## Black Dwarf Supernovae

“Black dwarf supernovae”. They sound quite dramatic! And indeed, they may be the last really exciting events in the Universe.

It’s too early to be sure. There could be plenty of things about astrophysics we don’t understand yet—and intelligent life may throw up surprises even in the very far future. But there’s a nice scenario here:

• M. E. Caplan, Black dwarf supernova in the far future, Monthly Notices of the Royal Astronomical Society 497 (2020), 4357–4362.

First, let me set the stage. What happens in the short run: say, the first 1023 years or so?

For a while, galaxies will keep colliding. These collisions seem to destroy spiral galaxies: they fuse into bigger elliptical galaxies. We can already see this happening here and there—and our own Milky Way may have a near collision with Andromeda in only 3.85 billion years or so, well before the Sun becomes a red giant. If this happens, a bunch of new stars will be born from the shock waves due to colliding interstellar gas.

By 7 billion years we expect that Andromeda and the Milky Way will merge and form a large elliptical galaxy. Unfortunately, elliptical galaxies lack spiral arms, which seem to be a crucial part of the star formation process, so star formation may cease even before the raw materials run out.

Of course, no matter what happens, the birth of new stars must eventually cease, since there’s a limited amount of hydrogen, helium, and other stuff that can undergo fusion.

This means that all the stars will eventually burn out. The longest lived are the red dwarf stars, the smallest stars capable of supporting fusion today, with a mass about 0.08 times that of the Sun. These will run out of hydrogen about 10 trillion years from now, and not be able to burn heavier elements–so then they will slowly cool down.

(I’m deliberately ignoring what intelligent life may do. We can imagine civilizations that develop the ability to control stars, but it’s hard to predict what they’ll do so I’m leaving them out of this story.)

A star becomes a white dwarf—and eventually a black dwarf when it cools—if its core, made of highly compressed matter, has a mass less than 1.4 solar masses. In this case the core can be held up by the ‘electron degeneracy pressure’ caused by the Pauli exclusion principle, which works even at zero temperature. But if the core is heavier than this, it collapses! It becomes a neutron star if it’s between 1.4 and 2 solar masses, and a black hole if it’s more massive.

In about 100 trillion years, all normal star formation processes will have ceased, and the universe will have a population of stars consisting of about 55% white dwarfs, 45% brown dwarfs, and a smaller number of neutron stars and black holes. Star formation will continue at a very slow rate due to collisions between brown and/or white dwarfs.

The black holes will suck up some of the other stars they encounter. This is especially true for the big black holes at the galactic centers, which power radio galaxies if they swallow stars at a sufficiently rapid rate. But most of the stars, as well as interstellar gas and dust, will eventually be hurled into intergalactic space. This happens to a star whenever it accidentally reaches escape velocity through its random encounters with other stars. It’s a slow process, but computer simulations show that about 90% of the mass of the galaxies will eventually ‘boil off’ this way — while the rest becomes a big black hole.

How long will all this take? Well, the white dwarfs will cool to black dwarfs in about 100 quadrillion years, and the galaxies will boil away by about 10 quintillion years. Most planets will have already been knocked off their orbits by then, thanks to random disturbances which gradually take their toll over time. But any that are still orbiting stars will spiral in thanks to gravitational radiation in about 100 quintillion years.

I think the numbers are getting a bit silly. 100 quintillion is 1020, and let’s use scientific notation from now on.

Then what? Well, in about 1023 years the dead stars will actually boil off from the galactic clusters, not just the galaxies, so the clusters will disintegrate. At this point the cosmic background radiation will have cooled to about 10-13 Kelvin, and most things will be at about that temperature unless proton decay or some other such process keeps them warmer.

Okay: so now we have a bunch of isolated black holes, neutron stars, and black dwarfs together with lone planets, asteroids, rocks, dust grains, molecules and atoms of gas, photons and neutrinos, all very close to absolute zero.

I had a dream, which was not all a dream.
The bright sun was extinguishd, and the stars
Did wander darkling in the eternal space,
Rayless, and pathless, and the icy earth
Swung blind and blackening in the moonless air.

— Lord Byron

So what happens next?

We expect that black holes evaporate due to Hawking radiation: a solar-mass one should do so in 1067 years, and a really big one, comparable to the mass of a galaxy, should take about 1099 years. Small objects like planets and asteroids may eventually ‘sublimate’: that is, slowly dissipate by losing atoms due to random processes. I haven’t seen estimates on how long this will take. For larger objects, like neutron stars, this may take a very long time.

But I want to focus on stars lighter than 1.2 solar masses. As I mentioned, these will become white dwarfs held up by their electron degeneracy pressure, and by about 1017 years they will cool down to become very cold black dwarfs. Their cores will crystallize!

Then what? If a proton can decay into other particles, for example a positron and a neutral pion, black dwarfs may slowly shrink away to nothing due to this process, emitting particles as they fade away! Right now we know that the lifetime of the proton to decay via such processes is at least 1032 years. It could be much longer.

But suppose the proton is completely stable. Then what happens? In this scenario, a very slow process of nuclear fusion will slowly turn black dwarfs into iron! It’s called pycnonuclear fusion. The idea is that due to quantum tunneling, nuclei next to each other in the crystal lattice within a black dwarf will occasionally get ‘right on top of each other’ and fuse into heavier nucleus! Since iron-56 is the most stable nucleus, eventually iron will predominate.

