eb(8,20) = 0.95 Eb(8,12)0'73 (.33) b b.

58 which once again, has an exponent appropriate for a spectrum that hardens, on the average, with increasing flux. The change in spectral slope of the slowly varying component, although minor, occurs throughout the range 1/2-20 A and has been reported by many others (e.g., Kreplin, 1961; Michard and Ribes, 1968; Wende, 1969)0 (One exception is Noci and Russo (1964) who correlated 0-8 A flux with ionospheric parameters to find that the spectrum does not vary with changes in the quiet sun's X-ray flux level. But the evidence from direct observations is overwhelming that this interpretation is incorrect.) Therefore, we cannot consider changes in the slowly varying component as being due solely to differences in the number or total volume of otherwise similar X-ray sources. At least some of the regions that exist during periods of high base-level flux must be substantially hotter than the regions observed when the base-level flux is low. Most likely, the same basic mechanism which is responsible for the increased level of general solar activity also gives rise to further enhancements in the temperatures of the Xray sources overlying active regions.

CHAPTER IV THE X-RAY BURST COMPONENT: STATISTICAL STUDIES Rapidly-varying bursts of solar X-radiation are often superimposed on the sun's X-ray base-level. These bursts usually accompany some optical phenomenon such as an Ha flare, disparition brusque, limb surge, or prominence eruption (Kreplin et al,, 1962; Friedman, 1963b; Muney and Underwood, 1968), but they can also occur in the absence of any other reported events (e.g., Pounds, 1965b; Drake, 1969; Teske, 1967, 1969a, 1969b). The present study will consider only the enhanced X-ray emission associated with well confirmed Ha flares, Specifically, we will examine the general time-profiles of such bursts, both in an absolute sense and relative to the associated Ha flares. We will also compare the peak emission rates of the soft X-ray and Ha events, as well as the total energies emitted by these two radiations during flares of various importances, In addition, an attempt will be made to identify some parameters accessible to ground-based observers which correlate with the X-ray burst's amplitude, A statistical approach will be used in this chapter, and in Chapter V three well observed events will be investigated in some detail. 1. SELECTION OF Ha FLARE EVENTS In order to facilitate the statistical study of flare-associated X-radiation, a catalog was compiled of all well confirmed flares of importance > 1 which occurred between 10 March and 31 December 1967. Since all reports of Ha flares are not equally reliable (Dodson and Hedeman, 1968), an attempt was made to eliminate events which were not clearly verified, The first such cata59

60 log included only those flares which were reported by three or more stations and rated importance 1 or greater in the Quarterly Bulletin on Solar ActivityO This list formed the basis of the studies reported by Teske and Thomas (1969), hereafter referred to as Paper I. Unfortunately, the above selection procedure strongly biased the sample toward those events which occurred in summer months and during European observing hours, when the number of stations monitoring the sun can reach three times the world-wide yearly average (Dodson-Prince, personal communication)o To avoid this difficulty, a second approach was taken for the catalog used in the present investigation. Each flare had to satisfy all of the following conditions to be included in this list: (1) at least two stations report the event, (2) more than 50% of the stations observing at its time of maximum report the event, (3) at least 50% of the stations observing at its time of maximum rate its importance as 1 or greater, (4) at least one station reporting the event must be photographic or cinematographic, and (5) the Quarterly Bulletin rates its importance as 1 or greater. This set of criteria requires that a photographic record of the flare exists, and that most of the stations which were monitoring the sun at the time actually saw the flare and agreed that it was indeed greater than just a subflare. To determine exactly which stations were observing at any given time, lists were used of the daily patrol-times for all flare-monitoring observatories which re

61 port to the World Data Center at Boulder, Colorado. (These patrol-times were obtained through the kind offices of Jo Virginia Lincoln.) The individual flare reports, which are tabulated in the "Revised" list of the ESSA Solar-Geophysical Data Bulletin (SGDB), gave data on the number of stations reporting the event and the various assessments of its importance. In addition to the above screening procedure, events were eliminated whenever it appeared that the X-ray record might be seriously affected by particle interference (discussed in Section II-6) or by the occurrence of two or more flares close together in time. The latter requirement is necessitated by the Michigan detector's lack of spatial resolution, which does not allow the individual contributions of simultaneous bursts to be determined. Unfortunately, this eliminates any possible examples of the so-called sympathetic class of flares discovered by Richardson (1951) and shown to be due to the "triggering" of one flare by another (Becker, 1958)o Therefore, the results of the present study do not necessarily apply to this very interesting class of events, 2, THE LIST OF Ha FLARES HAVING X-RAY COVERAGE After the culling process described in the previous section, we are left with 283 flares for which we have at least partial X-ray coverage, Although many valid events were no doubt excluded by this procedure, the flare reports which remain can be safely considered as highly reliable, Table 4.1 presents the resulting list of Ha flares along with some information about the associated 8-12 A X-radiationo (Since this list represents the second flare catalog constructed for events observed by the Michigan experiment, it will also be referred to as Catalog II in the following discussion.) The times of start and

TABLE 4.1 Ha FLARES WITH X-RAY COVERAGE (CATALOG II) Hc Flare Data E(8,12) Burst Data at Start Max. End Imp. Location Start Max. End Base Ampl. No. March 1967 16 2342 17 2152 18 0835E 20 1344 20 2310 21 1814 22 0022 23 1917 25 0709 25 1856 26 0458 26 1402 26 1605 26 1630 27 1558 27.1718 27 2107 28 0615 29 1726 30 0756 30 0851 30 2336 31 1258E 2349* 2202 0853 1350 1401 2345 1820 0033 0155 1932 0714* 1914 0509 1605 1652 1614 1730 2113 2129 0618 1740 0800 0902 2347* 1305 2402 2222 0948D 1418 2420 1835 0240 2017 0730 2024 0540 1428 1619 1750 1650 1800 2205 0626 1820 0835 0930 2420 1420 in N18E79 if N24E53 if S15E08 in N18E35 in N23E21 in N20E77 2b N24E68 lb N24E31 in N23E26 In N26E20 2n N23W01 in S19E67 lb N24E02 3n N26E05 In N24W06 in N25W23 lb N23W24 in N24W29 lb N21W30 in N22W40 2n N24W49 in N24W59 in N18W32 8733 8733 8727 8733 8733 8740 8740 8740 8740 8740 8740 8745 8740 8740 8740 8740 8740 8740 8740 8740 8740 8740 8741 2343 2152.5 2302.5 1818 0017.5 0705.5 0504.5 1604 1557 2110.5 o614 1722 2340.5 1257 2349 2200 0850.5 1403.5 39 54 42 130 1824 0038' 0157 1935 0714 1925 0513 1608 1617 1726.5 2117 2129 0619.5 1743 0807 0906' 2349.5 1311 73 73 84 2018 2055 0534 1426 1630' 1812 0642 53 53 106 73 53 84 84 62 53 84 116 137 175 258 116 128 56 41 48' 92' 84 54 1211" 257 104 94 231 236 107 82 363 225 388' 272' 592' 215 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ON 18 19 20 21 22 25

TABLE 4.1 (Continued) Hx Flare Data E(8,12) Burst Data Date Start Max. End Imp. Location Start Max. End Base Ampl. March 1967 (Concluded) 31 2212 2218 2232 2300 In N18W63 8740 2212.5 2219 2239 128 102 April 1967 1 o0l9 1 0618 1 0810 2 0407 2 0818 2 1116 9 0912 11 1112 11 1336 12 0533 14 2236 23 0020 27 1602 30 0938E 30 1304 0122 0621 0418 0424 0823 1120 1119 1124 1344 0542* 2241 0036* 1606 0945 1309 0140 0632 0848 0440 0840 1150 0938D 1142 1440 0558 2256 0050 1620 1010 1333 in N24W75 lb N19W70 in S20W07 in N24W86 In S24W79 in S23W81 if S20W40 in S21W65 8740 8740 8745 8740 8739 8739 8753 8753 8760 8753 8760 8777 8791 8791 8791 0118 0615.5 0814.5 0800.5 1116.5 0910.5 1315 2231 0939 1302 0128.5 0622 0822 0421 0425.5 0801 1125 1122' 1132 1343 0542.5 2240 0037 0946.5 1310 0637 0802 1220 2252 0113 1653 148 270 169 84 95 100 39 40 369 500 164 116 5 163' 33550' 25 26 27 28 29 30 31 32 33 34 35 36 37 38 59 lb lb If in in in in N22W24 S22W74 N21W66 S22W67 S22E80 S20E42 S22E40 34 93 35 262 38 16 30 86' 335 40 35 37 47 1 0519 0523 0531 1 0745 0755* 6 0435 0439 10 1145 1155 12 1755 1802 0545 0815 0545D 1240 1830 May 1967 In S22E31 8791 In S22E30 8791 3n S20W34 8791 2n S22W87 8791 In N24W68 8798 0507 0422 1758 0522 0754 0457 1212.5 1801 28 67 40 0824 0613 1809 26 38 22 1328" 15 316 14 8 41 42 43 44

TABLE 4.1 (Continued) Hat Flare Data E(8,12) Burst Data Date Start Max. End Imp. Location Start Max. End Base Ampl. N..... Ampl~[[ No.m May 1967 (Concluded) 14 1533 18 1934 19 1239 19 1524 20 1005 20 1508 21 1300 21 1535 21 1919 21 2354 23 1802 24 0300 25 0222 25 0632 25 1039 25 2043E 26 1516 27 0129 28 0529E 28 0714 29 1856 1547 1937* 1257 1538 1009 1302 1539 1926 2411 1814 1844 1947 0321 0227 * 0646 1053 2054 1531 1555 0203 0543 0732 0750 1640 1951 1310 1615 1025 1615 1316 1600 2025 2427 2200 0420 0313 0720 1225 2125 1700D 0257D 0700 0820 1930 In S27E08 In N25E80 lb N24E65 lb N24E70 lb N25E53 lb N23E51 In N26E61 lb N23E58 2n N24E39 2b N24E55 8807 8818 8818 8818 8818 8818 8818 8818 8818 8818 3b N28E26 8818 1532 1933.5 1241 1006 1917.5 2351 1758 0250 0631.5 2028.5 0127 1853 1935.5 1009 1306 1540 2410 2414 2417 0330 0230' 0637 1101.5 2055 1608 0555' 0734 0757.5 2007 1325 1649 1641 1611 2042 20 175 73 100 63 95 73 75 90 95 145 43 353 393' 2635 " 403 ON 4-p7 45 46 47 48 49 50 51 52 53 54 175 8060" in N22E10 in S20E15 lb N28Ell lb N22W06 In N27E05 In N30W05 In N26W18 2b N28W32 In N24W44 8818 8819 8818 8818 8818 8818 8818 8818 8818 0503 0308 0803 1229 0330' 1944 137 73 84 100 73 150 137 90 150 371 102' 738' 83 161' 3909" 170' 5.5 56 57 58 59 60 61 62 63 64 65 in N30W68 8818 84

TABLE 4.1 (Continued) Dae Ha Flare Data.E(8,12) Burst Data N. Dte Start Max. End Imp. Location Start Max. End Base Ampl. No. June 1967 1 1451 2 0056 2 0825 2 0847 2 2302 3 0226 4 0753 5 1839 11 1107E 16 0021 17 2120 18 1306 23 0037 25 0105 29 2331 1457 0105 0832 0852 2306 0304 0758 1844 1938 1115 0026 2125 1315 0039 0052 0135 2339 1512 0142 0856 0920 2345 0352 0840 2032 1155 0040 2220 1415 0110 0200D 2359 in N24E27 in N21W39 in N10W77 In N20W45 lb N20W53 in N23E12 in S17W39 2n S18W58 in N19E58 if S16W90 in N28E63 8831 8824 8821 8824 8824 8831 8829 8829 8843 8836 8854 0057.5 0823.5 0842.5 2303.5 0230.5 1105 2106 1258 0033.5 2332 1458' 0836 0852.5 2317' 0759' 1950 1117 0026 2131 2144 1313 1319 1531 0059 138 118 127 175 84 84 84 39 94 98 365' 66' 127' 66 67 68 69 70 71 72 73 In N26E55 8854 In N15E33 8863 11 12 40 22 20 159 44 256 27 27 120 26 47 74 75 76 On Vj 77 78 79 80 In N22E16 In N15W57 8863 8863 0138 2341 July 1967 2 0920 4 0643E 5 1832 7 1946 9 0110 20 0547 0928* 0648 1855 1953 0142 0551 0945 0700 1935 2016 0230 0630 lb N20W90 In S21W01 lb S21W18 in N27E24 in S23W64 In S22E50 8863 8875 8875 8880 8875 8901 0917 0927 - 0649 1832 2- 1954 - 0141 0547.5 0555.5 2005 29 55 22 51 27 25 48' 25 70.' 32 136 81 82 85 84 85 86

TABLE 4.1 (Continued) Hc Flare Data E(8,12) Burst Data N. Date Start Max. End Imp. Location Start Max. End Base Ampl. N July 1967 (Continued) 20 0717 21 2250 23 0538 23 1244 24 0024 24 0928E 24 0959 24 1148 24 1152 25 0010 0724 0739* 2303 0543 1302 0035 0933* 1000 1154 1202* 0014 0039 25 1055 1058 1120 25 1425 1429 25 1720 1728 25 2132E - 26 o654 0700 26 0918 0921 0940 28 1130E 1136* 28 1849 1854 29 0242 0246 29 0402 0432 30 0508 0513 30 0615E 0620 30 1410 1417 30 1555 1601 0810 2340 0600D 1310 0050 1015 1008 1210 1220 0100 1130 1500 1740 2157D 0720 o955 1150 1910 0320 0511 0532 0700D 1445 1615 if N24E82 in N12E84 lb N12E75 in NllE66 in N27E54 lb N10E63 in S23W04 in N27E53 if N29E43 8905 8907 8907 8907 8905 8907 8901 8905 8905 In S22E49 8901 0719.5 0727.5 0741.5 0515.5 0546.5 - 1301' 0018 0037 - 0947 0957 1001 1142 1156' - 1203.5 0012' 0013.5 0039.5 0046.5 - 1114'l 1138.5 1418 1429.5 - 1733 2112 2119' 0644.5 0701 32 209 lb N27E38 8905 lb N28E39 In N27E37 In N28E36 In N26E30 In N13E36 In N17E33 In N12E02 lb N16E19 2n S26W63 lb N24W27 2b N26W29 lb N15W10 lb N13W07 87 8905 8905 8905 8905 8907 8911 8907 8911 8901 8905 8905 8907 8907 1309 0057 1009 1158 1520' 1810 0946 1146 1913 0645 1450' 1612 63 84 63 63 75 235 100 200 84 120 137 179 250 128 116 84 135 95 95 106 116 84 95 0 191 187' 356 199' 213 143' 266' 230' 843 106 130' 247 85 44 112 130 390 190 119 88 89 90 91 92 93 94 95 96 O0 0T\ 97 98 99 100 101 102 103 104 105 106 107 108 109 110 1133 1851.5 0508.5 0618.5 1408 1556 1138 1854 0244.5 0436 0627.5 1419 1603

TABLE 4.1 (Continued) Date. Ha Flare Data.E(8,12) Burst Data. Date Start Max. End Imp,. Location Start Max. End Base Ampl. No July 1967 (Concluded) 30 1612 31 0808 31 0855 31 1115 31 1225 31 1950 31 2047 1635 0857 1120 1228 2004 2114 1654 0850 0920 1200 1250 2040 2140 In N26W36 In N25W42 In N13Ell lb S24E35 lb N23W44 In N27W45 lb N23W50 8905 8905 8913.8914 8905 8905 8905 1613 0808.5 0855 1115.5 1225 2048 0900 1124 1228 2005 0939 1242 2045 95 63 73 63 73 73 73 169 126 129 228 111 112 113 114 115 116 117 August 1967 1 1721 2 0043 2 1516 3 0918 6 1433 9 0812 9 1758 12 1547 15 2138 17 1206 18 0043E 18 1955E 18 2131 19 0530E 20 0025 1738 0048 1522 0920 0930 1449 1813 1830 1610 2145 1214 0046 1958 2026 2138 0026 0037 1810 0102 1544 0950 1520 0930 1930 1720 2205 1245 0130 2050 2156D 0620D 0048 2b N27W62 In N26W58 In N20W06 lb N27W85 In S23E75 In N25W38 2b S24E32 2n S24W06 in S23W28 In S22W77 In N08W17 In N24E87 In N26E90 lb N16E85 In N22E79 8905 8905 8913 8905 8926 8916 8926 1725 1513.5 0917.5 0807. 1755 1739.5 0049 1521 0922. 5 0933 1449.5 0841 1811.5 1612 2145.5 1214 0046 2027.5 0616 004o 63 950 63 913 71 65 73 516 118 119 120 121 ON 8926 8929 8926 8941 8942 1540' 1745 2230 0150' 23555' 0048 84 33 31 35 32 63 73 106 300 125 84 268 30 202' 25 159 620 419' 2163 " 501 122 123 124 125 126 127 128 129 130 131 132 8942 8942 8942 0530'

TABLE 4.1 (Continued) Date Ha Flare Data End ImP. E(8,12) Burst Data Base No. Start Max. Location Start Max. End Amnl. -~s:.43.> r_ _ _6 — X..S _ _6 6- C - August 1967 (Concluded) 21 21 22 23 23 24 25 26 26 26 28 0057 1830 0156 0515E 1016 0957 0625 0014 0940 2101 1402 0110 1844 0206 1020 0630 0023 0947 2111 1404 1414 1335 1948 2053 0030 0503 0827 0140 2000 0255 0540 1040 1012 0700 0108 1022 2140 1430 1444 2020 2135 0122 0528 0840D In N15E54 2n N23E48 In N22E52 lb N23E36 In N25E32 In N23E21 In S20Ell lb S19EOO In N22W05 In N13W06 In S22W32 2b N22W46 lb N22W5 0 lb N22W5 0 In N22W52 lb N24W53 In N17W71 8942 8942 8942 8942 8942 8942 8949 8949 8942 8942 8949 8942 8942 8942 8942 8942 8942 0107 1817.5 0514 0955.5 0012.5 0938. 2059.5 1328.5 1942 2037 0007 0453 0825 0116 1857 0210.5 0522 1024 0631.5 0025 2116 1415 1946 1950 2055 0034' 0505.5 0827.5 0259 0546 1042 1022 0710 1012 2148 73 43 95 255 63 116 63 289 73 81 63 53 152 53 460 73 95 122 73 177' 133 134 135 136 137 158 139 140 141 142 143 29 1330 29 1942 29 2036 30 0020E 30 0458 31 0826E 146 73 144 145 0128 84 506 79 241' 84 328 63 267 146 147 148 149 September 1967 1 0810 1 0911 2 2030 10 1156E 11 1325 17 1050 0810* 0928 2040 1215 1518 1328 0830 0954D 2105 1558 1340 1200D In N23W85 ln N22E63 In N27E23 ln N25W33 8942 8961 8957 8963 0806.5 0820 - 0928' 2036 2042.5 1129 1215 1521 1534 1047 73 75 53 29 64 43' 383 154 150 151 152 153 if N22W87 9861 in N18W58 8973 27 27 12 154 - 155

