THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING Department of Aerospace Engineering High Altitude Engineering Laboratory Scientific Report ON SOLAR X-RAY AND RADIO EMISSIONS FROM THE SUN S. N; Ghosh ORA Project 05627...~.. under contract with: NATIONAL AERONAUTICS AND SPACE ADMINISTRATION CONTRACT NO. NASr-54(05) WASHINGTON, D. C. administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR March 1968

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TABLE OF CONTENTS Page List of Figures iv Abstract v X-ray Emissions from the Sun 1 1. Introduction 1 2. Free-free Transition or Bremsstrahlung 3 3. Free-bound Transition 5 4. Line Emission 6 Table 1 Solar X-ray Emission by Different Mechanisms 7 5. Conclusions 8 Radio Emissions from the Sun 9 References 11 iii

List of Figures Figure Page 1. The variation of the solar X-ray flux at earth with the wavelength for the completely quiet condition of the sun (coronal temperature 7x1050K). Values obtained by Friedman and Nicolet are denoted by F and N. MIQ and Q refer to the minimum quiet and quiet conditions of the sun. 12 2. The variation of the solar X-ray flux at earth with the wavelengti for the quiet condition of the sun (coronal temperature lxlO10K). Values obtained by Friedman and Nicolet are denoted by F and N. MIQ and Q refer to the minimum quiet and quiet conditions of the sun. 13 3. The variation of the solar X-ray flux at earth with the wavelength for the active condition of the sun (coronal temperature lx107~K). Values obtained by Friedman and Nicolet are denoted by F and N. MIQ, MAA, D and F2 refer to the minimum quiet, max. active, disturbed and flare type 2 conditions of the sun. 14 4. The variation of the solar X-ray flux at earth with the wavelength for the flare condition of the sun (coronal temperature 1x108 oK). Values obtained by Friedman and Nicolet are denoted by F and N. MIQ, MAA, F2 and F3 refer to the minimum quiet, maximum active and flares types 2 and 3 condition of the sun. 15 5. The comparison of the observed solar radio flux at earth for the quiet sun with those calculated for free-free transitions for Ne=109cm-3 and for different coronal temperatures. 16 iv

Abstract Assuming a Maxwell distribution of electron velocities in the 5 6 solar corona, the X-ray fluxes at the earth for temperatures 7x10, lx10 lx107 and lx108~K are calculated for free-free transitions. These temperatures correspond to typical cases of completely quiet, quiet, active and flare conditions of the sun. The fluxes are then compared with those for free-bound transitions and line emissions obtained by Elwert and Kawabata. It was shown that during flares, the radiations are emitted primarily by freefree transitions, and that coronal temperatures and electron densities during different types of flares can be precisely determined from observations of solar X-ray emissions. For other conditions of the sun, line emissions predominate, and the spectrum becomes harder and the flux increases as the sun passes from the quiet to active condition. The emission of radio waves by free-free transitions for different conditions of the sun are also calculated and it was shown that the calculated 6 9 -3 flux for T = 1. 10 OK and n = 10 cm3 is the mean of the observed value e for the quiet sun. v

X-Ray Emissions from the Sun 1. Introduction Rocket observations of solar X-ray flux, its spectrum and penetration through the atmosphere have been obtained. It is observed that with the increase of solar activity, the X-ray spectrum becomes harder and the flux increases. Again, Friedman, (1962) obtained a high correlation of Elayer critical frequencies with solar X-ray fluxes. Observations through radio telescopes show that the cm and decimetric solar radio flux has a high correlation with solar activity. Also Kundu (1965) reported a remarkable correlation between radio flux and E-layer ionization of the sun (solar flare seems to have no effect on E-layer, but influences D-layer). The solar X-rays consist of both continuous and line emissions. The probable mechanisms for the emission of solar X-rays, which are supposed to be emanated from the corona, are the following: (1) Free-free transition or bremsstrahlung of high-velocity electrons in the field of protrons which is the main constituent ion in the corona. (2) Free-bound transition i. e. recombination of electrons with the heavy ions of the corona e. g. Fe, Ni, Si (ion-electron recombination). (3) Line emissions (mainly composed of the permitted lines of highly ionized elements e. g. Fe XXIV, Si XIII, Mg X etc. ) which are produced by electronic collisions. Since the energy differences between the various levels are great only the first level is excited producing resonance radiations. The hyperbolic free-free transition of electrons in the field of protons gives continuous emission. The wavelength for maximum emission depends upon the velocity of electrons i. e. on the temperature of the corona. 1

