User:Robert Treat/the universe's degenerate and dark eras

Degenerate/Black Hole Era
after 1014 (100 trillion) years

Star formation ceases
1014 (100 trillion) years

It is estimated that in 1014 (100 trillion) years or less, star formation will end, leaving all stellar objects in the form of degenerate remnants. Most of the mass of this collection, approximately 90%, will be in the form of black dwarfs, which will continue to assimilate dark matter. This period, known as the Degenerate Era, will last until the degenerate remnants finally decay.

Planets fall or are flung from orbits by a close encounters with other stellar remnants
1015 years

Sun has cooled to 5 K. Assuming that the Big Crunch or Big Rip scenarios for the end of the universe do not occur, calculations suggest that the gravity of passing stellar remnants will have completely stripped the dead Sun of its remaining planets within 1 quadrillion (1015) years. This point marks the end of the Solar System. While the Sun and planets may survive, the Solar System, in any meaningful sense, will cease to exist. This may occur sooner if there is a Milky Way Andromeda collision, or may take longer if the outer planets were made into a Dyson sphere after the sun becomes a white dwarf. It may not occur if the solar system is thrown out by the anticipated Milky Way-Andromeda collision. Solar systems so thrown out will instead decay by gravitational radiation.

By 1017 years all former white dwarfs will have cooled to 5 K, and will be black dwarfs.

Stellar remnants escape galaxies or fall into black holes
1019 to 1020 years

Over time, objects in a galaxy exchange kinetic energy in a process called dynamical relaxation, making their velocity distribution approach the Maxwell-Boltzmann distribution. Dynamical relaxation can proceed either by close encounters of two stars or by less violent but more frequent distant encounters. In the case of a close encounter, two brown dwarfs or stellar remnants will pass close to each other. When this happens, the trajectories of the objects involved in the close encounter change slightly. After a large number of encounters, lighter objects tend to gain kinetic energy while the heavier objects lose it. Because of dynamical relaxation, some objects will gain enough energy to reach galactic escape velocity and depart the galaxy, leaving behind a smaller, denser galaxy. Since encounters are more frequent in the denser galaxy, the process then accelerates. The end result is that most objects are ejected from the galaxy, leaving a small fraction (perhaps 1% to 10%) which falls into the central supermassive black hole.

Nucleons start to decay
>6.6x1033 years

The subsequent evolution of the universe depends on the existence and rate of proton decay. Experimental evidence shows that if the proton is unstable, it has a half-life of at least 6.6x1033 years. If a Grand Unified Theory is correct, then there are theoretical reasons to believe that the half-life of the proton is less than 1041 years. Over the next googol years or so positrons and electrons so formed by this decay can expect to annihilate each other or be drawn into black holes, or both. In the event protons do not decay as described above, the degenerate era will last longer, and will overlap the black hole era. Matter could be liquid at zero temperature some 1065 years from now. Apparently rigid objects such as rocks will be able to rearrange their atoms and molecules via quantum tunneling, behaving as a liquid does, but more slowly. Gravitational fields may affect the rate of proton decay, and protons may decay more rapidly inside black holes, and may decay via processes involving virtual black holes, or other higher-order processes with a half-life of fewer than 10200 years. Some models predict the simultaneous decay of two baryons (ΔB=2). Experimental evidence shows that the half-life of such particles would be at least 1030 years, but calculations show it would be around 10101 years. ,

It may also be that bound nucleons may resist decay more than free protons do, particularly in elements with magic numbers. "Double-magic" elements include oxygen-16, calcium-40, and lead-208, the heaviest stable element, and possibly zirconium-90,. Sulfur-32 may also be a double-magic element. Helium-4 is the only "triple-magic" element, where the proton, neutron, and electron shells are all filled.

Black Hole Era
Black holes are not immortal and will slowly evaporate via Hawking radiation. A black hole with a mass of around 1 solar mass will vanish in around 2×1066 years. However, many of these are likely to merge with supermassive black holes at the center of their galaxies through processes described above long before this happens. As the lifetime of a black hole is proportional to the cube of its mass, more massive black holes take longer to decay, but even these giants are not immortal... a supermassive black hole with a mass of 1011 (100 billion) solar masses will evaporate in around 2×1099 years.