TABLE 4.1 (Continued) Dat..EHa Flare Data E(8,12) Burst Data Date.. No Start Max. End Imp. -Location Start Max. End Base Ampl. -- End —: Base.....Ampi[. No.. September 1967 (Concluded) 18 2316 28 0338E 28 1127 30 1300E 2344 0342 1305 2545 0407 1245 1345 2b N16W60 In N19E55 2n N14E41 In N17E17 8973 9002 8999 8999 0328 1245 2350' 0341.5 1158 1319 1330' 30 44 35 29 400' 30 105' 55 156 157 158 159 October 1967 1 0935E 0955* 2 0756 0758 2 2151 2154 4 0600 - 5 1040 1044 6 1102 1103 1116 6 1218 1225 8 2029 - 14 2120 - 20 0004 0009 20 0225 0228 20 1050 1114 21 1945 2005 22 2211 2218 24 0740 0750 24 2014E - 25 1327E 1335 1350 25 2312E 2328 26 1012 1015 1035 0815 2212 0633 1110 1130 1245D 2106D 2225 0035 0240 1138 2035 2310 0820 2200 1445 2400 1030 In N12E03 In N16W34 In S20E46 In N17W31 In S18W22 In S18W36 In S17W37 In S17W69 In N17W49 lb N16E27 In N16E25 In N17E21 In N14E58 lb NlOE15 In N20E29 In S21WO1 In N09W24 8999 8998 9006 8999 9004 9004 9004 9004 9018 9032 9032 9032 9037 9034 9037 9035 9034 0932 0754 0554 1036 2000 2113 0003.5 2207 0724 2014 0957 0758.5 2158 0609 1045.5 1116.5 1236 0010.5 0234 1115 2006 2219' 0750 1355 0107 0259 2048 2432 1041 53.24 25 33 28 26 39 23 29 28 30 25 20 30 41 30 44 84 116 63 114' 113' 30 56 112 211 287 43' 38' 33 320' 43 83' 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 lb N10W28 9034 In N10W42 9034 2307.5 2331 - 1016.5 406 177 104' 178

TABLE 4.1 (Continued) -~rc~-~*rr ~ mnrc1C-.- BP-ICi~~C lC~r~~~~)l;i3~-iiC~~iP~~ CC =-Ir.-)I; iir~riPF-;T~-~l~Si —.l_ 1 ~9- ~- - —. - i-_% -~- L-L- - ~ - Dae L, AAI Utz:C Ha Flare Data End Iml E(8,12) Burst Data No. StaFrt Max. D. Location Start Max. End Base Ampl. 6.0 %.# d6 %# a ---,. s. K i...... = October 1967 (Concluded) 29 2347 31 1124 2351 2414 1130 2500D 1200 2b NO1W90 9034 2558 125 1294" 179 53 190' 180 2n S19E21 9047 1121 1132 1200' November 1967 2 0852 2 1141 3 1159 4 1151 5 0900 5 2234 10 0853E 10 1317 10 1517 10 2130 13 1808 16 -1002 17 0817 27 1602E 29 1852 0856 1210 1232 1210 1154 0906 2238 0855* 1330 1530 2133 1816 1011 0821 0840 1610 1902 0914 1250 1240 1220 0945 2253 0913 1410 1540 2140 1900 1100D 0935 1625 1912 2b S18W02 in N20W59 in N18W76 lb S18W33 in S25W41 in S18W48 lb S26W78 in S26W82 if S26W84 in S25W83 if N11E74 2n N10E38 lb N10E26 If N25W53 if S29W54 9047 9041 9041 9047 9053 9047 9047 9047 9047 9047 9073 9073 9073 9093 9091 1121 0854 2209 0851 1526 2130.5 1757 0951.5 0818 0918 1317' 1214 0908.5 2237.5 0901.5 1344 1531.5 2135 1818 1012.5 0838 1613 1240 2340 2149 1936 1009 1634 1921 32 30 30 53 36 29 36 73 63 146 30 42 38 44 53 417' 34 34 305 159 126 54 149 228 448 183.184 185 186 187 188 189 190 191 192 193 - 181 182 0 29 194 - 195 December 1967 1 0335E 1 1250 0345 1252 1304 0416 1315 In S27W70 9091 lb S28W75 9091 0304 1247.5 0339.5 0448 189 127 951 196 197

TABLE 4.1 (Continued) Date H_ xLHa Flare Data ____.......E(8___,12) Burst Data N.______ te Start Max. End Imp. Location Start Max. End Base Ampl. N. December 1967 (Continued) 1 1932 4 1302E 11 2154 13 0051 13 0332 13 0851 16 0941 16 1251 17 0440E 17 0643E 18 0242 18 1015E 21 0910 22 1315 23 2101 26 0611 26 1304E 26 2023 27 0838 27 1942 28 0218 28 1335 1947 1310 2200 2215 0056 0338 0856* 0944 0956 1255 0441 0646 0702 0259 0914 1320 2106 0627 1309 2027 0843 09o5 1948 2008 0223 2014D 1326 2235 0108 0341D 0905 1030 1300 0457 0750 0320 1030D loSoD 0940 1330 2200 0714 1325 2045 0920 2055 0304 1530 In S27W82 lb S19W90 lb N14W48 In N12W64 2f N12W65 In N13W70 In N20E13 In N19E11 In N18E03 lb N19E02 9091 9088 9101 9101 9101 9101 9115 1301 2149 0047 0331.5 0852 1946 1312 2200 95 21 198 53 85 199 50 - 200 0057 0337 0858 0944 1255 0444.5 0647 0705' 9115 9115 9115 0408 1311 0515' 0350' 0940' 1400' 2203 _1 39 37 39 100 106 125 137 150 147 116 95 84 73 147 100 73 213 248 291 315' 51 268' 563' 201 202 203 204 205 206 207 -4 H In In lb In In In In In In N19W11 N19W19 N26E04 N17W70 N25W19 S16E14 S14E80 S15E73 S17E59 9115 9115 9118 9115 9118 9128 9132 9132 9132 I (M lUVJ - 0911.5 0917 0547.5 - 1310.5 2020' 2050' 0838 0847 0853 0909 1940.5 1949 208 209 52 210 - 211 - 212 - 213 138 214 170' 215 211 216 lb S16W09 9128 84 212 lb S17W12 In S21W19 9128 9128 0217.5 1336 0227 1530 84 75 180 217 218 219

TABLE 4.1 (Continued) Ha Flare Data E(8,12) Burst Data Date Start Max. End Imp'. Location Start Max. End Base Ampl. December 1967 (Concluded) 29 0047 29 1120 29 1144 0050 1122 1149 1200 0100 1135 1225 In S27W78 lb S15W28 In S14E31 9120 9128 9132 0046 0050.5 1146.5 1149 1206.5 1137 73 362 73 73 47 220 221 222 January 1968 2 0519 3 1524 4 1719 5 0210 5 0458 6 0619 7 2153 8 2209 9 0507 11 1659 12 1807 14 0040 14 2400 17 0430 17 1228 18 0616 18 1514 20 0113 0531 1530 1721* 1724* 0217 0459 0622 2157 2218 2232 0511 1701 1708 1811 0046 2407 0436 1232 1245 0619 1525 0117 0124 0545 1543 1735 0240 0504 0641 2227 2335 0530 1728 1832 0120 2435 0442 1300 0632 1600 0134 lb S22E89 In S22W41 In N21E49 In N20E49 2b N12E72 lb N1E64 lb S22E13 In N23E67 2n N09E26 lb S25W38 2b S25W53 In N12W47 2b N17W44 In N16W80 In S16E85 lb S14E77 In S15E70 2n N27W90 9145 9133 9144 9144 9146 9146 9145 9153 0520 1716 0457 0613.5 2152.5 2212.5 9146 9145 1535 1723 1729 0502.5 0623 2201 1705 1813.5 0052 2410 0437.5 0619 1550 0120 1619' 0326 2226' 2340 0548 2434 0440 0630 0139 168 100 137 116 106 137 146 106 95 100 73 95 73 95 127 1912" 164' 193 434 338' 454 223 224 225 226 227 228 229 230 - 231 643' 232 9145 9146 9146 9146 9171 9171 9171 9153 1807.5 0040 2400.5 0436.5 0617 0114 476 137 749 11 183' 233 234 235 236 237 238 239 240 62 127 75 372' 44 31

TABLE 4.1 (Continued) Date Star Flare Data Ed E(8,12) Burst Data Date - F -End. mp. Location Start_ M-x. End Base Am. No __ Start Max. __End Imp. Location Start Max. End Base AmplN. January 1968 (Concluded) 20 0317 22 0440 28 0840 29 0801 29 1537 30 05053 30 1603 30 2006 31 1920 0319 0445 0844 0807 1540 0506 1608 2022 1923 0329 0515 0950D 0850 1558 0525 1652 2045 1937 In S16E50 lb S20W23 2n N15E35 lb N14E32 lb N14E28 In N21E42 in N23E37 In N13W04 In NllE77 9171 9167 9184 9184 9184 9188 9188 9184 9196 0316 0437 0839.5 0501 1920 0320.5 0446.5 0813 0506.5 1620' 1928' 16o6 2110 1939 43 36 158 116 95 95 116 116 127 73 70 267' 685' 1205' 127' 127' 241 242 243 244 245 246 247 248 249 February 1968 -w1 k j4 1 0925 1 1058 1 1613 1 1915 1 2042 2 0915E 2 1030E 2 1256 8 1825 10 1615E 10 1915 12 0758 15 0034 0930 1618 1629 1920 2044 2052 0921* 1103 1303 1827 1617 1628 1917 0803 0041 1030 1200 1649 2005 2110 0935 1130 1322 1832 1636D 2000 0843 0120 In N12W24 in N15W24 In N17W26 9184 9184 9184 in N16W16 9184 if N13W32 9184 In N1OW38 2b N13W37 lb N17W29 In S17E85 2n S17E57 In N20E45 In N17E22 In N20W10 9184 9184 9184 9206 9206 9204 9204 9204 0928' 1055.5 1614 1916. 2043 1257 1824.5 1606 0755.5 0027.5 1920 2056.5 0923.5 1107 1308 1630 1931.5 0804 0949 1132 1623 243 236 139 0944 1857 2016 159 212 150 175 243 62 62 243 364 541' 99 348 471' 193 319 250 251 252 253 254 255 256 257 258 259 260 261 262 95 588 44 103. 40

TABLE 4.1 (Continued) gDate __H! Flare Data E(8,12) Burst Data N Date Start Mx. End. Imp. Location Start Max. End Base Ampl. No February 1968 (Concluded) 15 1450 15 1809 16 2008 17 0252 17 0928 17 1254 17 2345 18 1055 18 1422 19 1520 21 0707 26 0623E 26 0817 26 1654E 1508 1524 1828 2015 0254 0934 1255 2351 1110 1424 1443 1526 0714 0625 0822 1657 1706 1540D 1855 2100 0313 0943 1312 2420 1135 1500 1550 0800 0642D 0840 1724 lb S14w11 9206 in N15W24 lb S27E03 lb N17W47 In N05E67 lb N07E65 in N17W54 In N25W14 if N19W61 in N17W77 in S28E32 in S25E23 in S26E23 in N12W90 9204 9211 9204 9216 9216 9204 9209 9204 9204 9218 9224 9224 9226 1449 1803.5 0250 0920 1255 2343 1102.5 1423.5 1518 0709 0815.5 1619.5 36 - 263 2019 0257 0936 1258.5 2358 1111 1437 0738 0629 0823.5 2100 0319 0950 1131 0702 0845 44 40 39 38 35 31 44 62 44 73 73 73 84 - 264 265 266 266 100 267 236 268 97 269 29 270 33 271 138 177 191 272 273 274 275 276 March 1968 13 0644 15 llllE 22 0543E 24 1635 25 1442 0646 1123* 0543 1645 1449 1507 0655 1207 0556 1735 1600 In N29E80 In N29E51 In N10W06 lb S12W02 lb S12W14 9267 9267 9281 9273 9273 0638 0525 1633.5 1444 0647 1126 0545 1647 1452 1507.5 1833 28 119 22 73 32 63 53 412 40 435 277 278 279 280 281

TABLE 4.1 (Concluded) HcR Flare Data. E(8,12) Burst Data Date Start Max. End Imp. Location Start Max. End Base Ampi. No. L __ t....' --..._' _ _':' _: _: _ _... _ March 1968 (Concluded) 27 1133E 28 0321 1140* 1155 in N18E44 9286 In S15W51 9273 1135 0322 1142 0337 1152 0329 40oo 53 31 282 62 75 283

76 maximum for each X-ray burst are measured to the nearest 1/2-minute; other times are to the nearest minute. All are given in Universal Time (UT). The standard notation E (or D) implies that the event started before (ended after) the time listed. The flare's importance is indicated by means of the present I.A.U. (International Astronomical Union) scheme which rates its area on a scale 1 to 4, as shown in Table 4.2, and the intensity of its brightest point as f (faint), n (normal), or b (bright). The location of the flare is given by its mean heliographic coordinates and the McMath serial number of its plage region. All Ha flare data were taken from the Quarterly Bulletin, except when that source did not give a time of maximum. In such cases, the value given by the SGDB was used if the individual reports of maximum were in agreement to the author's satisfaction. These are marked by * in Table 4.1. TABLE 4.2 CLASSIFICATION OF FLARE AREA Corrected Area Class (millionths of hemisphere) S <100 (subflare) 1 100 - 250 2 250 - 600 3 600 - 1200 4 > 1200 In addition to the timing values for the associated X-ray events, the table includes information on the E(8,12) base fluxes and burst amplitudes, both in units of 10-4 erg/cm2sec. The base flux (not to be confused with the daily base-level Eb(8,12) defined in Chapter III) is an estimate of the nonburst com

77 ponent of E(8,12) at the time of burst maximum, and is usually taken to be the flux value just prior to the onset of the event. This quantity will be referred to hereafter as EB(8,12). The burst amplitude AE(8,12) is defined as Ep(8,12) minus EB(8,12), where Ep(8,12) is the total flux at the peak of the XF B P ray burst. Whenever an event has more than one maximum, the tabulated value of AE(8,12) refers to the largest amplitude. In all cases, the symbol' means that a measurement is somewhat uncertain. The last column of Table 4.1 lists an identification number for each event of Catalog II. Three exceptions were made to the screening procedure described above. Flares #136 and #148 of the table were included even though no photographic record of either event exists in the ESSA flare-patrol network. However, both flares were reported by all the observatories which were monitoring the sun at the time (a disappointingly rare occurrence) and the internal agreement among the various reports for each flare was good, indicating that the time development of these two events was clearly marked. The third case, flare #202, was included because it is the only example during the period studied of a flare with an importance rating of 2f which might be considered valido This event was reported by just one station, Mitaka (Tokyo), which was the only station monitoring the sun at the time. Furthermore, it was recorded by cinematography, the most reliable flare-patrol technique. Therefore, the event was retained in this catalog, but with the explicit warning that it should be given little weight since it has not been properly verified. For one flare, #55 in Catalog II, the importance rating was not taken from the Quarterly Bulletin. This great event on 25 May 1967, one of only about two

78 dozen flares ever observed in white-light (DeMastus and Stover, 1967; McIntosh, 1967), gave rise to the largest hard X-ray burst (Kane and Winckler, 1969) and soft X-ray burst (Van Allen, 1968) yet recorded, and was accompanied by one of the greatest solar radio bursts measured to date (Castelli et al., 1968a, 1968b). Although the Quarterly Bulletin lists the event as three separate 2b flares, Dodson and Hedeman (1969a) conclude that the most plausible interpretation of the Ha film record is that a single flare of importance 3b occurred which had three distinct phases. This evaluation is used to describe the event in Catalog II. The 23 May 1967 flare also caused the greatest X-ray burst observed by the Michigan ion chamber, saturating the detector for over two hours. Even so, an estimate of AE(8,12) for this burst can be made by means of data from the University of Iowa's 2-12 A detector aboard Explorer 355 There is an excellent relation between the 2-12 5 and 8-12 a peak fluxes for bursts measured simultaneously by the Iowa and Michigan instruments, as shown in Figure 2-9 of Chapter II. Since the relation applies over a range of nearly two orders of magnitude, it seems unlikely that an extrapolation of another factor of 10 would be too much in error. On this assumption, the relation derived from Figure 2-9 was used with the Iowa measurement of the peak 2-12 A flux to determine Ep(8,12) for the 23 May 1967 burst. Then, subtraction of the observed 8-12 A base flux gives the value of AE(8,12) which is listed in Catalog II for this event. The identical procedure was used to find the approximate AE(8,12) for six other events which saturated the Michigan detector: #7, 53, 63, 130, 179, and 223 in the catalog. The burst on 6 May 1967 (#42) also saturated the instru

79 ment, but for such a short period of time that its peak flux could be estimated easily by inspection. (This X-ray burst is shown in Figure 2-2 of Chapter II.) The resulting values of AE(8,12) for all of the events just discussed are marked by the symbol " in the catalog to indicate that they were not measured directly. 3. CHARACTERISTICS OF THE Ha FLARES IN CATALOG II Several tests were made to investigate the possibility of bias in the selection of flares for this catalog. First, the frequency of occurrence N as a function of flare importance was considered, and the results are shown in Table 4.3 along with the "nominal" frequency distribution taken from Smith and Smith (1963). The latter distribution for given area classes is not significantly different from that found for the events of Catalog II. Unfortunately, no study has yet been made, to the author's knowledge, of this "nominal" distribution using the new I.A.U. classification scheme. TABLE 4.3 FREQUENCY DISTRIBUTION WITH FLARE IMPORTANCE Flare This Study Smith and Smith Importance N % if 14 4.9 in 172 60.8 lb 63 2253 1 (all) 249 88.0 78.6 2f 1 0.4 2n 15 5,3 2b 15 5.3 2 (all) 31 loO 19.2 3n 2 0.7 3b 1 0.4 3 (all) 3 1,1 2.2

80 Next, the number of cataloged flares occurring in the northern or southern hemispheres and eastern or western hemispheres was investigated. The results are given in Table 4.4, which also includes the probability P (derived from Chi-squared tests) that the observed north-south or east-west differences in flare occurrence are significant. For sunspots, an east-west asymmetry has been known since Maunder's (1907) early study, but apparently none exists for flares in general (Smith and Smith, 1963). Thus, the occurrence of events in Catalog II is not clearly atypical, since there is a large likelihood that its eastwest difference (opposite in sense from the sunspot's east-west asymmetry) is due purely to chance. On the other hand, the north-south asymmetry of the cataloged events is very striking and is almost certainly a real effect; but this is not unexpected. Behr and Siedentopf (1952) have shown that in both sunspot and flare occurrence there is a definite north-south asymmetry which changes sense pseudo-periodically with the solar cycle. During the interval covered by the present study, the sun's activity was clearly concentrated in its northern hemisphere, and Catalog II merely reflects this effect. In fact, Dodson and Hedeman (1969b) report that the north-south asymmetry in solar activity was stronger at the start of solar cycle 20 (1964-1966) than at the onset of any other solar cycle in the past 100 years. TABLE 4.4 FREQUENCY DISTRIBUTION WITH HEMISPHERE OF OCCURRENCE Hemisphere N P North 196 69.3 South 87 30.7 East 134 47.3 West 149 52.7