The amount of maximum emission is proportional to the product of electron and proton densities, or to the square of electron density. Therefore, if the emission is due to free-free transition, knowing the wavelength for maximum emission, the temperature of the corona can be determined and from the amount of maximum emission, the coronal electron density can be obtained. We shall show that when flare occurs, the radiations are emitted primarily by free-free transitions. Hence, coronal temperatures and electron densities during different types of flares can be precisely determined from observations of solar X-ray emissions. 2

2. Free-free Transition or Bremsstrahlung The power radiated by free-free transitions of electrons in the field of an atomic nucleus is given by J = nne hV dqvf(u) dowhere ni - ion density ne - electron density dq cross section for emission of a photon in the energy range dhv f(v) - velocity distribution function for electrons. Assuming the Maxwell distribution of velocities of electrons and Z = 1, Elwert (1948) showed that the above expression reduces to the following for free-free transition Jfd = C(X ) e KT g n.n dv ff KT r where 3/2 3 -40 3 C 2 -= (XH f x 1.7 x 104 fl erg cm In the solar corona, where the X-rays are supposed to originate, because of the strong gravitational field of the sun, the thermal velocity is less than the escape velocity. Hence, the majority of electrons suffer several collisions and the Maxwell velocity distribution is established (Shklovskii, 1965). The corona consists of about 80% H and 20%o He and is wholly ionized and hence Z = 1. 3

o( - Sommerfield's fine structure constant Grant factor =i in'iKT g - Grant factor = In 4KT h Euler's constant T - absolute temperature of electrons a - radius of the first Bohr orbit o CXH- ionization energy of the hydrogen atom f. - constant representing the uncertainty of cross section for photo-recombination. It is assumed to be unity. Therefore 6 ~ hv -41 10 2 h-3 -1 J d) = 7x10 ( ) e KT n.n dv erg cm sec ff T 1 e To calculate the flux, Ff, at the earth, J dV is integrated over ff - ff the volume of the emitting coronat and divided by 2. 4TrR2 where R = sun-eartl 13 distance = 1. 5x10 cm (the factor 2 accounts for the fact that one-half of the radiation falls on the earth). Therefore { Jffd d 7x10^ - 10 -hV/KT -2 ff 8 rrR2 8 iTR2 T 1 evrTd~n~rfgm2 ff 2 ( ddvergcm se-3 Assuming J ninedv = 3x10 cm (Elwert, 1954), Fff has been calculated for T = 7x10, x5, lx, x07 and 1x108 OK which correspond to typical cases of completely quiet, quiet, active and flare conditions of the sun. The fluxes per 1A wavelength interval have been plotted in Figs. 1-4.'-c ~',' a The Grant factor for untraviolet and X-rays is of the order unity (Allen, 1955; Shklovskii, 1965). t Solar X-rays are believed to be emitted from the inner corona and in the transition zone between chromosphere and corona. 4

3. Free-bound Transition The emission by free-bound transition for a frequency interval dv is given by (Elwert, 1954) Jfb dV Cn2 e KT ) (i) Xi d Jd - e KT hV>/XnZ. where C = 1.7x10 40f erg cm 2 nn i X Z./KT nZ i+l no Zi+1 ( XZi e n i Z1 ~ ne n H Z - same as Z n - number of unoccupied state in the nth energy level X3; - ionization energy of the atom for the n th energy level. 0o For T = 7x10 and 1x106 OK, the fluxes at earth calculated by Elwert (1952 7 8 and 61) are taken. For T = 1x10 and 1x10 OK, using Kawabata's data for Jfb/fl ne after numerical correction, the fluxes at earth are calculated. These fluxes for a wavelength interval of 1A are plotted in Figs. 1-4. 5