Hawking radiation has a thermal spectrum. During most of a black hole's lifetime, the radiation has a low temperature and is mainly in the form of massless particles such as photons and gravitons. As the black hole's mass decreases, its temperature increases, becoming comparable to the Sun's by the time the black hole mass has decreased to 1019 kilograms. The hole then provides a temporary source of light during the general darkness of the Black Hole Era. During the last stages of its evaporation, a black hole will emit not only massless particles but also heavier particles such as electrons, positrons, protons and antiprotons.

If bound nucleons resist decay more than free protons
Iron and nickel nuclei are the most tightly bound nuclei of all the elements, followed by chromium. If this binding energy helps them resist decay by the processes described above, they could still decay, but more slowly. The rest of this article assumes the following premises:


 * Free protons decay more readily than bound nucleons and have a half-life of between 1033 and 1041 years as described above. Long before this has happened, most hydrogen outside of biospheres would have been used up in stellar formation.


 * Next to disappear will be the lighter elements such as helium-3, lithium, boron, and nitrogen. These are often "odd-odd" elements. Helium-4 may last a little longer as a double-magic element. Deuterium, another odd-odd element, may get used up in stellar fusion before this happens. Lithium may also be largely used up before this happens, as stars tend to burn up lithium before they arrive on the main sequence.


 * While baryon-decay and tunnel-fusion are opposing processes for lightweight elements, in the case of heavy metals such as lead and mercury, baryon decay would help move them toward the iron group. Thus, gold and silver coins could decay to nickel--not that anyone will be around to care. If lead-208's double-magic properties somehow prevent baryon decay, its nuclei could fission into zirconium-90 and tin-118, with the latter (having a magic number of 50 for its protons) then fissioning into iron-56 and nickel-62. Both of these processes would also release electrons as beta rays. Zirconium may last a bit longer in this case, though it could fission to nickel, oxygen, and carbon nuclei, or to iron and two oxygen nuclei. It could also react with oxygen or sulfur nuclei to produce chromium or nickel nuclei, respectively, and without any conversion of neutrons to protons, or vice versa.

Different fates for different dwarfs?
If nuclear binding energy can impede baryon decay, we can postulate that some degenerate stars, specifically oxygen-neon-magnesium (O-Ne-Mg) dwarfs, or "1-mags", might tunnel to iron while the other dwarfs fade from existence by baryon decay. This hypothesis is based on the following premises:


 * Oxygen-16 is a double-magic element while carbon is not. An ignonomous end could be in store for carbon dwarfs--as their mass decays and internal pressures ease up, the "diamonds in the sky" turn to graphite. As the carbon component continues to decay, the graphite disappears and the remaining carbon should be bound with oxygen as carbon dioxide, or floating bits of "dry ice" that evaporate away. In the case of helium dwarfs, while helium is a double-magic element, it still has a lower binding energy than carbon because it is so lightweight.


 * The neon component in 1-mags decays to double-magic O-16, which can then tunnel-fuse with magnesium-24 to produce another double-magic element, calcium-40. Calcium-40 can then tunnel-fuse with another oxygen nucleus to give nickel-56, which then captures electrons to become iron-56. Three oxygen nuclei can in theory merge to form a chromium nucleus, but this would need to somehow acquire more neutrons in order to be stable. Sulfur, produced by merging of two oxygen nuclei, has recently been discovered to posess a magic number. Sulfur and calcium could fuse to produce such elements as zinc, germanium, and selenium, which then decay to nickel. Likewise, zirconium (see above) could react with magnesium-24 to produce iron-56 and iron-58 nuclei, while zirconium with calcium-40 could produce zinc nuclei, which decay to nickel.


 * A peculiar feature of degenerate stars is that their volume is inversely proportional to their mass, resulting in their internal densities being that much greater. These greater densities may help push nuclei together in the fusion processes described above.

The universe's "iron age"
101500 to 101600 years from now

As has been stated, iron and nickel are considered to have the most stable nuclei. Looking at their binding energies and mass/nucleon, we see some interesting results. Iron-56 has the lowest mass per nucleon, followed by nickel-62 and then nickel-60 when you include the electron cloud. Without the electron cloud iron-56 has the lowest mpn, but the relative positions of the two nickel isotopes are reversed. The fourth lowest mpn is chromium-52, followed by iron-58, though Cr-54 has a slightly higher binding energy than Cr-52. This is not inconsistent, as neutrons have a higher mass than protons. When one looks at binding energy, Ni-62 has the strongest binding energy, followed by Fe-58 and then Fe-56.