81 One investigation of the catalog did reveal a bias, however. As mentioned earlier, the major motivation for constructing another catalog was that a disproportionate number of events in Catalog I occurred during European observing hours. Unfortunately, Figure 4-1 shows that the second effort did not completely eliminate this effect since the number of events in Catalog II which occurred between 0800 and 1359 UT is again significantly too large (more than 3a above the mean). The effect cannot be attributed to the selection procedure described in Section IV-1, since it also exists for flare reports in general (Dodson and Hedeman, 1960). A more likely explanation is that European observatories may tend to assign a somewhat greater importance classification to a given flare than would their American counterparts, so that they may rate some events as importance 1 which would have been called subflares by observers in other parts of the world (Dodson and Hedeman, 1960; C. S. Warwick, 1965). This possibility will be discussed further in Section IV-6bo 4. CHARACTERISTICS OF THE SOFT X-RAY BURSTS IN CATALOG II Catalog II was constructed as a list of well-verified Ha flares for which valid X-ray coverage by the Michigan ion chamber was available; there were no requirements as to the nature of that X-radiation, However, all but one of the listed flares were accompanied by a measurable E(8,12) enhancement in excellent time-relation to the optical event. This section considers some of the general characteristics of these X-ray bursts themselves, and following sections will investigate the relation of these bursts to other phenomena. But it must be emphasized again that these studies relate to a very special type of soft X-ray

NUMBER OF EVENTS 40r 301 3<r 0o F\) 201 In I I I I I i I, I I I a a 0 oh 12h 18h TIME OF MAXIMUM (U.T.) a 24h Figure 4-1. Frequency distribution of Catalog II flares with Universal Time. The mean frequency is indicated by the dashed line. The "Universal day" is divided into 12 two-hour blocks, and flare membership is defined by the time of the Ha intensity maximum. If more than one maximum is listed in the Quarterly Bulletin, the time of the first is used here. Note the significant excess of flares between 0800-1359 UT, the period when European observatories are monitoring the sun.

enhancement, one associated with an Ha flare of importance > 1. The results found here may not necessarily apply to all X-ray bursts in general. a. Occurrence of the Bursts Many investigators have claimed that a substantial fraction of Ha flares of importance > 1 are not accompanied by an enhancement of solar X-ray emission (Kreplin et al., 1962; Acton, 1964; Lindsay et al,, 1965; Culhane et al., 1968; Culhane and Phillips, 1969; Hudson et al,, 1969a). As just mentioned, the present study does not substantiate that claim, Of the 283 flares listed in Catalog II, only one (#88) had no measurable X-ray burst associated with it, and that event was marginal in many respects, It was rated importance if, the weakest type considered for the catalog, and occurred very near the solar limb, where importance ratings are most difficult to assign, It was reported by just two stations, Lockheed and Ikomasan (Japan), the only observatories monitoring the sun at the time of flare maximum, which was 2303 UT on 21 July 1967. Ikomasan is a visual station and reported merely that the event began before 2302 and ended after 2306 UT, although it was observing continuously before and after these times. This might indicate that the flare was very faint indeed, Therefore, the reports of this flare were not as well verified as one would like. Furthermore, at the time of the event, the Michigan ion chamber was in its operating mode of low sensitivity, so that it could only detect changes in the solar X-ray flux of at least 95 x 10-4 erg/cm2sec, Two other bursts in Catalog II had measurable amplitudes less than that value. But, even if event #88 is taken to be an example of a flare with no associated soft X-ray enhancement,

84 this study implies that at least 99% of flares of importance 1 or larger are accompanied by soft X-ray bursts. The failure of earlier investigators to find this result is undoubtedly due to their utilization of flare lists which include spurious reports, as suggested by Teske (1969a). b. General Time-Profile Properties Solar microwave bursts usually fall into one of two categories, normally called gradual rise and fall (GRF) and impulsive bursts (Covington and Harvey, 1958). This classification also applies to hard X-ray events (Kane, 1969), but the situation is not so clear for X-ray bursts at longer wavelengths. Some authors claim that such a distinction can be clearly made for soft X-ray events (Chambe and Sain, 1969), some find only slight evidence for it (Culhane et al., 1963; Culhane and Phillips, 1969), while others feel no such distinction exists (Drake, 1969). The resolution of this problem is of great importance because of the insight it would give into the physical characteristics of the solar Xray emitting region. In the case of the microwave events, for example, it is generally agreed that the GRF bursts are thermal in nature, while impulsive bursts are due to nonthermal processes (e.g., Takakura and Kai, 1961, 1966; Holt and Cline, 1968). Two semi-related parameters can be used to distinguish gradual events from impulsive ones: the time between the start and maximum of a burst At, and the mean rate of flux enhancement AE/At. A total of 128 soft X-ray bursts in Catalog II were sufficiently well observed so that these parameters could be determined for them. The frequency distributions of events with various values of these parameters are depicted in Figure 4-2. Neither distribution shows any

NUMBER OF EVENTS 20 10 - O~~~~~~ (a) 20 40 60 RISE TIME (Minutes) NUMBER OF EVENTS 20 r \-n 10 0 (b).002.004.006 MEAN RATE OF RISE (erg/cm2 sec/min) Figure 4-2. Frequency distributions of Catalog II bursts with (a) rise-time and (b) mean rate of E(8,12) rise. Neither distribution is bi-modal in character.

86 evidence for two distinct burst types, which suggests that all E(8,12) events can be considered of thermal origin. (The time-development is much too gradual on the average to assume that they are all nonthermal.) Yet another attempt to identify impulsive bursts in Catalog II is shown as Figure 4-3. This plot of the soft X-ray amplitude AE versus the rise-time At is essentially the same method originally used to distinguish the two types of microwave bursts (Covington, 1959). Again, no clear grouping occurs for the X-ray events considered here. It must be pointed out once more that the list of X-ray bursts used in the present study is a very select one, consisting only of those which accompany well verified Ha flares. Thus, it is conceivable that the result found here does not apply to other soft X-ray bursts. But this does not seem to be the case, since it best agrees with Drake's (1969) investigation, the most extensive yet attempted, which includes over 2000 events observed during the period 2 July 1966 to 18 September 1968. DeJager (1965b), who first suggested that X-ray bursts be divided into "quasi-thermal" and "nonthermal" classes, also felt the majority of bursts observed at wavelengths longer than 1 a should fall in the former category. Other theoretical investigations led to similar conclusions (Kawabata, 1963, 1966a; Kundu, 1964; Culhane and Phillips, 1969). A possible explanation for the disagreement on this point among the observers mentioned earlier is that a relatively small, impulsive component is sometimes superimposed on the larger, more gradual soft X-ray burst (Donnelly, 1969b). Examples of such composite events have been recorded by the Michigan experiment (Figure 4-4), but they are infrequent. If this impulsive component

87 AE(8,12) erg/cm2 sec 0 10-1 10-2 0 0 00 0 0@0 0 0 *0 0 0 0 0 0 0* $$a. 0.0 0 * 0 so 0~ 0 ~~, 00 0 0 0. 0 0 0 0 1 A 0 0 0 0 0 0 ~* 0 0.a..-ww 0 0 0~ 0 00 * 0 0 00. 0 0 0 0* 0 0 *0 0 0 I I I 1 I 0 20 40 RISE TIME (Minutes) Figure 4-3. Scatter diagram of X-ray burst amplitude AE(8,12) versus rise-time for events of Catalog II. No evidence appears for distinct classes of soft X-ray bursts.

88 E (8,12) erg/cm2 sec..004.003 0.050 APRIL 11, 1967.025 1318 1338 U.T. Figure 4-4. Time-profile of the soft X-ray burst on 11 April 1967. The Michigan detector switched its operating mode from high (flux scale on left side of ordinate axis) to low sensitivity (scale on right) at 1326 UT. Note the minor impulsive burst at about 1321 UT superimposed on the initial rising phase of the major event (#33 in Catalog II).

89 becomes stronger relative to the gradual component at shorter wavelengths (as observed by Kane, 1969), one can account for the above, apparently contradictory reports. In any case, it is clear that the soft X-ray bursts of Catalog II are almost exclusively thermal in character. c. Mean Burst Durations It is well known that the total durations of Ha flares depend upon their importance on the average (e.g., Waldmeier and Bachmann, 1959; H. J. Smith, 1962). Unfortunately, Catalog II is not extensive enough to permit a similar study for the X-ray bursts associated with these flares. Of the 60 bursts in the catalog which had observed beginning and ending times, 52 accompanied importance 1 flares. For these, the median burst duration is 33 minutes, somewhat longer than the median duration of 24 minutes found for importance 1 Ha flares in general (H. J. Smith, 1962). The typical "importance 1" X-ray burst is probably of even greater extent, however, because the above procedure systematically discriminates against longer duration events. The end-time for such a burst is much less likely to be identified since it has more chance of being contaminated by other events or lasting into the unobserved period during satellite-night. Therefore, it is safe to say that the soft X-ray bursts have a greater duration than their optical counterparts on the average, a result which agrees with the observations of others (Acton et al., 1965; Lindsay, 1964; Paolini et al., 1968). With regard to the burst duration as a function of the associated flare's size, we can only state that our subjective opinion supports Teske's (1969a) claim that the X-rays tend to outlast the visible event for a length of

90 time which depends upon flare importance. As an example, the E(8,12) flux remained above its pre-burst level for more than two hours after the reported end of the great 23 May 1967 flare described earlier. This question should be reconsidered quantitatively in the future when more extensive data are available. d. Accuracy of Source Position and Burst Amplitude Although the Michigan experiment has no resolution of the solar disk, the location of each X-ray burst in Catalog II can be assigned with confidence to the position of its associated Ha flare. This follows, for example, from the exquisite X-ray photographs of the sun during a ln flare (Vaiana et al., 1968) which show not only that the X-ray and Ha flaring regions are coincident, but also that their general structures are remarkably similar. There is some indirect evidence that an X-ray burst which does not accompany a flare can occur in a region devoid of any type of solar activity (Zhitnik et al., 1966), but no examples exist, to the author's knowledge, of a flare-associated X-ray burst which was not located at the position of the optical event. It is also necessary to defend the reliability of the burst amplitude values listed in Catalog II. These values were derived on the assumption that the X-ray spectrum mimics that of a 2 x 106 K gray body and remains constant at all times. In reality, the X-ray spectrum during a burst bears little resemblance to that of a gray body (e.g., Neupert et al., 1969: shown in this paper as Figure 2-4) and the spectral distribution varies rapidly as the burst develops (Chubb et al., 1960; Pounds and Willmore, 1963; Friedman, 1964; Lindsay, 1964; Takao, 1967).

91 The analysis of this problem discussed in Chapter II implies that the Michigan results are only slightly affected by the poor choice of assumed spectrum. In the worst case, the relative error of E(8,12) appears to be about 30%. One of the strongest arguments for this point of view is the excellent relation between the peak fluxes of X-ray bursts as measured by the Michigan and Iowa experiments, two detectors with quite different spectral responses (Figure 2-9). Therefore, the burst amplitudes of Catalog II can be considered as reasonably valid as far as relative error is concerned. However, bear in mind that the absolute values of E(8,12) may be too large, perhaps by as much as a factor of 2 or 3. But this will not vitiate the qualitative aspects of the studies which follow. 5. TIME-RELATIONS BETWEEN Ha FLARES AND SOFT X-RAY BURSTS The timing of X-ray bursts relative to other solar events is naturally of interest for the information it would offer about the mechanisms giving rise to those events. But such a study gains additional significance because of the possibility that a soft X-ray enhancement is the very first manifestation, of a solar flare (Donnelly, 1968b). This possibility is of obvious importance to a flare early-warning system, for example, in future manned space applications. The time-relations between Ha flares and X-ray bursts have already been examined in some detail in Paper I (Teske and Thomas, 1969) using our first flare catalog. But, because of its importance, this investigation has been redone here with the more extensive list of events in Catalog II.

92 a. Starting Times As in the study for Paper I, the starting time used for the Ha event is the earliest flare start-time reported by a cinematographic station, if one was observing, or the earliest reported by a photographic station otherwise. (In general, this will not be the time listed in Table 4.1.) This procedure is followed since some Ha brightening must have appeared on the film at that time even though it may have been so subtle that other observers overlooked it. Unfortunately, possible clock errors at the various flare-patrol stations cannot be taken into account. However, if such errors exist in significant degree, they would bias the results of the present study toward earlier relative starting times for the Ha flares. The start-time of the X-ray burst is defined as that time when the E(8,12) curve first begins to rise, even though the increase may not necessarily be monotonic after that point. Since the flares in Catalog II were carefully screened to include only isolated events, any initial fluctuations which may occur in the X-ray burst are considered to be a part of a single comprehensive event as long as the flux always remains above the pre-burst level, (This point will be reconsidered later.) The bursts were divided into groups depending upon whether they started when our detector was in its operation mode of high or low sensitivity. Also, bursts associated with flares occurring within 60~ heliocentric of the solar disk center were considered separately from those associated with flares nearer the limb. The latter groups will be referred to as "center" and "limb" events, respectively. Table 4.5 shows the results of this study, which included a total

93 of 173 events. The average differences between start-times are given in minutes, and negative values mean that the soft X-ray burst starts first. The numbers in parentheses indicate how many events were considered in each average. Also listed is a "confidence" parameter P (calculated by Student's t-test), which shows the significance of the observed difference between two sample means. More precisely, 1.0 minus P gives the probability that a difference between two averages as large or larger than the one observed could have resulted by the random selection of values from two identical sample populations. TABLE 4.5 MEAN DIFFERENCES BETWEEN Hao AND SOFT X-RAY STARTING TIMES (All time differences are in minutes) Center Limb P Low sensitivity +0.2 (88) +0.1 (39) 8% High sensitivity -3.4 (33) -4.8 (13) 57% P: > 99% 97% One can see that there is probably no center-to-limb effect, at least not in the way these data have been divided. On the other hand, the results do show a marked dependence on the sensitivity of the detector. With the instrument in its low sensitivity mode, no advance warning whatsoever of the Ha flare is gained from the soft X-ray observations. Only the high sensitivity results show that the X-ray burst does indeed begin on the average significantly before the reported start of the flare. This finding suggests that the initial rise of the "average" soft X-ray burst is very gradual and of small amplitude for

94 the first few minutes. (This preliminary phase is called the X-ray burst precursor and will be discussed in more detail below.) Then the coincidence of start-times when the low sensitivity X-ray data are used implies that there is a stronger rise in flux at the instant the Ha flare begins. Both of these features are often clearly seen in the time-profiles of individual events. As an example, the burst on 17 June 1967 which accompanied a in flare (#76) is shown in Figure 4-5. Although the soft X-ray burst seems to begin early on the average relative to the Ha flare, there is a wide variation in the individual values. The range found in this study extends from X-rays starting early by 28 minutes to X-rays starting late by 12 minutes; and even when the detector is in its high sensitivity mode of operation, about 30% of the X-ray bursts begin after the reported start-time of their associated flares. This great dispersion of values is undoubtedly responsible for the conflicting results of timing studies which are based on only a few individual cases (cf. Landini et al., 1965; Falciani et al., 1968). b. The X-Ray Precursor Counterparts to the precursor component described above have also been reported for 1-1.5 A (Hudson et al., 1969a) and 3-4 A bursts (Culhane and Phillips, 1969). The possible existence of such a "pre-burst" phase is of interest not only for the flare-warning system mentioned earlier, but also for the information it would give concerning the physical mechanism which initiates the entire flare phenomenon. Unfortunately, the analysis leading to its "dis

95 E(8,12) erg/cm2 sec..005T.004t.003+ Imp. n /\ \ \ \ \>.002 JUNE 17, 1967.025 0 I I 2109 2129 2149 U.T. Figure 4-5. Time-profile of the soft X-ray burst on 17 June 1967 (Catalog #76). Note scale change at 2125 UT. The initial, very gradual rise in flux begins at 2106. A sharp increase in the rate of rise occurs at 2120, exactly coincident with the reported start of the Ha flare. A schematic representation of the flare's intensity development is also shown.

96 covery" contains two known sources of systematic error, at least in the case of 8-12 A radiation. The first involves the identification of the Ha flare's start, which was taken to be the earliest time reported by a cinematographic or photographic station in the present study. Cinematography offers the better time-resolution, but even so, filtroheliograms are normally made only once each 30 seconds. Furthermore, the observed flare start is given as the time of the first frame on which a visually detectable brightening appears, This combination of practices results in reported start-times which are consistently later than the "true" beginning of the event. In fact, photographic photometry indicates that the rapid-rise phase of an Ha flare may begin up to 1 to 1-1/2 minutes on the average before it is defined from a visual inspection of the film (Angle, 1968). The second source of systematic error is the existence of E(8,12) enhancements which are not related to any reported optical events (Teske, 1967). These fluctuations may be due to subflares which are usually not reported by European observatories as a matter of course (Teske, 1969a); to flares which occur just beyond the limb (Teske, 1969b); or to still other sources. But whatever the cause of these flux variations, the Michigan detector's lack of spatial resolution makes it impossible to distinguish them from physicallyconnected components of flare associated bursts if the two should occur.simultaneously. Although great care was taken to assure that the flares of Catalog II did not occur close in time to any other reported event, their X-ray bursts may still be contaminated by these background fluctuations. Thus, if a burst begins while such a flux enhancement is in progress, the start of the burst will be assigned mistakenly to the earlier start of the background fluctuation.

97 In order to estimate the influence of this systematic error on the mean start-time relation found in the previous section, the frequency and durations of such background fluctuations were investigated for the period of 10 March 1967 to 18 April 1967. Since the E(8,12) burst precursor normally appears just in data obtained by the detector's high sensitivity mode of operation (Section IV-5a), only these data were examined in detail, so that the total measured time came to 7371 minutes (called C hereafter), By determining the fraction of the test interval C affected by background fluctuations, one can calculate the amount of the average early rise given in Table 4.5 which is due to this effect. If N(d) is defined as the number of such fluctuations with duration d occurring in the test interval, the fraction of this interval in which burst starting times would be misidentified by t or more minutes is given by: 00 x(t) = E (d - t)-N(d)/C (4.1) d=t (Only integral values of d and t are considered for this study.) The fraction of the interval in which starting times would be assigned too early by exactly t minutes is then: X(t) = x(t) - x(t + 1) (4.2) Finally, the effect of background fluctuations accounts for y minutes in the average early rise-time of bursts occurring at random during the test interval, where y is given by: 00 y = E t.x(t) (4.3) t=O

98 The frequency distribution of N(d) for the time interval studied here is shown in Figure 4-6, and results in a value of y = 1.2 minutes, Since the interval 10 March 1967 to 18 April 1967 does not appear atypical, it seems reasonable to assume that this value can be applied to the relative start-time relations found for all Catalog II events. Thus, taking 1.2 minutes for the error caused by soft X-ray fluctuations and 1.5 minutes for the error due to the method of defining Ha flare start-times, we find that an E(8,12) burst begins just 1.1 minutes before its associated flare, on the average, if center and limb events are considered together. The above analysis of the background fluctuations' effect assumes that they are not physically related to the flare event itself. Culhane (personal communication) points out another possibility: namely, that they are manifestations of a flare triggering mechanism which is not always successful. By this interpretation, all observed precursors are valid components of the total burst, and the average early rise of E(8,12) relative to the Ha flare thus becomes 23. minutes. The hypothesis also implies that two presumably independent conditions must obtain simultaneously in order for the total flare phenomenon to be initiated; first, the existence of the triggering agent (which always gives rise to a soft X-ray enhancement), and secondly, perhaps some metastable, high energy configuration of the potential flare source. Thus, if this suggestion is correct, a careful examination of plage regions during flare-producing and nonflare-producing precursors might indicate the active center configuration necessary for a flare event to occur. Such a study obviously merits future consideration.