4. Line Emission The line emission can be calculated from the formula (Elwert, 1954) 2 b=4 ~ f CFrrX H K - T n Z JL =, f3 ao H (KT e i i f9 X1, 2 -3 -1 = 9. 5x10 19 f ) n L L YZ erg cm sec Z i Z where n n YZ. = e i 1 Cn 1 -hV/KT G (hY / Z -n 1 n- n e G3 (h /KT) i e 1 o o oo 0 f3 - a dimensionless parameter depending on the probable error of the method of calculating cross section. The values of 1 n 1 Cn and G3(h9/KT) are calculated by Elwert (1954). o o n 1 3 0 00 5 6 For T = 7x10 and 1x10 OK, the fluxes for line emissions at the earth are taken from Elwert (1954). For the other two temperatures, T = *7 R^2 1x107 and 1x108 OK, they are calculated from the values of JL/f3ne given by Kawabata. These fluxes are also plotted in Figs. 1-4. In these figures, the observed values of X-ray emissions from the sun are also plotted. f3 is assumed to be unity. For line emissions, free-free and free-bound transitions, the emission is proportional to n.n. Because, in the highly ionized plasma from which the radiations are emitted n. is proportional to ne, the emission is 2 proportional to ne. 6

Analysis of Figs. 1 - 4, leads to certain conclusions which are given in Table 1. Table 1 Solar X-ray Emission by Different Mechanisms T Mechanisms for Excitation Agreement of computed curves Observed Remarks ~~0 ~~~~~with trie observed values. Range of K Free-free Free-bound Line Observations transition transition emission 7x10 Max. emis- Moderately Most impor- 40-304 A Free-free (Completely sion at 1OOA; important, tant between contributed transition quiet sun) f the three Most impor- 40-304A; by line emis- is unimtypes of emis- tant below 40A strong lines sion only. portant. sions, it is and above cluster in the least important 304A. region 80-100OA. 6 1x10 Max emission Maximum Most important Line intensities and observed 22-304 con(quiet sun) at 70A; least emission at for 18-304, wavelength extent of emission tributed by -doimportant 45A;moder- around 60-70A agree with Hinteregger's ob- line emisately impor- lines cluster, served values during solar sions only. tant; most minimum. important below 18A and above 304A. 1x10 Max. emission Least im- Most important Nicolet's model for flare 2 4-25 contri- Free-bound (active sun) at'7A; most im- portant. for 6-25, strong bution by line transition is portant emis- lines cluster be- emission only unimportant. sion below 6 and tween 10-15 A. above 25A 1x10 Max. emission Least im- Only three Nicolet's model for flare 3.2-13 contri- Both free(solar flare) at,7A. Most portant. unimportant bution by free-bound transitimportant for lines, free emission, ions & line the whole emission are region. unimportant. *Assuming 6x10 -4 -2 -1I Assuming 6x10 erg cm sec is the limit of observation.

5. Conclusions The following conclusions can be drawn from the above theoretical considerations. 1. As the sun passes from the quiet (105 - 106 OK) to the flare condition (108 oK), the emission by the free-free transition increases due to higher temperature. At the sametime, ion-electron recombination which requires slow electrons, decreases and hence emissions by the free-bound transition become less important. 2. The amount of total solar X-ray emission does not increase significantly from the quiet to flare condition of the sun. When the sun is quiet, the velocities of electrons are sufficient to excite resonance radiations of ions, whereas during flares, the low intensities of line emissions are compensated by the higher free-free transitions (the energy differences between the various levels of the strongly ionized ions of the corona are so great that only excitation of the first level of the ions occurs). 3. Hard X-rays are emitted as the sun passes from the quiet to the flare condition. 4. Since at high temperatures, free-free transition predominates, the emission is continuous. 5. The wavelength for maximum emission and the amount of emission by free -free transition depends markedly on temperature (the wavelength for maximum emission shifts to shorter wavelength with increased emission for higher temperatures). Hence, the coronal temperature during different types of flares can be precisely determined by observing solar X-ray emissions. 8