So how would these isotopes stack up? Specifically, how would they interact? Fe-56 has both stronger binding energy and a lower mass per nucleon than Ni-60, while Ni-62 has both stronger binding energy and lower mpn than Fe-58. Thus, in theory Ni-60 could transfer an alpha particle to an Fe-58 nucleus, forming Fe-56 and Ni-62 nuclei. In such a scenario nickel-60 would similarly donate alpha particles to Cr-52 and Cr-54 nuclei, producing to Fe-56 and Fe-58. Thus iron-56 and nickel-62 would be considered “end-points” of this series of reactions.

In 101500 years, cold fusion occurring via quantum tunneling should make the light nuclei in black dwarfs fuse into iron-56 nuclei, leaving stellar-mass objects as cold spheres of iron (assuming these light nuclei are able to resist decay more than free protons). Heavy metals such as lead and bismuth lose mass through a combination of nuclear fission and ά-particle emissions, eventually becoming iron and nickel. Quantum tunneling may also make iron stars collapse into neutron stars in around 101600 years, or possibly later. Also, if iron stars are magnetic they could concievably attract other iron or nickel objects, a process that might push them over the Chandrasekhar limit. Neutron stars may in turn collapse into exotic stars. Non-degenerate matter has been calculated to tunnel to iron in approximately years.

On the other hand, if iron's nuclear binding energy does not prevent proton decay, its nuclei will decay to lighter nuclei, including oxygen and hydrogen. In theory iron could rust in outer space!

We've also seen that the electron cloud can influence nuclear binding energy. If this is the case, then binding energy can also be influenced by whether iron or nickel is combined with other elements. In addition to rust, other compounds include iron(II) sulfate and nickel sulfate. Non-hydrated compounds include ferric sulfate, pentlandite and lodestone. There are also iron-nickel alloys.

The neutrino era $$10^{10^26}-10^{10^76}years$$
Quantum tunnelling should also turn large objects into black holes, which then decay by Hawking radiation. Depending on the assumptions made, the time this takes to happen can be calculated as from 10 10 26 to 10 10 76 years. The lower figure is based on the concept of Planck-sized portions of matter collapsing to black holes and releasing Hawking radiation in the form of neutrinos. In the case of degenerate stars, only neutrinos would be able to escape through degenerate matter, so neutron and quark stars would decay to neutrinos over a period of 10 26 years. Preon stars, if they exist, are of planetary mass and impervious to neutrinos, and may take 1010 32 years to collapse to black holes, which will then disappear by Hawking radiation quickly on these time scales. The only baryonic matter still extant will be dust particles smaller than a tenth of a micron in diameter. Through a process of random fluctuations these elements may then merge to create a new "big bang" in 1010 56 years. On the other hand, some stellar remnants may persist to 1010 76 years before collapsing into black holes.

So just how big are these numbers? Well, 10 10 26 is 10100000000000000000000000000, or one followed by 100 septillion zeroes. Take this number to the millionth power to get 1010 32. Now take that number in turn to the septillionth power to get 1010 56. Now take that number to the hundred quintillionth power to get 1010 76.

$$10^{10^76}={10^{10^26}}^\sqrt{googol}$$

Dark Era
$$10^{10^76}-10^{10^{10^2.08}} years$$

The lowly photon is now king of the universe as the last of the black holes evaporate. After all the black holes have evaporated (and after all the ordinary matter made of protons has disintegrated, if protons are unstable), the universe will be nearly empty. Photons, neutrinos, electrons and positrons will fly from place to place, hardly ever encountering each other.

By this era, with only very diffuse matter remaining, activity in the universe will have tailed off dramatically, with very low energy levels and very large time scales. Electrons and positrons drifting through space will encounter one another and occasionally form positronium atoms. These structures are unstable, however, and their constituent particles must eventually annihilate. Other low-level annihilation events will also take place, albeit very slowly.

Even photons and neutrinos may not be immortal. Light is known to be bent by traveling near mass objects because of their gravitational field, and when objects are accelarated by these fields a portion of their mass is lost as gravitational radiation. Thus matter and electromagnetic radiation can expect to eventually decay to gravitational radiation. By 1010 120 years the universe may finally experience heat death.

According to one model, the total number of universes is about $$10^{10^{10,000,000}}$$.