NUMBER OF FLUCTUATIONS 20 10 0 10 20 30 DURATION (Minutes) Figure 4-6. Frequency distribution of E(8,12) background fluctuations as a function of duration. Such fluctuations are soft X-ray enhancements which do not accompany any reported optical activity on the sun. This distribution refers to the 7371 minutes of high-sensitivity data recorded by the Michigan detector between 10 March 1967 and 18 April 1967.

100 In any case, the present study shows that the pre-flare warning provided by 8-12 A X-rays is much shorter than previously believed, and that it exists only in a statistical sense even if high sensitivity data are used. Furthermore, the relatively frequent background fluctuations closely mimic the initial "early-rise" phase of flare-associated bursts. A soft X-ray monitor therefore appears somewhat less attractive as a flare-alarm device than first indications implied. But it is probably still the best technique available for at least three reasons (Friedman, 1964; Pounds, 1965a; Donnelly, 1968b): (a) the soft X-ray enhancement is indeed one of the first known manifestations of the flare phenomenon on the average, (b) soft X-ray bursts exhibit large percentage increases over the baselevel flux of the total solar disk, thus permitting a simple patrol of the entire visible hemisphere, and (c) a solar X-ray monitor is capable of very high time resolution. An additional advantage is the fact that such relatively inexpensive X-ray monitors can be carried aboard polar-orbiting satellites, which would then allow completely continuous, "all-weather" coverage of solar activity by a single instrument, a truly noteworthy goal. Co Maximum and Ending Times The time-relations for the maximum and ending phases of the events in Catalog II have also been determined in a manner similar to that described in Section IV-5a. The results are shown in Table 4.6, where the terms "center" and "limb" and the confidence parameter P are defined as before. Here, the positive values mean that the relevant X-ray burst times all occurred after

101 their counterparts in the average Ha flare's intensity profile. No separation into sensitivity ranges was considered for the timings at maximum since these bursts almost invariably caused the detector to switch into its low sensitivity mode at their peak. Some events remained at their peak flux for several minutes, and in these cases the time of maximum used was dne minute after the flux first reached this value. Thus, the difference of about 3 minutes between the times of Ha and X-ray maximum might actually be a slight underestimate of the true delay. It appears to be quite rare for the X-ray burst maximum to precede the peak intensity of the Ha flare; this occurred in only 5% of the events studied here. TABLE 4.6 MEAN DIFFERENCES BETWEEN Ha AND SOFT X-RAY MAXIMUM AND ENDING TIMES (All time differences are in minutes) Center Limb P Times of Maximum + 3.6 (160) +2.3 (71) 96% Times of End +13.9 (75) +9.6 (31) 80% The fact that the X-ray burst clearly reaches its maximum well after the Ha intensity peak may necessitate the reevaluation of some ionospheric parameters derived from SID studies. Mitra (1965) points out that such studies normally assume that the ionizing radiation (principally X-rays below 20 A) follows the same time curve as the Ha flare's intensity, and in particular that their times of maximum are identical. The present results show that this assumption is incorrect.

102 The ending time for an X-ray burst is often difficult to identify correctly, and the difficulty may be even greater in the case of the Ha flare (Dodson and Hedeman, 1964). Thus, the time-relation given in Table 4.6 for the event's end must be treated as just an approximation. Even so, the result found here, that the X-ray burst outlasts the flare by roughly 10 minutes on the average, agrees nicely with the event duration study of the previous section where a different set of events was used for the investigation. The scatter among the individual values is very large, however, ranging from the X-rays ending early by 38 minutes to the X-rays ending late by 58 minutes, Because of the uncertainties just described, the center-to-limb difference for the relative ending times in Table 4.6 cannot be considered as definitely established. On the other hand, the difference between relative times of maximum for flares at the center and near the limb, although small, does appear to be significant. If this effect is real, it may imply a variation of the optical flare's characteristics with height, since only the higher levels of the flare are visible when it is near the limb. No center-to-limb change is expected for the soft X-ray burst itself because the solar atmosphere is optically thin to X-radiation (Allen, 1969). Of course, the latter argument assumes that the X-ray emitting region radiates isotropically, but this is certainly a reasonable assumption for a thermal source (see Section IV-4b)o A word of caution must be given: the significance of the center-to-limb effect for maximum times and for starting times found in the present study are exactly opposite to the conclusions drawn in Paper I, although data from the same experiment were used for both. Since the events considered here are some

103 what less biased (see Section IV-1) and are about three times as numerous as those in the previous study, the present results are probably more reliable. But this discrepancy does serve to point out that the significance of centerto-limb variations in these relative timings cannot be determined conclusively until more extensive data are available. 6. COMPARISON OF SOFT X-RAY BURST AMPLITUDES WITH OTHER PHENOMENA The X-ray bursts listed in Catalog II display a wide range of E(8,12) amplitudes, spanning more than three orders of magnitude from the smallest measured, 0.0005 erg/cm2sec (#29), to the largest inferred, 0.806 erg/cm2sec (#55). (See Section IV-2 for the method used to estimate the amplitudes of bursts which saturated the Michigan detector.) The investigations discussed in this section were carried out in order to find some parameters accessible to ground-based observers which correlate with the amplitude of soft X-ray bursts, Such a study could be used to help identify those physical conditions which are important in influencing the production of soft X-radiation during a solar flare. Alternatively, it might form the basis for a purely empirical prediction of a soft X-ray burst's amplitude from ground-based observations (in addition to SID measurements, of course), a, Ha Flare Importance One obvious parameter to consider in this connection is the importance of the associated Ha flare. The results of previous studies regarding this point are quite contradictory. Some investigators report that there is a definite relationship between X-ray burst amplitude and Ha flare importance (Dodson et al.,

l04 1956; Warwick and Wood, 1959 (both by means of SID data); Paolini et al., 1968; Teske, 1969a), some believe that the relation, if any, is either weak or variable (Culhane et al., 1968; Culhane and Phillips, 1969; Hudson et al., 1969a), while others claim that no such relationship exists (Conner et al,, 1964; Friedman, 1964; Kreplin and Gregory, 1965). The present study implies that soft X-ray burst amplitudes are indeed related to the importance of the associated flare, but only in a statistical manner. This was found by calculating the mean amplitude AE for all E(8,12) bursts in Catalog II which occurred during flares of a given importance. Table 4.7 gives the results for all importance classes in the catalog, along with the probable error (p.ee) of each mean, the number of events (N) used to find the mean, and the minimum and maximum burst amplitudes in the catalog for each flare importance. TABLE 4.7 MEAN E(8,12) AMPLITUDES FOR FL (All flux values are in Flare AE p.e. ] Importance If.0052.0010 In.0183.0014 1 lb.0345.0028 2f.0248 -- 2n.0423.0127 2b.0970.0209 3n.1328 -- 3b.8060 -- ARE-ASSOCIATED BURSTS erg/cm2sec) Minimum Maximul AE AE 11.0000.014< 38.0005.2161 50.0043.191 1 13.0031.2635 11.0390 390( 1 m 2 2 5

105 The table clearly shows that the average amplitude is directly related not only to the flare's area but also to its brightness. The mean burst amplitude becomes larger with an increase in either of these factors. One reason that some of the earlier investigators did not arrive at a similar conclusion is undoubtedly due to their use of unverified flare lists. But Table 4.7 suggests an even more important source of confusion: the very large range of individual values within a given flare class. For example, observed amplitudes vary by more than two orders of magnitude in the case of bursts associated with In flares. Thus, the relationship which does exist can be revealed only by a statistical analysis of a large number of events, as in the present study. In order to present the relationship in a quantitative form, a crude estimate of the peak enhancement in the Ha emission-rate was obtained by means of the average flare area and maximum Ha intensity appropriate for each flare importance. Because of difficulties caused by the well known limb-darkening effect, only Ha values for the center of the solar disk were considered. These were taken from the photometric study of solar flares made by Dodson et alo (1956), and converted into flux units by the procedure derived in the Appendix of the present paper. The mean flux amplitudes for both the Ha and soft X-ray events were then used to find the emission-rate enhancements at the sun, AS(Ha) and AS(8,12), which are listed in Table 4.8. These entries are tabulated in order of increasing AS(Ha) and include values for subflares which were measured during the construction of an earlier catalog. The latter naturally should not be given as much weight as those derived from Catalog II flares, but are included to point out that the relation found here may also extend to smaller events.

106 TABLE 4.8 MEAN EMISSION-RATE ENHANCEMENTS FOR Ha AND SOFT X-RAY EVENTS (Emission-rates in 1025 erg/sec) AS(Ha) AS(8,12) Flare Importance 5.8 1.5 if 6.9 1.1 Sn 12 3.0 Sb 29 5.1 In 53 10 lb 55 7 2f 110 12 2n 170 27 2b 290 37 3n 380 227 3b The values derived in this study agree fairly well with results found by other investigators. Vaiana and Zehnpfennig (1969) estimate that the peak 3.5 - 14 A flux during a In flare was about 5 x 1024 erg/sec, but they note that this was really a rather small event. For the optical flare, several observers report a peak Ha emission rate about 1027 erg/sec both with events of importance 2 (Severny, 1952; Billings and Roberts, 1953) and importance 3 (Teske, 1962; Ellison, 1963a)o The relation between rates of soft X-ray and Ha emission is even more clearly seen in Figure 4-7 which shows a graph of the Table 4.8 values, with a straight line indicating the best linear fit to the plotted points. Obviously, there is an excellent statistical relationship between Hey and soft X-ray enhancements which is well represented by a direct proportionality. Thus, the present study implies that the following expression holds on the average: AS(8,12) = 0.16 AS(Ha)

AS(8, 12) erg/sec'3'II 0 27 1026 1025 5-.04'3 / T 1-0 4 12 0-_ 1 l2 0 0 J. 1 T q - Of I I I I I I I. I i, i I I. I I 1026 1027 S {Hno) erg/sec i028 Figure 4-7. Relation between AS(8,12) and estimated AS(Ha) for various flare importance classes. Points are plotted for faint (o), normal (.), and bright (x) flares. The error bars for the mean X-ray values refer to the probable errors derived from Table 4.7. Those for the estimated Ha values result from an assumed uncertainty of ~0.1 in the flare's intensity relative to the center of the undisturbed solar disk (see the Appendix). No error can be assigned to AS(8,12) associated with 2f, 3n, or 3b flares since there is only one example of each type of these bursts. The straight line indicates the best fit by a linear relationship (i.e., unity slope).

108 It should be noted, however, that the relationship found here applies to emission rates at the maximum of the Ha flare and X-ray burst. As shown in Section IV-5c, these maxima occur at different times in general. To obtain the relation given in (4.4), the soft X-radiation was assumed to be isotropic into 41T steradians because of the thermal nature of 8-12 A emission (see Section IV-4b). Since the solar atmosphere is optically thin at such wavelengths (Allen, 1969), any possible effects of X-ray photon scattering were neglected. On the other hand, semi-isotropic radiation into 2- steradians was assumed for the Ha emission, following Pottasch's (1965) belief that all resonance-line photons created by collisional excitations ultimately escape from the solar surface. (See, however, the discussion by Athay, 1966.) Uncertainties caused by these assumptions also apply to the constant of proportionality in expression (4.4), of course, but the value of this constant is unreliable for an even more fundamental reason. Namely, the Ha flux is strongly overestimated by using the maximum intensity of the flare's brightest point, as in the above method, rather than some mean intensity averaged over the entire flaring region. Isophotometry of three flares (to be described in Chapter V) indicates that the correct method leads to Ha flux values which are lower by a factor of 5. However, this difficulty is not critical for the present study since the important result here is the existence of a proportionality between mean soft X-ray and Ha enhanced emissions, rather than the exact value of the proportionality constant involved. Because the flare importance does have such a major statistical influence on the amplitude of the associated X-ray burst, the remainder of this chapter (unless otherwise noted) will only consider bursts

109 which accompany In flares, the most numerous importance class in Catalog II. The amplitudes of these bursts will be referred to by the symbol AE (8,12) and the bursts themselves will be called "in" X-ray bursts. b. Time of Occurrence As mentioned in Section IV-3, there is some evidence that European observatories as a whole tend to rank flares on a slightly higher importance scale than do observatories in other parts of the world (Dodson and Hedeman, 1960; C. S. Warwick, 1965). To investigate this question using the X-ray data of Catalog II, the mean E(8,12) amplitudes were determined for all "in" bursts whose maxima occurred during "European," "American," and "Asian" observing hours: defined here as 0600-1359, 1400-2259, and 2300-0559 UT, respectively. Table 4.9 shows that "in" bursts do have lower average amplitudes when associated with reported flares that can be attributed roughly to European observers. This is exactly the result expected if these observers did indeed rate flares as importance In which would have been assigned somewhat lower rankings elsewhere. This is not meant to imply in any way, of course, that the reports from some flarepatrol stations are correct while others are not, Rather, it merely indicates that world-wide ratings of solar flare importances are not made on a uniform basis at the present time. This fact undoubtedly accounts for a part of the burst amplitude variations described earlier, and points out again the advantage of studying flare characteristics by means of statistical investigations of a large number of events, which tend to average out such effects,

110 TABLE 4.9 MEAN E 1(8,12) AMPLITUDE VERSUS UNIVERSAL TIME Time of AE (8,12) TMimue of Observers ln Maximum (UT) erg/cm2sec 2300 - 0559 "Asian".0238 +.0034 p.e. 0600 - 1359 "European".0147 +.0008 1400 - 2259 "American".0211 +.0040 c, Location on the Disk The average amplitude of "In" X-ray bursts was also considered as a function of the position of the burst on the solar disk. This was done in two ways: (a) by dividing the sun into its various hemispheres and quadrants, and (b) by comparing limb bursts with those that occurred nearer the center of the disk. As in the relative-timing investigations described in Section IV-5a, events that occurred within 60~ heliocentric of the solar disk center are called "center" bursts while those beyond 60~ are "limb" bursts. Table 4.10 gives the results of these studies and shows that there are no strong statistical differences among the categories tested. The same result has been reported for similar studies using data from the effects of Sudden Ionospheric Disturbances (Giovanelli, 1938; C. S. Warwick, 1963; Reid, 1969).

ll TABLE 4.10 MEAN E (8,12) AMPLITUDE VERSUS LOCATION ON THE DISK A-l (8,12) Location n erg/cm s.ec Northern hemisphere.0191 +.0015 p.e. Southern hemisphere.0150.0015 Eastern hemisphere.0174 +.0016 p.e. Western hemisphere.0182.0015 N-E quadrant.0186 +.0022 p.e. N-W quadrant.0197.0019 S-E quadrant.0143.0013 S-W quadrant.0156.0026 Center.0161 +.0012 p.e. Limb.0218.0024 However, there is some suggestion of a moderate center-to-limb effect since the most significant difference in Table 4.10 is between the center and limb bursts. Student's t-test implies that this difference has only a 15% probability of being due purely to chance. The variation is such that soft X-ray bursts associated with In flares near disk center have a slightly lower mean amplitude than those near the limb. This effect is shown even more clearly in Table 4.11, where the data are subdivided into smaller intervals of R, the distance of the flare from the center of the disk in units of solar radii. The intervals of R used here were chosen to include roughly equal numbers of events, The trend of the mean burst amplitudes is obvious, with the tabulated values increasing monotonically as the limb is approached. This result is consistent with the study by Dodson et al. (1956), which showed that SID's were larger on

112 the average for limb flares of a given importance. Such an effect is most likely due to the reduced visibility of Hoa flares near the limb (Dodson and Hedeman, 1964) which leads to the general tendency for their importance to be underestimated (Sawyer, 1967). TABLE 4.11 MEAN E (8,12) AMPLITUDE VERSUS DISK-CENTER DISTANCE R AEln (8,12) solar radii erg/cm2sec.000 -.400.0139 +.0027 p.e..401 -.600.0146.0014.601 -.800.0173.0024.801 -.960.0213.0026.961 - 1.000.0249.oo61 As an aside, it is interesting to note that both in Tables 4.10 and 4.11, the mean amplitudes for bursts nearest the limb have the largest probable errors, which is due to the fact that they contain the widest range in individual values. This result also appears in the SID study by Dodson et al. (1956), and again is probably caused by the Ha visibility difficulties at the limb. Another way to investigate the possible center-to-limb effect is to examine the frequency of X-ray burst occurrence as a function of disk-center distance. If there is a variation in the mean burst amplitude with position on the disk, this variation will be reflected in the frequency distribution of the observed bursts. Unfortunately, the method has been improperly applied so often by others as to require some special comment,

113 Many investigators, including Culhane and Phillips (1969), Drake (1969), Ohki (1969), and Pinter (1969a), have reported very strong center-to-limb differences in the frequencies of X-ray bursts, In each case, these variations have been attributed to some intrinsic property of the X-ray burst itself; for example, a "beamed" radiation field due to nonthermal emission processes. Only Drake has suggested that the effect might be influenced by the well known centerto-limb variation in the frequency of reported Ha flares (see for example DeFeiter, 1966). Yet the variation in the visibility of Ha flares is of paramount importance to these studies. Since they all utilized data from experiments with no spatial resolution, the assignment of an X-ray burst's position required a simultaneous, reported Ha flare. For example, an X-ray burst which occurred at the limb could not be identified as such if the Ha event associated with it was not seen. Thus, the correct question to ask here is: given an Ha flare at a particular disk-center distance, what is the probability of occurrence of a detectable X-ray burst? The present study indicates that the probability is very nearly unity, so that no "directivity effect" exists for the radiation field of soft X-ray bursts, This result is therefore consistent with the finding that soft X-radiation is thermal in character even during burst conditions (Section IV-4b) and the assumption that the burst emission is isotropic into 4- steradians (Section IV-6b). Obviously, conclusions drawn from studies which did not take the visibility function of Ha flares properly into account should be treated with caution.