Radio Emissions from the Sun The emission of radio waves from the sun can occur by several mechanisms. It is calculated for free-free transition. The free-free transition (bremsstrahlung) per unit solid angle per unit volume for the frequency range d ) is given by (Allen, 1955) 1 6 2 1 i 3 (= 6 c 3 m (KT) gexp(-hl /KT)n n. d) -39 2 U~ -3 -1 5. 443 x 109Z g exp(-h)/KT)T 2ne n ergcm sec sterade jL (Tin OK, n and n. in cm 3) The flux at the earth for the frequency interval dV F 4-Tj d dV F ff J 87rR2 1 -39 2 -2 -1 -= -x 5. 443x 10392g exp(-hv/KT)T 2 ni n dV ergcm sec 2R2 49 -3 Assuming J nin dV =3x10 cm, exp(-hV/KT) = 1 in the radio 1 e 13 region, Z = 1 and the sun-earth distance R = 1. 5x10 cm, F = 3.628x0 -1 g T 2 d9 erg cm sec ff 3. 628x g T 2 RU IRU =022 w m 2(c/s)] (1) The Grant factor for radio waves is given by (Allen, 1955) ~43 2 1/3 g 1 ln(4KT/e ne 1 10 = 1.2695 (3,38 + logOT - loglo ne) (2) 9

Using formulas (1) and (2) and assuming the electron density 9 -3 5 6 in the corona, ne= 10 cm, F has been calculated for T= 7x10 1x10, lx107 and 1x108 OK and is plotted in Fig. 5. In the same figure, observed values of Fff for the quiet sun are also plotted. The curves show the following: 1. The flux decreases with the increase of coronal temperature. 2. For a particular temperature, the flux remains constant with wavelength. 3. For the wavelength range 1-450 cm, the calculated flux for T=l. 106 OK and n=10 cm is the mean of the observed value for the quiet sun. 10

References Allen, C. W., Astrophysical Quantities, University of London, The Athlone Press, 1955. Elwert, G., Der Absorption skoeffizient an der langwelligen Grenze des Konlinuierlichen R'ntgenspektrums, Z. Naturforsch, 3a, 477-481, (1948). Elwert, G., Das Kontinuierliche Emission spektrum der Sonnen Korona in fernen Ultraviolett und bei weichen Rontgenstrahlen, Z. Naturforsch., 7a, 202-204, (1952). Elwert, G., Die Weiche Rontgenstrahlung der ungestorten Sonnen Korona, Z. Naturforsch., 9a, 637-653, (1954). Elwert, G., Theory of X-ray Emission of the Sun, J. Geophys. Res., 66, 391-401, (1961). Kawabata, K., The Relationship Between Post-burst Increases of Solar Microwave Radiation and Sudden Ionospheric Disturbances, Report of Ionospheric Res. (Japan), 14, 405-426, (1960). Kundu, M. R., Solar Radio Astronomy, Interscience Publishers, New York, 1965, Chapter 13. Skhlovskii, I. S., Physics of the Solar Corona, Translated by Fenn, Pergamon Press, 1965, Chapter 5. 11

Io Id' -' -t xNe VIII 2 t0 SOLAR X-RAY FLUX AT EARTH xFe X FOR T =7x 10 K xFe XII xHe II x Fe X xFeX Ne VII x VI xMa VIII Si IXx xSi Vl FeXIII XS VIII s ixD -N -~ 3 xN V C gX XSi xFe IX - FREE-FREE TRANSITION X Fe IX Tsb:~ ~ (Fff) xS VII -E FREE-BOUND TRANSITION xMgX (Ffb) o x LINE EMISSION (CALCULATED) (FL) Ne IX.0- / -4 LL C 1 s~l F+ He III MIQ IO10 100 1000 Fig. 1 The variation of the solar X-ray flux at earth with the wavelength for the completely quiet condition of the sun (coronal temperature 7x1050K). Values obtained by Friedman and Nicolet are denoted by F and N. MIQ and Q refer to the minimum quiet and quiet conditions of the sun. 12

