The Degenerate Era

When stellar evolution comes to an end, we enter the Degenerate Era. Most ordinary stars will be done with the business of nucleosynthesis as stellar bodies. In our inventory of stars, we have about equal numbers of brown dwarfs and white dwarfs, and about three in a thousand black holes and neutron stars. Since the white dwarfs are quite a bit larger than the brown dwarfs (by about a factor of 10 in mass), the vast majority of the actual (baryonic) mass — the protons — are embedded in these white dwarfs. Although a lot of gas is also left behind in this future universe, it's very diffuse and wispy.

In sum, what are left in the Degenerate Era are degenerate stellar remnants (degenerate here refers to a quantum mechanical property of dense matter, not to a moral statement about the universe). From cosmological decade 15 to perhaps 37 (10¹⁵-10³⁷ years), these degenerate objects are the most important stellar objects in the universe.

At this point the brown dwarfs — the failed stars — start to come into play because they can collide. In our universe today, astronomers never worry about stars colliding, and the reason is simple. The amount of space that is filled by stars is phenomenally small. Populating the universe with stars is like taking little tiny sand grains and putting them miles and miles apart. With that much space between the stars, collision is very rare. However, if you wait long enough, sometimes things that are unlikely do, in fact, happen. And if you wait long enough, stars are going to collide in our galaxy. When two brown dwarfs collide at a sufficiently head-on angle, then the merged product can have enough mass to sustain hydrogen fusion. The result is a star with enough mass to turn on and become a red dwarf just over the hydrogen-burning limit. It will then burn up the hydrogen it has previously hoarded. This star won't be large like our sun; it will be another one of these typical little red stars that lives for trillions of years.

Since we know how many brown dwarfs there are, and we know the galaxy they live in, and we know the collision rate of these stars, and we know how long the merged products will live, you can add all these things up and calculate how many such stars should be shining in a large galaxy like our Milky Way at any given time in the Degenerate Era. And the answer is two or three such stars. Today, as Carl Sagan has told us, there are billions and billions of stars in every galaxy, and they are bright. In this dark galaxy of the future Degenerate Era, there will be two or three stars from these merged brown dwarfs, and they will be about 10,000 times dimmer than the sun.

Every once in a while the white dwarfs will also collide. But most white dwarfs are small, so when they collide they will just form weird stars and will not do anything interesting. But, occasionally, when the big white dwarfs collide, the merged product can be large and fat enough that it will explode in a different kind of super nova explosion. So every once in a while this dark galaxy of the future will be punctuated by a spectacular super nova.

White dwarfs also sweep up dark matter particles. Over time, inside the white dwarf, these particles annihilate each other, turn into radiation, and become the dominant energy source in the universe. The power generated by such a white dwarf is about quadrillion watts, which is quite small compared to the sun, but that's a healthy fraction of the energy that our earth intercepts from the sun.

Over longer times, the galaxy itself changes its structure by evaporating its stars out into the intergalactic void. We would have a continual hierarchy of these dynamic processes, but protons will eventually decay. For purposes here, let's say that 37 cosmological decades (10³⁷ years) is the typical proton lifetime. Most of the protons that we care about at this late stage in history will be embedded in white dwarfs, which is a very dense medium. Not only will there be protons, but also there will be the corresponding electrons around. When a proton decays into a positron, this positron will very quickly find an electron to annihilate with. The net result of a proton decay event inside a white dwarf star is thus to turn all of the mass energy into radiation. In particular, you get four photons. Those photons then interact with the other things in the star and transform into more and more low-energy photons as the energy works its way out of the stellar surface. The star surrenders its mass in the process.

With that picture in place, we can know, for the first time, the complete evolution of the sun, which will become a red giant and then a white dwarf once it cools and becomes smaller. In the long run, the proton decay process is the most important mechanism driving stellar structure. As the white dwarf radiates its mass and energy away, it grows larger even as it loses mass because degenerate objects work backwards. A white dwarf star undergoing proton decay will generate something like 400 watts of power — about as much as you can do on a rowing machine if you're working pretty hard. This process of degeneration will continue until the mass of the object has decreased from about the mass of the sun down to something close to the mass of Jupiter. At that point the object loses its degenerate properties, but the protons keep decaying. The star is now much like a block of hydrogen ice, with a dwindling store of mass and internal radiation escaping out of the body. Eventually, the block of hydrogen ice no longer exists and stellar evolution comes to an end. That is the long-term fate of our sun, and most other stars.

We began the Degenerate Era with an inventory of brown dwarfs, white dwarfs, neutron stars and black holes. We've seen that stars continue to form through these brown dwarf collisions. Dark matter gets captured in white dwarfs and endows the white dwarfs with a luminosity source, a power source that they wouldn't otherwise have. Against this backdrop, the galaxy rearranges its structure over time scales of 10²⁰ years or so, relaxes dynamically, and evaporates most of its stars out into inter-galactic space. All the while, black holes that capture stars and gas and anything that they can get into their event horizons grow somewhat larger during this time. The Degenerate Era ends rather cleanly after the protons decay. For the numbers we're using here, this era ends after 10⁴⁰ years, or cosmological decade 40.