114 d. General Solar-Activity Level Table 4.12 gives the mean amplitudes of "ln" bursts as a function of whether they began while the Michigan detector was in its high or low sensitivity mode of operation. The table shows that "low sensitivity" X-ray bursts have a significantly higher amplitude on the average, since Student's t-test implies that the observed difference between these two categories has less than 1% probability of being due to chance. The nonburst soft X-ray flux is a valid index of the general solar-activity level (Chapter III) and, whenever this flux exceeds 0.0044 erg/cm2sec, the Michigan experiment automatically switches into its low sensitivity mode (Chapter II). Thus, the above result indicates that X-ray bursts accompanying In flares tend to have greater amplitudes on those days when the general level of solar activity is high. This agrees with the similar effect reported by Teske (1969a) for the amplitudes of E(8,12) bursts associated with subflares. TABLE 4.12 MEAN E n(8,12) AMPLITUDE VERSUS INITIAL DETECTOR MODE In Initial Operating E (8,12) ln Mode of Detector erg/cm2sec High sensitivity.0094 +.0009 pe. Low sensitivity.0212 +.0015 The same result is derived from Table 4.13, which gives the correlation coefficients for AEn (8,12) versus the base flux EB(8,12) and the Zurich Sunspot number RZ. Specifically, the latter coefficient is for the monthly mean

115 of the final Zurich Sunspot numbers (taken from the SGDB) versus the mean AE n(8,12) for all events in Catalog II which occurred during the month in question, In addition, the table indicates the probable significance P for each of these two coefficients. TABLE 4.13 CORRELATION OF AE ln(8,12) WITH SOLAR-ACTIVITY INDICES Index of General Correlation Solar-Activity Level Coefficient P EB(8,12) + 0.41 > 99% Rz + 0.60 96% The first correlation shown in Table 4.15 merely indicates that the relation found by crudely dividing the data into "high" and "low" levels of solar activity also holds when the solar-activity level is more precisely defined by EB(8,12). The relationships based on sensitivity levels and on E (8,12) involve parameters which can be measured only by detectors above the earth's atmosphere, but the expressed purpose of this chapter was to investigate parameters accessible to ground-based observers. This is not a problem, however, since the nonburst soft X-ray level used above is known to be closely associated with the classical indices of solar activity (e.g., Teske, 1969a, 1969b). Thus, any of these indices should also correlate well with the "in" X-ray burst amplitude. Table 4.13 shows that this is indeed the case, at least when the index R is considered. The relationship indicated by this study is probably a result of the general The relationship indicated by this study is probably a result of the general

116 density increase in the corona which accompanies a rise in the level of solar activity (see, for example, Elwert, 1963; DeJager, 1964), This possibility will be considered again in the next sub-section. e, Characteristics of the Associated Plage If the general level of solar activity over the entire disk is related to the amplitude of "In" soft X-ray bursts, as shown above, then it seems reasonable to expect that a similar relationship might also exist with the specific activity level of the burst-associated plage itself. In order to test this possibility, three indices of plage activity were considered: the flare-richness of the plage, its age, and the area of its major spot group. The frequency distribution of the active regions as a function of their flare-richness is shown in Figure 4-8, which indicates how many plages were responsible for a given number of events in Catalog II. The plages were then divided into those which produced more than 10 cataloged events and those which produced 5 or less, called "prolific" and "nonprolific" regions, respectively. The group of prolific flare-producing regions consisted of McMath #8740, 8818, 8905, 8942, and 9184. Plage regions McMath #8791, 8907, 9047, 9115, 9146, and 9204 were not included in either category, being considered as moderately flarerich. (Note that this division is not exactly the same as the one made in Paper I because of the different flare catalogs used.) The first two entries of Table 4.14 show that the mean amplitude of "in" bursts is significantly higher for those which are associated with prolific plage regions; there is only a 2% probability that this result could be due to chance. Such a result had

NUMBER L 30 OF PLAGES PrNoli- -4-'Moderate" +- "Prolific" Prolific"'- M 20 i — H 10 0 -7 I_ —, I I I m -I 5 10 15 20 25 NUMBER OF FLARES IN CATALOG I1 Figure 4-8. Frequency distribution of plages having a given number of events in Catalog II. Plages which produced more than 10 cataloged flares are considered "prolific." Those which produced 5 or less are defined as "nonprolific."

118 already been suggested in Paper I by an investigation of median burst amplitudes, although the division of plages into prolific and nonprolific categories was somewhat different in that study. Using the plage division given in Paper I, Culhane and Phillips (1969) have also found the same effect for 3-4 A soft X-ray bursts. TABLE 4.14 MEAN En (8,12) AMPLITUDE VERSUS PLAGE CHARACTERISTICS Plage (8,12) Characteristic erg/cm2sec....... ____________________erg/cm sec Flare-richness: prolific.0244 +.0025 p.e. nonprolific.0155.0014 Age (rotations): 1.0190 +.0023 p.e. 2.0181.0013 3.0169.0021 4.0165.0050 5.0125.0031 The second parameter considered was the age of the plage as measured by the number of solar rotations it had been visible since its formation, All cataloged bursts were used which occurred in plages with a single age given by the SGDB. (Two plages may merge together forming a single active region; if the ages of the parent regions were different, the SGDB lists both for the resulting plage.) The bottom portion of Table 4.14 shows that there is a steady decline in the mean "in" burst amplitude as the associated plage region becomes older. Unfortunately, there were too few qualified events in these averages (especially for plage ages of 4 and 5 rotations) to make the result statis

119 tically conclusive, and a much more extensive set of X-ray burst observations will be necessary to confirm this finding. But the monotonic decrease in the mean amplitude values derived here is certainly very suggestive that a region's age is somehow related to its X-ray producing capability during a flare. A plausible, physical basis for such a relationship has been reported by Neupert (1967, 1968), who claims that the temperature and density of the condensation overlying a plage both decline as the region ages. (Also see Chapter III of the present paper.) All realistic thermal mechanisms for the production of soft X-radiation predict that the only physical conditions directly related to the X-ray emission rate are the temperature and density (as well as volume) of the radiating source. Thus Neupert's finding is completely consistent with the result of the above study if these physical conditions normally undergo the same percentage change in the X-ray source during an Ha flare of a given importance. (This requirement also seems necessary to explain the relationships described in the previous section.) Further support for this hypothesis is given by Svestka (1963), who finds that anomalously high X-ray enhancements accompanied importance 1 flares which occurred in a region with an abnormally high density according to one interpretation of its optical spectrum. It should be noted, however, that the two effects indicated in Table 4.14 are not completely independent because flare-rich plages are usually also young. Typically the flaring frequency within a region diminishes as the plage grows older (e.g., Giovanelli, 1939; Witte, 1951). Another semi-independent index of a region's activity level is the area of its sunspots, Since a plage may sometimes contain two (or more) sunspot groups,

120 we used here the total area of the group nearest the flare itself, as tabulated in the Rome Solar Phenomena Bulletin (Cimino, 1967). Whenever the identity of the proper spot group could not be established unambiguously, the event was eliminated from further consideration. Furthermore, this study examines only those bursts which accompanied in or lb flares in McMath plage regions #8740, 8818, 8905, or 8942, and occurred within 720 heliocentric of the solar disk center (R < 0.95)0 Figure 4-9 shows the resulting distribution of X-ray burst amplitude as a function of the related sunspot area. Clearly, no direct relationship exists between individual values. But the absence of points in the lower-right portion of the figure might be interpreted as implying that the region associated with a given size sunspot can give rise to an X-ray burst of any amplitude up to a certain limiting value, and that the amplitude limit increases with the size of the spot group. This finding is consistent with the results of the Dodson and Hedeman (1970) examination of major flares (importance 2 or larger) which occur in plages with very small or no sunspots. They report that these flares were associated with a lower than normal percentage of both great SWF's and large amplitude 2-12 A X-ray bursts. They further note that: "These flares usually occurred during the late, flare-poor phase of a center of activity," a statement which agrees precisely with aspects of the present study described previously. A relationship such as the one found above could be explained if the X-ray emission rate were governed by the temperature and density of the source region (as implied by the first two studies in this section), but confined to a range

121 SPOT AREA (Millionths of Hemisphere) 1500r 0 x 0 x x x 000o x x x x 500 *0. 46 0 *D x Ox x x I I.00.05.10 AE (8,12) erg/cm2 sec..15 Figure 4-9. Scatter diagram of AE(8,12) versus total area of the related sunspot group. X-ray bursts associated with In flares are shown as *; those with lb flares as x. Note the relative absence of points to the right of the line arbitrarily drawn in the figure.

122 given by the region's magnetic energy density (which is crudely indicated by the area of the associated sunspot group). To test this suggestion properly, one should also consider the classification of the sunspot group's complexity and measured magnetic field strength, in addition to its total area, but this will be left for future investigation. f. Characteristics of the Associated Radio Bursts Teske (1969a) has already reported that there is a good correlation between the amplitude of soft X-ray bursts observed by the Michigan detector and the amplitude of corresponding 2800 MHz bursts, Furthermore, Paper I showed that 2800 MHz bursts accompanying flares in "prolific" regions tend to have larger amplitudes than those associated with flares in "nonprolific" regions, an effect identical to that for X-ray bursts (see the discussion in the preceeding section). Two additional studies relating the amplitude of E(8,12) bursts to some properties of their radio counterparts will be described here. Tandberg-Hanssen (1967) has noted that the most "active" flares so far as X-ray production is concerned are also those that produce strong Type IV radio bursts. The present study indicates that at least some X-ray enhancements do not follow this general relationo Table 4.15 lists the nine events in Catalog II which were associated with a Type IV radio burst reported in the SGDB and which had soft X-ray coverage at the time of maximum. Type IV bursts are quite rare; they occur with only about 5% of the well verified flares in Catalog II (15 cases out of 283, six of which had no amplitude data available). They also occur preferentially with very large flares; only four of these 15 cases accompanied flares

123 Catalog II Number 7 8 53 55 140 156 176 232 259 TABLE 4. 15 SOFT X-RAY EVENTS ASSOCIATED WITH TYPE IV RADIO BURSTS Ha Flare Type IV Burst AE(8,12) Importance Importance erg/cm2 sec 2b 2.1211 lb 2.0257 2n 3.2635 3b 3.8060 lb 3 o46o 2b 3.0400 In 3 o0083 lb 2.0643 2n 3.0319 AE/AE 1.2.7 6.2 1 3.4.5 1. 9.8 of importance In or less, although the latter account for nearly 70% of all flares in the catalog (see Section IV-3). In addition, Boischot and Denisse (1957) have shown that type IV emission is most likely due to the synchrotron radiation of electrons accelerated to relativistic energies, again indicating the extraordinary magnitude of the physical process giving rise to this phenomenon. However, flares having Type IV bursts are not invariably associated with great X-ray bursts, as can be seen in Table 4.15. Except for events #53 and 55, the E(8,12) amplitudes do not appear to be exceptionally large. This is seen even more clearly by noting the ratio of the observed burst amplitudes to the mean amplitudes for the appropriate flare importances which were determined in Section IV-6a. (The ratio was not calculated for event #55, the great 23 May 1967 flare, because this was the only example of its importance class in Catalog II. Therefore, the 23 May event will not be considered in the following discussion.) Of the 8 remaining bursts, only 4 had amplitudes larger than

124 the mean value for their associated flare importance. Moreover, of the remaining 5 events that accompanied "great" Type IV bursts (rated intensity 3 in the SGDB), more than half had amplitudes below the mean. While this sample is obviously too small to draw any definite conclusions about average behavior, it does seem clear that Type IV association is not restricted solely to events with exceptional soft X-ray enhancements, The other investigation to be described here concerns the mean E(8,12) amplitude for bursts accompanying radio events with two types of spectra. Actually, the radio burst spectrum used for a given event is "synthetic" in the sense that the flux values at various frequencies were not necessarily measured simultaneously, but rather refer to the maximum flux attained at each frequency during the burst. This procedure was followed in order to utilize the standardized reports of radio events in the SGDB. With the spectral distributions derived in this manner, the radio bursts were divided into two morphological groups: Class A, characterized by spectra having the greatest reported flux at the highest frequency listed (normally about 10,000 MHz); and Class B, with spectra having the greatest reported flux at some smaller frequency. Thus, Class A bursts have stronger cm-wavelength radiation relative to those of Class B. Since a particularly complete set of radio observations is necessary to categorize these bursts properly, only 54 events were found with clearly defined spectral type and for which an X-ray burst amplitude was listed in Catalog II. The first line of Table 4.16 shows that the mean E(8,12) amplitude for all X-ray bursts accompanying Class A radio events is higher than that for Class B, with a 96% probability (as given by Student's t-test) that this effect is real.

125 TABLE 4. 16 MEAN E(8,12) AMPLITUDE VERSUS SPECTRAL CLASS OF RADIO BURST..(8,12) erg/cm2sec Spectral Class A Spectral Class B All events.0983 ~.0293 p. e. 0308 ~ 0049 p.e. 96% "In" events 0526 ~.0191.0199 ~.0018 94% But there is a tendency for the Class A bursts to be associated with the very largest Ha flares; 61% of these bursts occurred during flares of importance lb or greater, compared to only 44% of the Class B bursts, Thus it is conceivable that the higher mean amplitude of X-ray bursts accompanying Class A radio events is accounted for by the relation found in Section IV-6a between AE(8,12) and Ha flare importance. The second line of Table 4.16 shows that this is not the case, however. Here only events which occurred during in flares were considered, thus eliminating the influence of the flare importance effect. Yet the mean X-ray amplitude still is higher for bursts accompanied by Class A radio events, with just a 6% probability that this observed difference is due to chance. A similar result for hard X-ray bursts can be inferred from the report by Arnoldy et al. (1968a), that the probability of detecting a 0.2-1.2 A X-ray event is negligible unless the spectrum of the associated radio burst includes cm-wavelength enhancements. Unfortunately, the interpretation of a "synthetic" spectrum, as obtained from the peak fluxes of a radio burst at various frequencies, is by no means straightforward (cf. Kundu, 1962), so that the physical meaning of the relationship found above is not clear. Furthermore, there is a possibility that the sample of events studied here was somehow biased, Kundu (1965) finds that the peak

126 flux of a cm-wavelength radio burst usually increases with increasing frequency, while only 33% of the events in the present investigation showed that property. In any case, the relation indicated here between the X-ray burst amplitude and the spectral type of the associated cm-wavelength event needs to be confirmed by a more refined analysis. Although such a refined analysis would require a great deal of effort, a careful comparison of the simultaneous X-ray, visible, and radio aspects of the total flare phenomenon should lead to new insights concerning the physical processes involved, 7. TOTAL X-RAY BURST ENERGIES It would be of considerable interest to know the total energy emitted in the X-ray band during flares of various importance. Both as absolute amounts and as amounts relative to the total emission at other wavelengths, such values would serve as helpful guides for the construction of new flare models and as stringent tests for models already proposed. There are two ways to determine the mean X-ray burst energy as a function of flare importance using data from the Michigan experiment. The first and more accurate method is to planimeter the time-profile curve for each burst associated with a given class flare, and then average the individual energy values so derived. Unfortunately, the records for most of the X-ray bursts in Catalog II were interrupted at least once during the event's time development by one or more of the sources of data-loss (satellite night, tape recorder playback, and trapped particle interference) described in Chapter IIo The statistical uncertainties in the calculated means would be quite large if just the events with complete flux curves were used. Furthermore, the results would be biased since

127 this method systematically discriminates against longer duration events. Thus, it is not possible to take full advantage of the potentially higher accuracy afforded by the above procedure. Therefore, the second method was used which gives a rougher estimate of the total X-ray energy but by a much easier procedure. Here the burst's time-profile is approximated by a simple triangle, so that the time-integrated E(8,12) flux is given by one-half the burst's amplitude times its duration. Average values for the amplitude and duration of bursts associated with flares of various importance were used to simplify the procedure further. Mean E(8,12) amplitudes were taken directly from Table 4.7, and converted into the corresponding enhancement values of the solar X-ray emission rate by assuming isotropic radiation into 4j steradians with no photon scattering (see Section IV-6a). The values 2000, 4000, and 8000 seconds were used for the mean durations of bursts associated with flares of areal importance 1, 2, and 3, respectively. The mean duration for "importance 1" E(8,12) bursts was taken from the results of the study described in Section IV-4c; the other values were estimated from the author's subjective impression of the longevity of these great bursts. In all cases, the durations were deliberately chosen to be underestimates in order to compensate for the fact that approximating the burst's time-profile by a triangular area will tend to overestimate the event's total emission. This occurs because the rise and decay of soft X-ray enhancements are more nearly exponential than linear changes. Table 4.17 shows the results found by the above procedure. The absolute values given are probably accurate to within a factor of 4; they are most likely correct within a factor of 2 relative to one another. Comparable estimates of

128 TABLE 4 17 TOTAL 8-12 A EMISSION DURING Ha FLARES Ha Flare Mean Total 8-12 A Importance Emission (erg) f 2 x 1028 In 5 x 1028 lb 1 x 1029 2f 1 x 1029 2n 2 x 1029 2b 5 x 1029 3n 1 x 103 3b 1 x 1031 the total flare emission at other wavelengths have been reported by many investigators and are summarized in Table 4.18. Values listed as "Visual" refer TABLE 4.18 REPORTED VALUES OF TOTAL FLARE EMISSION Wavelength Flare Total Energy Interval Importance Emission (erg) 0-1.2 A lb 3.0 x 1026 Kane (1969) 3.5-12 A "typical" 1028 _ 1029 Krieger and Vaiana (1969) 3.5-12 A "great" > 1030 Krieger and Vaiana (1969) 8-12 A 1 6.0 x 1028 Teske (1969a) 0-14 a 2b 1.4 x 1029 Van Allen (1967b) 3-95-14 ~ 28 5.5-14 A In few 1028 Vaiana and Giacconi (1968) 10-1030 lb 6. 0 x 1029 This paper, Chapter V Hab lb 1.0 x 1029 This paper, Chapter V HaC 2 l031 J. W. Warwick (1962) Ha 2+ 3.0 x 103 Billings and Roberts (1953) Ha 2+ 3.0 x 1029 Van Griethuysen and Houtgast (1959) Ha 3+ 1031 Bruzek (1967) Visual 2 6.0 x 1029 Kiepenheuer (1964) Visual 3+ 1032 Kiepenheuer (1964) Visual 3+ 102 Parker (1957) Visual 3+ 1032 Ellison (1963b) Visual 3+ 102 Bruzek (1967) Microwave lb 8. 0 x 1022 This paper, Chapter V

129 to radiation in all emission lines and the continuum at optical wavelengths; the "Microwave" value includes emission between 2,000 and 15,000 MHz. Clearly, the amount of energy emitted as X-radiation accounts for a significant portion of the total electromagnetic energy lost during a flare event. This point will be considered again in the next chapter, which describes the individual characteristics of three selected flares. To summarize the results of the present chapter, we have shown that all 283 of the well confirmed Ha flares observed by the Michigan experiment were accompanied by a detectable enhancement in soft X-radiation, with one possible exception. Properties of the general time-profiles for such enhancements imply that 8-12 A X-radiation is thermal in nature even during flare-associated bursts. In addition, the times of start, maximum, and end for X-ray bursts are similar to those of the Ha flare, although the X-ray enhancement tends to start first by a few minutes on the average. We have also shown that there is a definite correlation between the peak amplitude of the X-ray burst and the associated flare's area and intensity. For a flare of a given importance, the peak amplitude of the X-ray burst is a function of its distance from the solar limb, an effect which is most likely due to the Ha observations, The peak amplitude also depends on the general level of solar activity at the time of the burst and on the age and "flare-richness" of the associated plage. The latter effects are probably due to density variations in the X-ray emitting region itself. Furthermore, it appears that the amount of

1530 energy emitted as 8-12 A X-radiation accounts for a significant portion of the total electromagnetic energy lost during a flare event, Some of the statistical relationships found above will be re-examined in the next chapter in order to determine the degree to which they can be considered valid during individual events. For that purpose, three especially well observed flares will be investigated in some detail.