IO 10" 10 SOLAR X-RAY FLUX AT EARTH FOR T=1xIO6 ~K oo FREE-FREE TRANSITION (Fff) FREE-BOUND TRANSITION xNe VIII -2 (Ffb)10-. \ -1062 x LINE EMISSION (CALCULATED) \ xFeH r \ (FL) / -e \ - FLUX OBTAINED BY N V1 xFe XIV He lix HINTEREGGER et.al. I FOR QUIET SUN x I xSi X xO VI I /, N al q IMgX / 3 INi ~C/S Fe X V t / /.sx -Y /Si X I / xNV c ^( / F MiQ Ne IXM0 /He I -5 / -5 5F MIQ MIO O6 -- -I lo I 10 100 1000 Fig. 2 The variation of the solar X-ray flux at earth with the waveFig. 2 The variation of the solar X-ray flux at earth with the wavelength for the quiet condition of the sun (coronal temperature lx106K). Values obtained by Friedman and Nicolet are denoted by F and N. MIQ and Q refer to the minimum quiet and quiet conditions of the sun. 13

-I IO-I IO110 SOLAR X-RAY FLUX AT EARTH FOR T= lxIO7~K FREE-FREE TRANSITION (Fff ) -2 ^ 10 - FREE-BOUND TRANSITION - 1 xNe X (Ffb) N x LINE EMISSION (CALCULATED) F2 (F.) xFe XXII (FL) XFe XXIII F xO VIII MAA xFe XXI. 3 ~ Si XIII x xFe XXIV,* / Si XIVx xMg XI \ L / xS XV o ~ I / \I l1O- 0 \ -10"4 fi^ ~~~N VII s XVNeX 10 ~ NI / VII \- 1~5 io06 / I I \ i(o6 10 100 1000 X(A) Fig. 3 The variation of the solar X-ray flux at earth with the wavelength for the active condition of the sun (coronal temperature lx1070K). Values obtained by Friedman and Nicolet are denoted by F and N. MIQ, MAA, D and F2 refer to the minimum quiet, max. active, disturbed and flare type 2 conditions of the sun, 14

idd SOLAR X-RAY FLUX AT EARTH FOR T =I x10~K -2 F -2 F 1/\ MAA - Ijf~~ xFe XXV AA lo-3 _ |xFe XXVI \ MIQ 1o F3 F2 ~~~~T~~~~~~~~~~~- Ni U - \ -4 0' I. F2 FREE-FREE TRANSITION (Fff) - FREE-BOUND TRANSITION XS XVI 1"5- (Ffb) -I5 X LINE EMISSION (CALCULATED) (FL) * LINE OBSERVED Fe XXVI St I Ne X 0 VIII N VIl lc VI i0 10I O. a~10 10" x(A) Fig. 4 The variation of the solar X-ray flux at earth with the wavelength for the flare condition of the sun (coronal temperature lx108OK). Values obtained by Friedman and Nicolet are denoted by F and N. MIQ, MAA, F2 and F3 refer to the minimum quiet, maximum active and flares types 2 and 3 condition of the sun. 15

f (Mc/s) 104 103 102 10 I 1 SOLAR RADIO FLUX AT EARTH _ | ~- Observed for Quiet Sun C ^^ - Calculated for Free - Free C\T 10 ~ \ Transition for Ne= O19cm EJ 3 I- _ ------ T=Ix0-K z -2T=lx \ -22 I I. i 10 100 1000 X (cm) Fig. 5 The comparison of the observed solar radio flux at earth for the quiet sun with those calculated for free-free transitions for Ne= 10 cm-3and for different coronal temperatures.

UNIVERSITY OF MICHIGAN III3 9015 02826II 106III IIII 3 9015 02826 1066