CHAPTER V THE X-RAY BURST COMPONENT: STUDIES OF INDIVIDUAL EVENTS Numerous studies have examined the relation between the soft X-ray flux and Ha intensity during solar flares (Landini et al., 1965; Culhane and Phillips, 1969; Teske, 1969a). Others have compared the X-ray flux with the area of the associated Ha event (Valnicek, 1967; Hudson et al., 1969b). However, the relation of an area or intensity to a flux is difficult to interpret. A much more meaningful comparison would be between the X-ray flux and the corresponding Ha flux of the flare. The previous chapter described a crude approximation to such a relationship for the time of flare maximum, but this gives no information about the time development of the relation during an event. Using a method similar to that of Chapter IV (i.e., taking the total flare area times the intensity of its brightest point), Coutrez et al. (1963), have compared rough Ha flux values during a flare with the effects of solar X-radiation as observed by SEA monitors. Even this is not completely satisfactory, as the results are still just estimates based on indirect measurements. To overcome such objections, the time-profiles of the enhanced Ha flux for three flares were determined and directly compared to their associated E(8,12) bursts as observed by the Michigan X-ray experiment. For each flare, about twenty frames of the McMath-Hulbert Observatory's Ha patrol films were analyzed by isophotometry with up to seven iso-density contours at the times of maximum intensity. (The flare patrol photographs were made with a 0.5 A interference filter of the Lyot type.) 131

132 These measurements were then reduced to values of the solar Ha emission rates by the procedure derived in the Appendix. Using the resultant Ha emission curves for these events, the statistical relationships found in Chapter IV were then re-examined to see how closely they apply to individual flares. 1. SELECTION OF EVENTS A flare had to satisfy the following criteria in order to qualify for this study: (1) filtroheliograms of the flare were obtained by McMath-Hulbert Observatory's Ha flare patrol program, (2) the filtroheliograms were of high quality, (3) they were continuous (at least one each thirty seconds) from the flare's start to ten minutes after its maximum intensity, (4) the Michigan experiment's record of E(8,12) covered the above interval with no interruptions, (5) the flare was included in Catalog II (see Chapter III for a description of this catalog), and (6) the flare occurred within 45~ heliocentric of the center of the solar disk (R < 0.7). These criteria insure that the event was well observed and not strongly affected by the various difficulties associated with limb flares (cf. Appendix). Of the 283 flares in Catalog II, only three satisfied the above requirements. Each of these flares was rated importance lb and occurred within a region undergoing its third rotation. Other data are given in Tables 5.1

and 5.2, which, with two exceptions, are taken directly from Catalog II. The exceptions are that (a) the Ha starting time is the earliest start reported by a cinematographic station; and (b) the disk-center distance R (in units of solar radii) is from the SGDB. Figures 5-1, 5-2, and 5-3 show the McMath-Hulbert flare patrol filtroheliogram near the time of maximum intensity for each flare. (Note the image of the clock impressed on these photographs. This clock was calibrated with WWV time signals three times a day to insure that each exposure could be identified to within a few seconds.) TABLE 5.1 Ha DATA FOR THE ANALYZED FLARES Date Start Max. End Imp. Location R No. 26 March 1967 1603 1605 1619 lb N24E08 8740.51 13 24 March 1968 1632 1645 1735 lb S12W02 9273.09 280 25 March 1968 1442 1449 1600 lb S12W14 9273.25 281 1507 TABLE 5.2 E(8,12) DATA FOR THE ANALYZED FLARES Date Start Max. End Base Ampl. No. 26 March 1967 1604.0 1608.0 1630.0084.0236 13 24 March 1968 163355 1647.0 1833.0053.0412 280 25 March 1968 1444.0 1452.0 - 0040.0435 281 1507.5

134 Figure 5-1. Ha filtroheliogram of lb flare on 26 March 1967. The exposure was taken at 1608 UT, two minutes after the flare's maximum intensity. This photograph is from the McMath-Hulbert Observatory's flare-patrol records, as are the next two figures. Note the clock image and calibration spots impressed on each exposure.

135 Figure 5-2. Ha filtroheliogram of Ib flare on 24 March 1968. The exposure was taken at 1644 UT, near the time of the flare's maximum intensity.

136 Figure 5-3. Ha filtroheliogram of lb flare on 25 March 1968. The exposure was taken at 1506 UT, near the time of the flare's maximum intensity.

137 Quite by chance, two of the events selected by the above procedure are closely related to one another. Flare #281 occurred just 22 hours after flare #280 and in the same plage. As can be seen by comparing Figures 5-2 and 5-3, the flaring regions were almost identical in appearance for these two events. The existence of a class of successive flares which take place in the same region and show a common pattern of structure was first reported by Waldmeier (1938) and confirmed by Dodson and Hedeman (1949). Ellison et al. (1960), suggested the term "homologous" be used to describe this class of flares. The term can also apply to successive radio bursts which have similar characteristics (Fokker, 1968), as well as to similar X-ray bursts (Fortini, 1965). In fact Pinter (1969b) notes that the very events investigated in the present study are excellent examples of such homologous X-ray bursts. Thus, the fact that the events of 24 and 25 March 1968 belong to this special class should be kept in mind when considering the results described below. 2. Ha ISOPHOTOMETRY Selected frames of the film record for the three flares just discussed were analyzed by the McMath-Hulbert Observatory isophotometer. An early version of the instrument used in the present study has been described by Mohler and Pierce (1957). Basically, the isophotometer has an analyzing light beam which is focused on a small portion of the film being measured. The light transmitted by that point on the film is sensed by a photoelectric cell which controls the rotation of a mechanical cam. At certain positions of the cam, it trips a microswitch which causes a pen to mark a precise position on a sheet of paper. Thus,

138 a mark is made whenever the analyzing light beam encounters one of several, discrete values of photographic density on the film. The film itself is mounted on a carriage which moves it past the analyzing beam according to a preselected routine. In order to photometer the entire area of interest on the film, this routine proceeds as follows: first the area is scanned over its full width; then the film carriage is returned by the identical path to the side on which it began; next it is displaced a small amount in the perpendicular direction and the above steps are repeated. This continues until the whole area has been covered. A mechanical coupling causes a sheet of paper to be moved beneath the marking pen in exact synchronism with the motion of the film carriage. Thus, while the analyzing light beam is scanning the film, the pen "scans" the sheet of paper marking those points which correspond to positions on the film having certain photographic densities. The microswitch which activates the pen operates only when the film carriage is travelling in a given direction, eliminating the effects of backlash in the associated gear trains. The above procedure slowly builds a set of contours, called isophotes, which represent lines of equal density on the film being photometered. Figure 5-4 shows some examples of the isophotes derived from the 25 March 1968 flare. Also shown is the relative size of the analyzing light beam, which was selected to match the resolution of the flare image on the patrol film. This resolution is about 5 arc-sec, which is equivalent to 4 x 103 km at the center of the solar disk. In addition to controlling the rotation of the mechanical cam, the isophotometer's photoelectric cell also drives the pen of a chart-recorder. Thus,

139 Ha ISOPHOTES OF lb FLARE 25 MARCH 1968 0/ D 0 14h 43m 36 U.T. 15h 03m04s U.T. a 15h 07m 36S U.T. 15h 14m36s U.T. Figure 5-4. Representative Ha isophotes of the lb flare on 25 March 1968. Each contour represents a line of constant photographic density on the filtroheliogram and thus constant intensity within the flaring region. The filled circles are the contours of the main sunspot in the plage. The small rectangle indicates the size of the isophotometer's analyzing light beam.

140 a given density on the film gives rise to a corresponding deflection D on the chart-recorder. It will be implicitly understood in the following that any reference to the photographic density of some feature actually refers to its measured chart-recorder deflection. In the Appendix of this paper, it is shown that the enhancement of Ha emission during a flare can be related to the parameter R' which is defined as: c c(max) P' - P R' = Z (A - A ) c- (5.1) c c c c+l P o where: A is the area (actually the corresponding solid-angle in steradians) c within contour c, c(max) is the innermost contour, P and P are the measured, undisturbed Ha intensities at the o heliocentric distance of the flare and the center of the solar disk respectively, and P' is a flare intensity which falls between contours c and c+l c as defined in the Appendix. To find the appropriate intensity values for this expression, the characteristic curve P = f(D) must be determined for the film. This was done by measuring the photographic densities for the set of calibration spots which are impressed on each filtroheliogram (see Figure 5-1, 5-2, or 5-3) and using Teske's measurements of the relative intensities of these spots (personal communication). As mentioned in the Appendix, we have found that the derived value of R' is very sensitive to slight changes in the characteristic curve used. Therefore, we

have determined it individually for each exposure analyzed in the present study. Once the characteristic curve is known and the photographic densities of the various contours D and undisturbed disk center D are measured, the intensity c o ratios P'/P necessary for equation (5.1) can be found by means of the relations c o given in the Appendix. The area values A were measured by planimetering the appropriate contours c in each isophote. To improve the accuracy of these measurements and eliminate one source of systematic error, each area was planimetered four times in one direction and an equal number in the other direction. The mean of these eight values was then taken to be the area within the contour in question. The intensity ratio P /P which appears in equation (5.1) is the same for b o all filtroheliograms of a given flare. The ratios used for the three flares investigated here were taken from the limb-darkening study by 0. R. White (1962) and are listed in Table 5.3. TABLE 5.5 DATA FOR THE REDUCTION OF THE ANALYZED FLARES Date W (Ha)/W (Hca) P/P P/P z 26 March 1967.858 o.88 0.96 1.24 1.36 3.3 24 March 1968.995 1.00 1.00 1.25 1.27 3.3 25 March 1968.967 0.97 0.99 1.24 1.12 535 Also listed are the appropriate values of the following parameters: At, the flare's heliocentric distance (cos 0);

142 W (Ha)/W (Ha), the ratio of the undisturbed Ha equivalent width at p to that at the center of the solar disk (derived from David, 1961); P/P, the relative intensity to which all measurements of a given flare were standardized; cp, the conversion factor between the total relative flux and the relative flux standardized to P*/P; z, the figure of merit for the filtroheliograph (kindly supplied by Dr. Dodson-Prince, personal communication). (A more comprehensive definition of these parameters can be found in the Appendix.) The above values are needed in order to convert the relative flux values R', given by (5.1), into the total enhancement of Ha emission during the flare c AS(Ha,t). This is done in two steps. First the standardized relative flux R' is derived from values of R' for a given isophote by one of the relations *x- c (A.27 or A.29) given in the Appendix. Then AS(Ha,t) can be found from R' by the following expression: AS(Ha,t) = 7.2 x 1033p R(t) erg/sec (5.2) W (Ha) Rj(t) erg/sec o which is derived from equation (A.30) of the Appendix. It is difficult to know the relative error in AS(Ha,t) resulting from the above reduction procedure. However, we have investigated the internal consistency of the isophote planimetry and the effects of reasonable inaccuracies in the determination of photographic densities and the films' characteristic curves for measurements made in the present study. From this analysis, we have estimated

143 the relative error for the March 1968 flares to be about 6%. Because the film record for the March 1967 flare was somewhat lower in quality, we have assigned a 10% uncertainty to its values. The enhanced Ha emission curves for these three flares are presented in the next section. 5. GENERAL COMPARISON OF THE SOFT X-RAY AND Ha EVENTS For the 24 March 1968 flare, Figure 5-5 shows the time development of the 8-12 A emission rate AS(8,12;t) observed by the Michigan soft X-ray detector, the Ha emission rate AS(Ha,t) derived in the previous section, and the intensity of the flare's brightest point I /I as found by the method described max o intheAppendix. To the author's knowledge, this is the first direct comparison of the absolute rates of X-ray and Ha emission during a flare. The X-ray emission remained enhanced until about 1834 UT, so measurements made at 1738 and 1834 UT are also indicated on the figure. Although it may not be obvious by casual inspection, the X-ray emission curve follows more closely the total Ha emission curve than it does the Ha intensity curve. For example, the emission curves peak simultaneously, while the intensity reaches its maximum about three minutes earlier. In addition, the intensity falls to its pre-flare level before 1738 UT, while the total Ha emission remains enhanced after that time, as does the X-ray emission. However, it should be noted that by 1834 UT the X-ray burst has ended, yet the Ha emission still remains high due to a great post-flare increase in the size of the associated plage. Another similarity in the two emission rate curves is

144 12x 1025 A S (8,12; t ) erg/sec 8 4 0 x 8 x 105 A S (Ha, t) erg/sec x 18h34m 17h38m 4 0 2.8r'max/I 2.2 F \ 1.6 17hOm U.T. 17hoom U.T. 16h30m 40m 50m Figure 5-5. Comparison of the 8-12 A emission rate (top), Ha emission rate (middle), and Ha intensity (bottom) during the lb flare on 24 March 1968. Additional values at 1758 UT and 1834 UT are indicated by x. The relative error for measurements of the total Ha emission rate is 6%, while that for the intensity is 4%.

145 the "bump" at about 1638 UT. But the existence of this feature is somewhat doubtful in Ha since it is defined by only one measured point. Figure 5-6 shows the corresponding curves for the 25 March 1968 flare. Here each of the three features in the Ha emission curve is definitely established and each has a clear counterpart in the associated X-ray burst. This excellent correspondence implies a. very close relation indeed between the energetics of the Ha and soft X-ray events. The Michigan detector was in its operating mode of high sensitivity for the first few minutes of this burst (indicated by the short, elevated segment in the AS(8,12;t) figure). When this portion of the event is plotted on the same vertical scale as the rest of the burst (shown in the main curve of the figure), it becomes apparent what a subtle enhancement this initial rise represents. It is evident that this initial, very gradual rise would not have been detected if the Michigan instrument had been in its low sensitivity mode, which agrees with the statistical results discussed in Chapter IV. But even considering the high sensitivity data, the Ha enhancement starts before the X-ray enhancement in the present case; indeed, this is true for all three of the features in the emission curves for the 25 March 1.968 flare. In fact, for all three of the flares investigated here, the Ha event starts before its associated soft X-ray burst. This is atypical, but by no means rare, for soft X-ray bursts which accompany Ha flares in general, as demonstrated in Chapter IV. Figure 5-6 shows that the 25 March 1968 flare consisted of two main phases, one at roughtly 1450 UT and another at 1505 UT. The ratio of the amplitudes of these two peaks is less than 2:1 for the Ha intensities, nearly 3:1 for the Ha

146 12x 105 |A S(8,12 t) erg/sec 8 4 0 1024'JO 12 x 1025 I AS(Ha,t)erg/sec 8 4 0 3.5 2.5 1.5 Figure 5-6. Comparison of the 8-12 A emission rate (top), Ha emission rate (middle), and Ha intensity (bottom) during the lb flare on 25 March 1968. The short, raised segment in the graph at top shows X-ray data obtained by the Michigan detector while in its high sensitivity mode of operation. This segment is plotted on a magnified ordinate scale. The relative error for measurements of the total Ha emission rate is 6%, while that for the intensity is 4%.

emission rates, but almost 10:1 for the emission rates of the 8-12 A radiation. This implies that during the flare (a) the X-ray producing mechanism is much more sensitive than the Ha mechanism to changes in the physical conditions of the emitting region, (b) the physical characteristics of the X-ray emitting region undergo much stronger variations than those of the region emitting Ha radiation, or (c) some combination of the above. It is also interesting to note that the Ha emission rate peaks before the intensity curve during the first phase of this flare but after it during the second phase. Both Ha curves peak well before the first X-ray maximum, while the Ha and X-ray emission rates peak simultaneously at the second maximum. Although there are many minor differences, the main impression given by the comparisons just described is the notable similarity in the time profiles of the soft X-ray and Ha emission rates. This is all the more remarkable considering the great differences that must exist in the physical conditions of the two emitting regions. For example, a typical temperature derived from observations of soft X-ray bursts is on the order of a few 10 K (see Table 2.2 of Chapter II). Hydrogen would be virtually 100L ionized at such a temperature and thus any Ha emission would be completely negligible. Actually, the temper4 ature appropriate for the Ha emitting region during a flare is roughly 10 K (e.g., DeJager, 1959; DeFeiter, 1966). In addition, the densities of the two regions are far different. For the Ha flare, densities of a few 103 cm3 are normally found (DeJager, 1959; Fritzova-Svestkova and Svestka, 1967) while the 11 -3 source of the X-ray burst seems to have a density no greater than 10 cm (Vaiana and Giacconi, 1968; Culhane and Phillips, 1969; Friedman and Hamberger,

148 1969; Hudson et al., 1969a). It is a clear challenge for theoreticians to account for the fact that two emissions arising from such distinct sources can show the remarkable degree of time correlation which is observed in the flares just discussed. However, the 26 March 1967 flare shows that the relation between the Ha and soft X-ray emission rates is not always a simple one. This flare took place in a relatively small portion of a very large, fragmented region. In that respect, it is different from the two flares previously described, which involved nearly all of the smaller, more compact region in which they occurred. The time development of the X-ray emission rate, total Ha emission rate, and Ha intensity displayed in Figure 5-7 are not at all similar to one another. (To check the reliability of the Ha measurements, eight of the nineteen exposures analyzed for this flare were completely isophotometered a second time. Very good agreement resulted for each pair of values thus obtained.) The disparities among these curves include the differing times of start and maximum as well as the fact that the X-ray burst is a simple one while the Ha event shows two definite components. These peculiarities also appear in Figure 5-8, which plots the total Ha and soft X-ray emission rates at one-minute intervals during the time development of the three analyzed flares. Times of maximum Ha intensity are indicated by circles in the figure. Although the 26 March 1967 event has such an irregular trace, at least the general slopes of the rising portions for all three flares are nearly the same. In addition, the relation between the Ha and X-ray emission rates on the rising segment of the curve is almost identical

149 8x1025 AS 4 0O (8,12; t) erg/sec 12x 1025 A S (Ha, t) erg/sec 8 4_ 0 2.8 2.2 1.6 Imax/i 0o 16ho0m I Om 20m U.T. Figure 5-7. Comparison of the 8-12 A emission rate (top), Ha emission rate (middle), and Ha intensity (bottom) during the lb flare on 26 March 1967. The relative error for measurements of the total Ha emission rate is 10%, while that for the intensity is 4%.

150 S (Ha,t) erg/sec ~-. 0S:!. 6hi0m 10 x 10"lo~~~~10 x 10o":-'2 26 MARCH 1967 5 - 116ho0m ~10 r iG'^W1^ —^16h50m I 0 1834 17h38.r X/ 1i6h30m 15 0o /.." 25 MARCH 1968 ~. 5 - \t><t15h 00 1/4h50 I 7! 0 — 14h41m 4 8 12 x 1025 S (8, 12; t) erg/sec Figure 5-80 Comparison of the Ha and 8-12 A emission rates for the lb flares on 26 March 1967 (top), 24 March 1968 (middle), and 25 March 1968 (bottom). Values are plotted at one-minute intervals. Circled points refer to times of maximum Ha intensity.

151 to that on its falling portion for both 1968 events. The slope that best fits the linear part of these curves shows that near maximum the 8-12 A emission rate varies roughly 3 times as rapidly as the flare's Ha emission rate. Thus soft X-radiation is a much more sensitive indicator of changes in the flaring region, as had also been implied by the comparison of the two phases of the 25 March 1968 event described earlier. 4. COMPARISON WITH THE RESULTS OF CHAPTER IV In the previous chapter, several statistical relationships were found between various aspects of an Ha flare and its associated X-ray burst. It would be of interest to investigate the degree to which these relationships hold during individual events, and this has been done for the three flares just discussed. Unfortunately, the pre-flare levels of the Ha emission rates for these events were not determined wiell enough to assign a definite photometric starting time to the flares. However, we have already noted that in each case the enhancement in the Ha emission rate was clearly established at the time of the first increase in X-radiation, which is an atypical (but by no means rare) occurrence for flares in general. The photometric times of the principal maxima for the three flares are listed in Table 5.4.

152 TABLE 5.4 PHOTOMETRIC TIMES OF MAXIMUM (All times are in UT) Date Ha 8-12 A Intensity Emission Rate Emission Rate 26 March 1967 1606 1614 1608 24 March 1968 1644 1647 1647 25 March 1968 1449 1447 1452 1506 1507 1507 The times of maximum Ha intensity found here all agree nicely (plus or minus one minute) with the flare maximum times for these events listed in the Quarterly Bulletin, and shown in Table 5.1 of this paper. Thus, for flares with well defined maxima, visual inspection of patrol filtroheliograms seems to be a reasonably accurate method for determining the time of a flare's peak intensity; and so studies utilizing these reported maximum times can be regarded with some confidence. In each of the four cases considered here, the X-ray emission rate peaks after the intensity maximum of the Ha flare, typically by a few minutes. This is precisely the result found by the statistical analysis in Chapter IV. However, (if the average of just four cases is meaningful) the total X-ray and Ha emission rates both reach maximum simultaneously. This is yet another indication of the very close correlation shown by these two components of the flare phenomenon. All three flares investigated in this chapter are rated lb, and the photometric analysis described above shows that they have areas and peak

153 intensities which are typical for that importance. Thus, we cannot consider here the relation between the peak enhancements in soft X-ray and Ha emission rates, AS(8,12) and AS(Ha), as a function of flare importance. But we can see how closely the peak emission rates for these individual flares match the rates found for lb flares in general. Table 5.5 lists the values resulting from this study along with the emission rates appropriate for lb flares as derived from the statistical study in Chapter IV. TABLE 5.5 PEAK ENHANCEMENTS IN EMISSION RATES (All emission rates are in 1025 erg/sec) Date AS(Ha) AS(8,12) 26 March 1967 10 7 24 March 1968 8 12 25 March 1968 12 12 "Average" lb 53 10 Note that the rough approximation method of Chapter IV does indeed result in an overestimate of AS(Ha), as had been suggested in that chapter. Apparently, the method predicts values which are about a factor of 5 too high. On the other hand, the individual values of AS(8,12) are exactly in line with the "average" amplitude of bursts associated with lb flares. The most important result given by this comparison is that, at least for these three flares, the peak enhancement in 8-12 A radiation is virtually identical to that in Ha. The absolute value of each measurement may be in error by

!54 as much as a factor of 2 (see Chapter II), but even in the worst case, the peak Ha and soft X-ray emission rates would be equal within an order of magnitude. Finally, we have investigated the time-integrated Ha and soft X-ray energies which were emitted during these flares. Since none of the events was traced continuously to its conclusion, the Ha and X-ray curves for each event were extrapolated down to their pre-flare levels. These extrapolations were made with care but, of course, are little more than well-intentioned guesses. However, in each case the majority of the emission occurred during periods which were covered by observations, so that these extrapolations should not give rise to significant errors. The results of this study are shown in Table 5.6, along with the appropriate X-ray value found by the statistical study in Chapter IV. The total amounts of 8-12 A energy emitted during the three flares seem to be quite typical for bursts accompanying lb flares. But the most important result here is once again the striking similarity in the values of the total energy emitted as Ha radiation and as 8-12 A X-radiation by these flares. Even considering the possiblity of errors in the absolute calibrations of the above measurements, one must conclude that emission in Ha and in soft X-radiation both contribute very nearly identical amounts to the energy losses of these flares.

155 TABLE 5.6 TOTAL FLARE EMISSION IN Ha AND 8-12 A (All emission values are in 1028 erg) Total Ha Total 8-12 A Date Emission Emission 26 March 1967 9 6 24 March 1968 10 10 25 March 1968 11 13 "Average" lb - 10 5. OBSERVATIONS AT OTHER WAVELENGTHS Observations of the hard X-ray, EUV (Extreme Ultraviolet), and microwave bursts which accompanied the 24 March 1968 flare were also compared to the Ha and soft X-ray events. The data for the hard X-ray burst were supplied by S. R. Kane (personal communication) and refer to the total emission between 0-1.2 A. The EUV data were derived from SFD observations by R. F. Donnelly (personal communication) using an ionospheric electron-loss rate of T = 20 seconds. These latter data refer to the emission at 10-1030 A and should be correct to within a factor of 4. In each case, the measurements were in the form of a time-profile for the burst. These profiles were then planimetered to obtain the time-integrated energies within the appropriate wavelength intervals. For the microwave burst, the peak emission rates and durations at individual frequencies were taken from the reports listed in the SGDB. The emission values which resulted were then integrated between 2000 and 15000 MHz to find the total energy emitted in the microwave burst.

156 Table 5.7 summarizes the values of the energy involved in each wavelength interval considered for the 24 March event. Hard X-ray emission and microwave radiation, at opposite ends of the spectrum, account for the smallest amounts of energy. In addition, these latter spectral intervals show a very high correlation in their time variations, even with regard to the detailed fine structure of the bursts (e.g., Arnoldy et al., 1967, 1968b; Parks and Winckler, 1969). A much larger amount of energy is released in the form of 8-12 A Xradiation and Ha emission, which likewise display notable similarities in their time variations as shown by the present study. Of the wavelength intervals considered here, the major source of energy loss in this flare seems to be EUV radiation. The time profile of this emission is often closely related to those of hard X-ray and microwave bursts (Neupert, 1964; Donnelly, 1969a) but also shows characteristics which are comparable to those of soft X-ray and Ha events (Donnelly, personal communication). TABLE 5.7 TOTAL ENERGY EMISSION DURING THE 24 MARCH 1968 FLARE Wavelength Total Energy Interval Emission (erg) o 26 Hard X-ray 0-1.2 A 3 x 10 Soft X-ray 8-12 A 1 x 1029 EU 10-1030 A 6 x 1029 Ha 6563 A 1 x 1029 Microwave 2-15 cm 8 x 10

157 The explanation of these relationships among such diverse radiations offers a challenging problem indeed for any potential model of the total flare phenomenon.

CHAPTER VI SUMMARY All known mechanisms that may be important for the production of soft solar X-radiation imply that the X-ray emission rate depends mainly upon three characteristics of the emitting region, namely its temperature T, density N, and volume V (Acton, 1964). The relevant temperature and density are normally the electron temperature T and the electron density N, although this is not e e always the case (e.g., Boldt and Serlemitsos, 1969). Other parameters, such as the magnetic field strength, may also affect the emission rate, but only by their influence on the region's temperature, density, and volume, Unfortunately, it is not possible to derive, unambiguously, values for all three of these characteristics from the observations made by the Michigan X-ray experiment because it has no spatial or spectral resolution. Thus, a rigorous model of the X-ray emitting source cannot be constructed by means of the Michigan data alone, but these data can be used to place general constraints on some aspects of such a model. We will discuss here very briefly several of these general considerations based on the results of studies described in previous chapters. 1. THE SLOWLY VARYING COMPONENT The investigations discussed in Chapter III of this paper point out the close relation between calcium plages and the source of the slowly varying component of solar soft X-radiation. Even without spatial resolution, the data

159 indicate that the X-ray emitting regions are physically connected with these plages. Their areas, if not identical, are at least closely associated, as shown by the correlation of Eb(8,12) and EA. The fact that Eb(8,12) forms an even better correlation with E A x I implies that the variations in the temperature and density enhancements which determine the plage's intensity also relate to the X-ray emitting region. The major part of the soft X-radiation apparently originates from a source whose thickness does not depend strongly on its area, since the correlation of Eb(8,12) with E A3/2 x I is no better than that with E A x I. A study of individual values within the latter relation gives some evidence that the temperature and/or density of the X-ray emitting region declines as it ages and that emission of soft X-radiation can occur at significant heights above the chromosphere. The existence of X-radiation from such elevated sources requires localized regions of enhanced temperatures and/or densities within the cooler ambient corona. Comparisons of X-ray observations at several wavelength intervals show that these condensations cannot be isothermal, but apparently consist of a small core at a very high temperature surrounded by more extensive regions of material which becomes cooler with distance from the core. Furthermore, these comparisons indicate that at least some of the condensations which exist during periods when the general level of solar activity is high must be substantially hotter than those observed when the activity-level is low, Perhaps the same basic mechanism which is responsible for increased levels of solar activity also gives rise to further enhancements in the temperatures of the X-ray sources overlying chromospheric plages,

160 2, THE BURST COMPONENT The present investigation considered only those X-ray bursts which accompanied well verified Ha flares of importance 1 or greater. In addition, all bursts associated with "sympathetic" flares were eliminated, Thus, the results described here may not apply to all X-ray bursts'in general, The total flare phenomenon almost invariably includes a significant enhancement in soft X-radiation. Some cases of a relatively weak, impulsive component in 8-12 OA bursts have been observed which might be due to nonthermal processes, However, the properties of the general time-profiles for flareassociated enhancements, as well as their frequency of occurrence from center to limb, imply that they are predominantly thermal in nature, There are three possible mechanisms for this radiation, viz, thermal bremsstrahlumg (free-free), recombination (free-bound), and line emission (boundbound) The standard expression for thermal bremsstrahlung indicates that the flux between 8-12 A from this mechanism is given by: -12/T 18/T6 1/6 rg/cm2 e c E(8,12) = 5 x 10-5 T/2(e- 6 e8' EM erg/cm2sec (6.1) where T6 is the temperature in millions of degrees Kelvin and EM is the radiating region's emission measure in units of cm-3, as defined by: EM = N2 dV (6,2) e To obtain (6.1), a Gaunt factor of unity was assumed and the emitting plasma was taken to be pure hydrogen. As found in Chapter IV, the average peak en

161 hancement in the 8-12 a radiation accompanying a in flare is 0.0183 erg/cm2sec, which represents only a moderate-sized burst. Table 6.1 gives the emission measure which would be necessary at various temperatures to account for this peak X-ray enhancement if it were due solely to thermal bremsstrahlung emission. TABLE 6.1 "in" X-RAY EMISSION MEASURES DUE TO THERMAL BREMSSTRAHLUNG Temperature Emission (106 K) Measure (cm-3) 1 6.0 x 1054 2 1.1 x 1052 5 2.6 x 1050 10 8.5 x 1049 20 5.8 x 1049 50 5.8 x 1049 100 7.1 x 1049 The smallest value listed is still more than two orders of magnitude greater than most emission measures reported for any burst observed with detectors having either spatial or spectral resolution-,(Vaiana and Giacconi, 1968; Beigman et al., 1969; Culhane and Phillips, 1969; Hudson et al., 1969a). Furthermore, of the experiments just cited, the two which most closely match the Michigan detector's response gave rise to determinations of emission measures which were much less than those found at shorter wavelengths. In addition, the smallest value given in Table 6.1 exceeds the emission measure for the entire quiet corona (Mandel'shtam, 1965a)' Therefore, it seems clear that thermal bremsstrahlung radiation is completely negligible at 8-12 A during flare associated bursts. The dominant mechanisms at these times are therefore recombination and line emission,

162 The above result is supported by several theoretical calculations of the soft X-ray spectrum, We have already indicated that temperatures in excess of 10 x 106 K have not been observed for X-ray bursts near 10 A (see Chapter II). Culhane (1969) finds that at temperatures less than that value, free-bound radiation dominates all other sources of continuous emission. (He does not explicitly treat line emission.) In addition, Kawabata (1960) reports that for 2-8 A radiation, free-bound and/or line emission is greater than thermal bremsstrahlung up to temperatures of 30 x 106 K. Similar results are also found by Cox and Tucker (1969). The amplitude of the soft X-ray burst depends in a statistical sense on the area of the Ha flare which it accompanies. Thus, the sizes of these emitting volumes are presumably somehow related, In addition, larger X-ray bursts are associated with flares of a given size which are exceptionally bright. Using measurements of the halfwidth of high Balmer lines during flares, Svestka and Fritzova-Svestkova (1967) have found that such intensity variations in the case of Ha radiation are due to changes in the density of the flaring region, Therefore, these same density variations quite likely also extend into the region of the X-ray burst's emission. Soft X-ray bursts tend to have larger amplitudes when the general level of solar activity is high, or when the burst accompanies a flare which occurs in a young, flare-rich plage. This fact can again be explained by the effect of additional density enhancements in the X-ray emitting source under these conditions, Furthermore, there is some evidence that a region associated with a sunspot group of a given area can give rise to X-ray bursts no greater than a

165 certain limiting value in amplitude, and that this amplitude limit increases with the size of the spot group. Thus, it is possible that the X-ray emission rate is governed by the temperature and density of the source region, but confined to a range given by the region's magnetic energy density, Bursts of soft X-radiation also tend to have larger amplitudes when accompanied by radio bursts which have strong cm-wavelength enhancements, Unfortunately, the physical interpretation of this observation is not at all clear from the Michigan experiment. The time-profile of the soft X-ray burst is quite similar to that of its associated Ha flare. This is true when the Ha intensity of the flare is considered; but the time-correlation is even more striking when the X-ray and Ha flux curves are comparedo It is not obvious how to account for such a close correlation between these two emissions since they originate from regions having completely different physical characteristics, One possibility is that the time variation of each emission process is governed by the energy source term rather than the decay term as is normally assumed (cf. Acton, 1964; Hudson et al,, 1969a; Takakura, 1969), Thus the temperature and/or density enhancements which give rise to the Ha and X-ray events must be continuously maintained by the flare's source of energy (commonly believed to be the reconnection of magnetic field lines), By this hypothesis, the decay time-scale of the temperature-density enhancement in the absence of such a supporting mechanism would be small compared to the time scale of the flare itself. Furthermore, the mechanism which causes this temperature-density enhancement would have to affect both the Ha and X-ray emitting sources at the

same time and by proportionate amounts. Such a hypothesis is not totally new since many workers have found it necessary to suggest that a continuous supply of energy must be involved even during the flarets decline (Kawabata, 1966b; Oster and Sabatino, 1966; Holt and Ramaty, 1969; Zirin et alo, 1969). X-ray observations are important to our knowledge of the flare phenomenon because they refer to the hottest portions of the event, But they are of even greater interest since an enhancement in the soft X-ray emission appears to be the very first manifestation of a solar flare, at least on the average, Thus, such observations give information about the earliest phases of the event and may eventually lead to an understanding of the conditions which cause a flare to occur, This would be a strong step toward the very desirable ability to predict accurately the onset of a solar flare well in advance, Yet there is another, more fundamental, reason for the importance of soft X-ray observations. Emission in the form of soft X-radiation accounts for a significant portion of the total electromagnetic energy released by a solar flareo The amount is nearly identical to that emitted as Ha radiation, which has historically been considered as "the" flare phenomenon, Indeed the energy released in just the four-Angstrom interval between 8-12 A may actually comprise about one-tenth of the flare's total emission over the entire electromagnetic spectrum!

165 Obviously, the present studies, described at such great length above, have by no means answered all of the questions that can be posed concerning flareassociated soft X-radiation. In fact, they undoubtedly have raised more questions than they have answeredo But if the problem of solar flares has not yet been solved, it has not been through lack of effort. Indeed, these phenomena have been the object of countless observational and theoretical investigations since 1859, when the first recorded observations of a solar flare were reported independently by Carrington (1859) and Hodgson (1859)o In spite of this enormous amount of work, many aspects of the flare's mechanism(s) remain obscure, Perhaps the problem is too difficult. As Parker (1964) has cautioned: "We should be aware that we are observing an extremely complex phenomenon. There is always the chance-which we don't want to think about yet-that we will not succeed in unraveling the basic nature of the flare process" However, the present author is more optimistic. With the advent of observations made from space vehicles, measurements of the flare's emission throughout the entire electromagnetic spectrum are now becoming available for the first time, Such measurements will provide a vast amount of new information to aid in the explanation of the flare phenomenon and its cause0 We believe that much of this information will come from observations of the sun's soft X-radiation. Future investigations of this spectral region will undoubtedly greatly enhance our knowledge of the energetic processes associated with solar flares and, in turn, will lead to a better understanding of the sun itself0

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175 REFERENCES (Continued) Parks, G. K., and Winckler, J. R., (1969), Ap.J. 155, L117. Peterson, L. E., and Winckler, J. R., (1958), Phys. Rev. Letters 1, 205.,__ (1959), J.G.R. 64, 697. Pinter, S., (1969a), Solar Phys. 8, 142. __, (1969b), Solar Phys. 8, 149. Pottasch, S. R., (1965), BoA.N. 18, 7. Pounds, K. A., (1965a), I.A.U. Symposium 23, 61. ___, (1965b), Ann. d'Ap. 28, 132. ___, (1970), Ann. de Geophys. (In press.) __, and Russell, P. C., (1966), Space Research 6, 34. ___, and Sanford, P. W., (1963), Proc. Intern'l Conf. Ionosphere, July 1962, p. 50. ____, and Willmore, A. P., (1963), Proc. Intern'l Conf. Ionosphere, July 1962, p. 5135 _, Evans, K., and Russell, P. C., (1968), I.A.U. Symposium 35, 431. Quarterly Bulletin on Solar Activity, (1968), I.A.U. Publication, Zurich, No. 157-161. Ramsay, J. V., Norton, D. G., and Mugridge, E. G. V., (1968), Solar Phys. 4, 476. Reid, J. Ho, (1969), J. Atmos. Terr. Phys. 31, 859. Reidy, W. P., and Vaiana, G. S., (1966), Space Research 7, 1247., Vaiana, G. S., Zehnpfennig, T., and Giacconi, R., (1968), Ap.J. 151, 3335 Richardson, R. S., (1951), Ap.J 114, 356.

176 REFERENCES (Continued) Rugge, H. R., Personal Communication. ___, and Walker, A. B. C. Jr., (1967), Space Research 8, 439. Sawyer, C., (1967), Ap.Jo 147, 11355 Severny, A. B., (1952), Izvestia Krymsk. Astron. Obs. 9, 3. Smith, H. J., (1962), "Some Synoptic Flare Data, 1937-1960," GRD Research Note: AFCRL-62-827. and Smith, E. v. P,, (1963), "Solar Flares," Macmillan Press: New York. Solar Geophysical Data Bulletin, (1967-1968), issued by the Institute for Environmental Research, U.S. Department of Commerce, No. 272-289. Stock, J., and Williams, A. D., (1962), "Photographic Photometry" in "Astronomical Techniques" (ed. W. A. Hiltner), University of Chicago Press, po 374. Svestka, Zo, (1963), Space Research 4, 768. and Fritzova-Svestkova, L., (1967), Solar Physo 2, 75. Kopecky, M., and Blaha, M., (1961), Bull. Astron. Inst. Czech. 12, 229. Takakura, To, (1969), Solar Physo 6, 1335 ____, and Kai, K., (1961), P.A.SoJ. 13, 94. __, (1966), P.A.S.J. 18, 57. Takao, K., (1967), Rep. Ionos. Space Res. Japan 21, 125. Tandberg-Hanssen, E., (1967), "Solar Activity," Blaisdell Press: Waltham (Mass.)O Teske, R. G., Personal Communication. __, (1962), Ap.J. 136, 534., (1967), A.Jo 72, 832 (Abstract).

177 REFERENCES (Continued) Teske, R. G., (1969a), Solar Phys. 6, 193. ___, (1969b), OSO Workshop, Boulder, Colorado, August 1969. __, and Thomas, R. J., (1969), Solar Phys. 8, 348. Tindo, I. Po, and Shurygin, A. I., (1965), Kosmich. Issled. 3, 262. Underwood, J. H., (1968), Science 159, 383., and Muney, W. SO, (1967), Solar Phys. 1, 129. Vaiana, G. S., and Giacconi, R., (1968), Proc. Conf. Plasma Instabilities in Astrophysics, Asilomar, October 1968., and Zehnpfennig, T., (1969), Bull. Amer. Astron. Soc. 1, 294 (Abstract). _, Reidy, Wo P., Zehnpfennig, T., VanSpeybroeck, L., and Giacconi, R., (1968), Science 161, 564. Valnicek, Bo, (1967), Astrono Inst. Czech. 18, 249. Van Allen, J. A., (1967a), J.G.R. 72, 59035 _ (1967b), A.J. 72, 833 (Abstract). __, (1968), Ap.Jo 152, L85Van Griethuysen, I. G., and Houtgast, J,, (1959), B.A.N. 14, 279. Vegard, L., (1938), Geofysiske Publikasjoner 12, 5. Victoreen, Jo A., (1949), J. Appl. Phys. 20, 1.141 Waldmeier, M., (1938), Zs.f.Ap. 16, 276. _, (1940), Zs.f.Ap. 20, 46. ____, (1947), J. Terr. Mag. Atmos, Elect. 52, 3335, and Bachmann, H., (1959), Zsof.Ap. 47, 81.

REFERENCES (Concluded) Walker, A. B. C. Jr., Rugge, H. R., Chater, W. T., and Howey, C. Ko, (1967), Trans. Amer. Geophys. Union 48, 1510 Warwick, C. S., (1963), "The Sudden Ionospheric Disturbance" in "Radio Astronomical and Satellite Studies of the Atmosphere" (ed. J. Aarons), North-Holland Press: Amsterdam, p. 457o (1965), ApJ. 142, 767. Warwick, C., and Wood, M., (1959), ApJ. 129, 801, Warwick, Jo Wo, (1962), P.ASo.P. 74, 302o Wende, C. Do, (1969), J.GoRo 74, 4649. White, Oo Ro, (1962), Ap.J. Supp. 7, 3335 White, W. A., (1963), Space Research 4, 771. ____, (1964), AAS-NASA Symposium on the Physics of Solar Flares, NASA SP-50, po 131. Winckler, J. R,, (1964), AAS-NASA Symposium on the Physics of Solar Flares, NASA SP-50, p. 117. Witte, B., (1951), "A Contribution to the Study of the Relation Between Solar Flares and Sunspot Groups," HAO Solar Research Memorandum. Yefremov, Ao Io, Podmoshensky, Ao L., Yefimov, 0. No, and Lebedev, A, A., (1962), Space Research 3, 8435 Zhitnik, I. A., Krutov, V. V., Maljavkin, Lo P., Mandel'shtam, S. L., and Cheremukhin, G. S., (1966), Space Research 7, 1263o, (1967), Kosmich. Issled. 5, 274. Zirin, H., Ingham, W., Hudson, Ho, and McKenzie, D., (1969), Solar Physics 9, 269.

APPENDIX TWO METHODS FOR THE DETERMINATION OF FLARE EMISSION IN Ha It is by no means a simple task to interpret flare filtroheliograms in terms of the quantitative enhancement of the flaring region's Ha emission rate. To the author's knowledge, a complete, detailed description of the necessary reduction procedures does not seem to exist in the standard literature. Therefore, the two methods used in the present paper will be derived here. 1. GENERAL FORMULATION The exact shape of the Ha line's profile depends upon heliocentric position (j) for undisturbed areas of the solar disk, and also upon time (t) for regions which are flaring. Thus the following set of conventions has been adopted for the present derivation: Ig(C): Continuum intensity (near Ha ) at heliocentric distance A; IL(X): Intensity within undisturbed Ha profile at A; IU(k,t): Intensity within the flare's Ha profile at time t and position g. In addition, the following relations have been defined: r(X) = Ix(X)/I1(C) (A.1) r'(k,t) = IA(X,t)/Il(C) (A.2) Other conventions used are: (a) any value measured at the center of the solar disk is designated by subscript o, e.g. I (C); 0 179

18o (b) any symbol pertaining to the Ha flare is indicated by superscript', e.g. r'(k,t). The enhancement in Ha flux observed at the earth during a flare is then given by: AE(Hc, t) = fAdA lH [r'(X,t)-r(\)]Ij(C)dX (A53) where A is the flare's area in steradians as seen from the earth. Note that, in general, the Ha line profile also varies as a function of position within the flaring region. Assuming that the profile is filled uniformly during the flare's development, we can write: r'(X,t) = r(X) + p(t) [l-r(\)] (A.4) (The validity of this assumption will be discussed later.) Thus (A.3) becomes: AE(Ha,t) = I(C) fAP(t)dA H[l-r(X)]dX (A.5) A ha By definition, the equivalent width of Ha is: Wg(Ha) = i [l-r(\)]dX (A.6) Substituting (A.6) into (Ao5), we have: AE(Ha,t) = Wg(Ha)Ig(C) JAP(t)dA (A.7) Then, with the assumption that the flare's Ha radiation is semi-isotropic into 2r steradians (see the discussion in Section IV-6a), the enhanced Ha emission at the sun can be written as:

181 AS(Ha,t) = 2jtd2Wk(Ha) Ig(C) J p(t)dA (A.8) where d = 1.50 x 1013 cm is the distance between the sun and the earth. The value of the equivalent width for Ha at the center of the disk is W (Ha) = 4.02 A (Moore et al., 1966). The disk-center continuum intensity at 6563 A is taken to be I (C) = 2.93 x 106 erg/(cm2sec [ sterad>. (This is the intensity 0 of a black body with a brightness temperature of 6200 K.) Expression (A.8) thus becomes: as(fPt) = 1.66 x lo (A. 9) AS( t) =1.W66 x(Ha) I(C) fAP(t)dA erg/sec (A. 9) if f p(t)dA is determined in units of steradians. A We now consider how this equation can be put into a form which contains only measurable parameters. Observing techniques normally used do not directly measure the intensity of the Ha line center. Instead, they record the line's intensity as folded into the detector's instrumental transmission profile T(), which may also include the effects of scattered light. Such intensity measurements will be indicated here by the symbol P, with some of the same auxilliary notations as given for the "pure" intensities I. For example, an instrumental measurement of the Ha intensity for a flare occurring at heliocentric distance J is: Pg(Ha, t) = /o T(X)I(kt)dX (A. 10) Thus, the measurement of a flare's intensity relative to the nearby undis

182 turbed Ha background would be equivalent to: T()I4(%,t)d% f T(X)r'(X,t)ddX P^(Hc, t) _ _o____________ _o____________ 0 0 Substituting the expression for r'(X,t) given by (A.4) into (A.11), one can show: Pg(Ha, t) =1 + ( )d (A. 12) Now we define a parameter z: J T(X)dX z= (A. 13) fI O T(X)r(k)dX This may be considered as a "figure of merit" for the monochrometer because it measures how much contrast the instrument can provide between observations made attti the center of the absorption line and those made in the continuum. The highest value of z possible is l/r(center), which for Ha is 6.5 (LoPresto, personal communication). Note that it is not at all necessary (as Van Griethuysen and Houtgast (1959) had mistakenly assumed) to know the instrumental transmission T(X) in detail to find the appropriate figure of merit for a given monochrometer. One need only measure the ratio of the continuum intensity to the ooHa intensity at some i, since:

183 PM(C) 0 T(X)It(C)dX fTo T(X)dX m, ^ —-— = = = z (A. 14) Pg(Ho) 0T( )I( )d( 0o T(k)r(X)dX Furthermore, the measurement can be made at any heliocentric distance, because this ratio remains constant over the entire solar disk (DeJager, 1952; Dodson et al., 1956). Expressions (A. 12) and (A.13) can be combined to give: P'(Ha, t) p(t) = [ H ) - z-l) (A.15) Note that it is just this quantity, integrated over the solid angle of the flare's area, which gives the enhanced Ha flux by means of (A.9). Now, if we define R'(t) as: R (t) = P (H t) -P(Ha) dA steradians (A.16) SA P (Ha) O and take advantage of the fact that: P (Ha). _ = 1 (A. l7) Io(C) P (H) (A.17) equation (A.9) becomes: /S( Ht) = 1.66 x 104 W'(HA8) ASnSW(Ha.z) R (t) erg/sec (A.18) 0 The next two sections will describe the specific methods which were used

to integrate p(t) over the area of the flare. But first some comment should be made concerning the validity of the formulation to this point. In particular, we will discuss the effects of two potential sources of error; (a) misadjustment of the monochrometer, and (b) deviations from even-filling of the flare Ha profile. Most flare-patrol stations now observe with some type of commercial "filteroptics" monochrometer, such as the Lyot filter. (This includes the McMath-Hulbert Observatory, at which the film examined in the present study was secured ) Ramsay et alo (1968), claim that most Lyot filters may be in poor adjustment when delivered from the manufacturer, perhaps even with a transmission-profile minimum near Ha center' But the above analysis shows that no systematic error will result from such a misadjustment as long as the measured ratio of continuum to Ha intensity z is greater than unity. This is true whether the manufacturer is at fault or the observer merely sets the filter's line-shifter improperly. The only effect of some misadjustment will be to make the measurements less sensitive to subtle changes in the Ha emission, and thus lower the precision which can be attained. We must also examine the assumption that the Ha line fills uniformly during a flare (equation (A.4)). Dodson and Hedeman (1969c) have found that spectra of flares near the central part of the solar disk consistently have exhibited little or no evidence for major Doppler shifts. This eliminates one possible cause of an emission-line asymmetry, at least for events far from the limbo Van Griethuysen and Houtgast (1959) state that the even filling of the Ha line is a good approximation for faint and medium flares; but Ellison (1952, 1957) and Teske (1962)

185 have observed Ha emission profiles with strong central reversals for very large, bright flares. However, such reversals may be relatively rare, since many investigators (e.g., Ellison, 1949, 1963a; Comper, 1959; DeJager, 1959) have pub+ lished spectra taken during the time-development of 3 and 3 flares which show Ha emission profiles that quite closely approximate the shape predicted by equation (A. 4). Svestka et al. (1961), present some evidence that the number of flares with strong self-reversal increases toward the limb, which again suggests that the formulation derived above may be more appropriate for events near the center of the disk. Therefore, it is difficult to estimate the error introduced by line-profile irregularities in general. Ironically, an instrument with a narrower band-pass, and thus a higher potential precision, is affected even more strongly by this type of error. Smith and Smith (1963) have noted yet another possible source of uncertainty which cannot be taken quantitatively into account. They point out that flares, particularly large ones, may change the physical conditions of the chromosphere's deeper layers. Moreover, although flares appear to be thin, surface phenomena, it is not known at what depths they originate. Therefore, it may be rather naive to assume simply that the line profile of the region below the flare is identical to that of the undisturbed disk. However, it does not seem advantageous to alter the present formulation for that reason alone without any positive evidence to suggest a more accurate assumption. Thus we will hold to the "naive" viewpoint until such evidence is available. The "uniform-filling" hypothesis of equation (A.4) predicts that the flare's pure emission profile (total intensity minus pre-flare intensity) is just a

186 scaled version of the normal Ha profile, and thus has a constant half-width. Therefore, taken at face value, the well known time-variation of the flare's Ha emission line-width (first reported by Giovanelli (1940) and Waldmeier (1940)) would seem to indicate that the line profile is not filled uniformly during the flare. But these line width measurements actually refer to an "effective halfwidth" (also called the visibility range) which is defined as that distance from the Ha line-center where the flare is just visible by contrast with its surroundings (Ellison, 1943). Ellison (1949) has found that the Ha "effective halfwidth" is roughly proportional to the flare's central intensity up to a certain value, and then increases more rapidly. One can easily show that this is exactly the effect predicted by the "uniform-filling" hypothesis (equation (A.4)) if the eye can only discriminate intensity differences of some limiting value (or percentage).. Therefore,it appears that equation (A.4) is indeed a close approximation to the flare's emission profile, except perhaps for limb flares or for some (hopefully rare) cases of very large and bright disk events. 2. METHOD A: "TYPICAL" TOTAL AREA AND PEAK INTENSITY A crude estimate of the Ha emission can be made by means of "typical" values for the total area A and measured peak intensity P'(Ha) appropriate for each flare class. Because of difficulties caused by the well known limb-darkening effect, only values for the center of the solar disk are considered here. Thus, (A.18) becomes:

1.66 x 1034 AS(Ha) = (z- 1 * R' erg/sec (A. 19) (The time-variable has been eliminated since all values in this section will refer to the time of flare maximum.) Now, R' can be roughly approximated as: P (Ha) RT = A o(HIa) 1 (A 20) where A is in units of steradians. The flare area used was the middle value of the range defined by the I.A.U. for each importance class (see Table 4.2 in Chapter IV). This may be slightly higher than the actual area for a typical flare of that class, since flare frequency decreases rapidly with increasing peak area. But a correction for such an effect would be unnecessarily precise for the rather crude level of accuracy attainable by the present overall method. Measurements of the flare's peak intensity were taken from the Dodson, Hedeman, and McMath (1956) paper "Photometry of Solar Flares." Specifically, this paper lists measurements of the peak Ha intensity relative to the continuum at the center of the disk, i.e. P (Ha)/P (C). In order to convert these into the proper form for equation (A.20), they must be multiplied by P (C)/P (Ha) (which expression (A.14) shows is nothing more than the value z). The instrument used by Dodson et al., was characterized by z = 3. 1, so that equation (A. 19) can be written as: P (Ha) AS(Ha) = 7.9 x 1033 A * l ( — ) (A. 21) 0 C

188 The values of area and measured intensity which were used in the present study are given in Table A.. The enhanced Ha emission rates which then result by means of equation (A. 21) are listed in Table 4.8 of Chapter IV. They are also plotted in Figure 4-7 relative to the enhanced emission rates of the associated soft X-radiation. TABLE A. 1 "TYPICAL" AREAS AND PEAK INTENSITIES FOR Ha FLARES Flare P (Hca)/P (C) Importance (steradians) (Dodson et al., 1956) Sn 9.9 x 10 0.6 ~ 0.1 -9 Sb 9.9 x 10 0,8 + 0.1 If 2.4 x 10 0.4 ~ 0.1 In 2.4 x 10 0.8 ~ 0.1 -8 lb 2.4 x 10 1 2 ~ 0.1 -8 2f 5.8 x 10 0.7 ~ 0.1 -8 2n 5o8 x l 1.1 ~ 0.1 2b 5.8 x l 1.5 ~ 0,1 3n 1o2 x 107 1.3 0.1 b 1.2 x 10 1. 6 ~ 1-7 3b.12 x 10 1.6 + 0.1 3e METHOD B: ISOPHOTOMETRY In order to accommodate further notation complexities, some simplification of the previously used conventions will be made here: (1) the heliocentric distance g will not be explicitly noted for values that refer to the flare itself (values marked by superscript'), (2) the time dependency of all values will be implicitly understood, (3) unless otherwise indicated, all measurements will be made at the center of the Ha line.

189 Basically, the technique of isophotometry involves the construction of constant-intensity contours within the outline of a flaring region from film records of the flare. This can be done either by purely photographic methods (Falciani et al., 1968) or by means of a photometric isophotometer (Stock and Williams, 1962). If the film has been properly calibrated, the intensity of each contour relative to the center of the solar disk can be determined. Then, knowing the area enclosed by each curve, one can calculate the enhanced emission being radiated between these contours and thus, by summing over the entire set, find the whole flare's Ha emission. Measurements of many filtroheliogram frames made during the development of the flare then give the time-history of the event's enhanced Ha emission. However, the quantity actually measured at a given point on the film is not the relative intensity P/P (where P is some arbitrary value), but rather the photographic density D. These quantities are related by a logarithmic expression, normally called the characteristic curve, which can be written as: P log - = f(D) (A.22) s For any quantitative study, this relation must be known for the film being photometered. In fact, we have found that the procedure described here is very sensitive to slight changes in the characteristic curve. Therefore it is necessary to exercise great care in measuring this relation and advisable to determine it individually for each frame considered. To find some feature's intensity relative to the undisturbed Ha intensity

190 at the disk's center P/P the following expression is used: P P P 0o f(D) - f(D log = log - log f(D) - f(D) (A.25) P P P o 0 S S where D is the photographic density of the undisturbed region. Now, if D is O c the density at contour c, we can define a mean relative intensity P /P for the flare emission between contours c and c + 1 as: -t P 1AD +D 2\ log = f (D D) - f(D) (A.24) o 0 Then, following equation (A.16), the relative flux R emitted within contour c c is approximately: c (max) /P'-P' R = c (A A - ) (A.25) c c c -+l P \ o where c(max) is the innermost contour measured, and A is the area (in steradians) within contour c. One slight modification of the above procedure is desirable. It has been found that the relative flux between the outermost two contours, 1 and 2, is better represented by a mean intensity defined as: -lo 1 2D1D+ D_ (A. 6) log - f (D (A.26) PO 3 0) Therefore, the mean intensity given by expression (A.24) is used only for c > 1.

191 Isophotometry also allows an accurate measurement of the flare's peak intensity P /P, in addition to the relative flux emitted within each contour c. max o (Note that P is not necessarily the intensity of the innermost contour P. ) max c(max) This can be done most precisely by plotting R as a function of the intensity of c contour c, and extrapolating the curve to the point where the value of the relative flux vanishes. The intensity value at that point is then P /P. However, max o this procedure is useful only when enough contours are measured to make the above extrapolation reliable. In other cases, a subjective estimate based on the area within the innermost contour is reasonably accurate. Of course, the higher the figure of merit z for the monochrometer used to make these measurements, the closer they will be to the "true" peak intensity values. Unfortunately, the method described above for the determination of relative fluxes must be refined further. This is necessary since the outermost contour does not in general fall at the same intensity level from one exposure to another. Thus, in order to compare fluxes measured for a series of filtrograms (such as for a study of the flare's time development), all values must be standardized relative to some uniform level P*/P0. Flux values converted to such a standard intensity level will be referred to as R1. The present study utilized one of the following three interpolation methods for this standardization, depending on the circumstances involved: (1) if only two values of Rc were known (including the value zero at P /P ), a linear interpolation in log (P/P ) was used, i.e.: max/ 0 0 o

192 Y -Y R' = R + (R -R ) (A.27) c2 cl c2 Y1-Y where Y. = log (P*/Po) and Y = log (P./P ); (2) if only three values of R were known and C -- log max _ log c(max <0.04, (A.28) P P 0 0 a linear interpolation was again used; (3) otherwise, a parabola was fitted through the three values of R nearc est to P*/Po by the following relation: (Y -Y ) (Y -Y T * T 2 * R R cl (Y1-Y2) (Y1-Y3) (Y -Y1) (Y -Y) + R (A. q9) c2 (Y2-Y) (Y-Y)(A29 (Y -Y ) (Y-Y2) + R c3 (Ys-Y1) (Ys-Y2) At this point in the analysis, we can determine the relative enhanced flux of the plage plus flare Ha radiation which is emitted at intensity levels above P*/PAo But there is no way to measure directly the flux emitted at intensities P/Pi between unity (the adjacent undisturbed intensity) and the intensity of the outermost isophote-contour. (A contour at P /Pgu = 1 is not possible.) One method of estimating the total flux R is to plot the measured values of R as a function of P /Pj and extrapolate this curve to a relative intensity of unity.

193 But this is practicable only if three or more contours have been measured. Therefore, in the present study, we have made such an extrapolation only for times near flare maximum (when up to seven contours were recorded). Then the mean ratio for these times R /RI was applied to all the measured frames of the flare in question. Finally, if this ratio is called cp, equation (A.18) can be written: s(~ ) 1.66 x 1034 Wg(Ha) R AS(Ha, t) = ) R(t) erg/sec (A.50) 0

UNIVERSITY OF MICHIGAN 3 9015 03526 8732