Iron is more dense than lighter elements, so as this happens the black dwarf will shrink. It may eventually shrink down to being so dense that electron pressure will no longer hold it up. If this happens, the black dwarf will suddenly collapse, just like heavier stars. It will release a huge amount of energy and explode as gravitational potential energy gets converted into heat. This is a black dwarf supernova.

When will black dwarf supernovae first happen, assuming proton decay or some other unknown processes don’t destroy the black dwarfs first?

This is what Matt Caplan calculated:

We now consider the evolution of a white dwarf toward an iron black dwarf and the circumstances that result in collapse. Going beyond the simple order of magnitude estimates of Dyson (1979), we know pycnonuclear fusion rates are strongly dependent on density so they are greatest in the core of the black dwarf and slowest at the surface. Therefore, the internal structure of a black dwarf evolving toward collapse can be thought of as an astronomically slowly moving ‘burning’ front growing outward from the core toward the surface. This burning front grows outward much more slowly than any hydrodynamical or nuclear timescale, and the star remains at approximately zero temperature for this phase. Furthermore, in contrast to traditional thermonuclear stellar burning, the later reactions with higher Z parents take significantly longer due to the larger tunneling barriers for fusion.

Here “later reactions with higher Z parents” means fusion reactions involving heavier nuclei. The very last step, for example, is when two silicon nuclei fuse to form a nucleus of iron. In an ordinary star these later reactions happen much faster than those involving light nuclei, but for black dwarfs this pattern is reversed—and everything happens at ridiculously slow rate, at a temperature near absolute zero.

He estimates a black dwarf of 1.24 solar masses will collapse and go supernova after about 101600 years, when roughly half its mass has turned to iron.

Lighter ones will take much longer. A black dwarf of 1.16 solar masses could take 1032000 years to go supernova.

These black dwarf supernovae could be the last really energetic events in the Universe.

It’s downright scary to think how far apart these black dwarfs will be when they explode. As I mentioned, galaxies and clusters will have long since have boiled away, so every black dwarf will be completely alone in the depths of space. Distances between them will be doubling every 12 billion years according to the current standard model of cosmology, the ΛCDM model. But 12 billion years is peanuts compared to the time scales I’m talking about now!

So, by the time black dwarfs start to explode, the distances between these stars will be expanded by a factor of roughly

$\displaystyle{ e^{10^{1000}} }$

compared to their distances today. That’s a very rough estimate, but it means that each black dwarf supernova will be living in its own separate world.

### 33 Responses to Black Dwarf Supernovae

1. Toby Bartels says:

Imagine life developing in the cooling aftermath of a black-dwarf supernova.

It wouldn't it be life as we know it, with no stars to provide a continuous source of power and no planets to live on, but as long as there are regions of higher and lower entropy, then there's the chance of complex processes developing on the interface, and this might include some form of life. Even if it's not common, as long as it's possible, it will happen somewhere.

Imagine intelligent life developing in the aftermath of a black-dwarf supernova.

Imagine intelligent life after a black-dwarf supernova with the wherewithal to conduct experiments and perform calculations, discovering the fundamental laws of physics and figuring out their consequences.

Imagine working out the theoretical possibility of a big bang, star formation and decay, black holes, black dwarfs, and black-dwarf supernovas. Imagine recognizing your surroundings as matching your predictions of the aftermath of a black-dwarf supernova.

Imagine realizing that the universe was once a much more vibrant place, that you were born too late, and that you are alone at the end of time.

• John Baez says:

Imagine realizing that the universe was once a much more vibrant place, that you were born too late, and that you are alone at the end of time.

Indeed.

Even in this much more lively early portion of the Universe, I’ve spent a certain amount of time getting used to the idea that someday everything will fizzle out. So much of our civilization seems premised on the assumption that things are worthwhile only if they will continue to have some effect. This seems to make sense over time scales of years, decades or maybe centuries—but somehow not millions or billions of years.

If the Universe fizzles out, was it “all in vain”?

• Paul Blann says:

As usual Penrose has an answer.

• Jon1 says:

If the Universe fizzles out, was it “all in vain”?

No, because there was fun to be had, and awe-inspiring stuff to learn & discover.

• arch1 says:

Yes indeed. And even creatures that never had a chance to experience our universe in its heyday will likely have different expectations and still potentially appreciate the specialness of their circumstances relative to the overwhelming majority of spacetime.

I don’t think one can conclude from this that every Hubble volume has a silver lining, though. If there can be Boltzmann brains there can be Boltzmann sufferers. And if we are in one of those multiverses containing an infinity of Hubble volumes exhibiting each physically possible history of quantum states, some of those histories will be unpleasant for all involved. I suppose all we can do in that case is what we should be doing in any case- make the most of and profoundly appreciate our own little piece of reality.

• If the Universe fizzles out, was it “all in vain”?

Well, with room temperature approaching absolute zero, quantum computers will at least start being feasible at some point.

• Ezequiel says:

Imagine any life evolving during one of the eras right after the big bang where the universe was the density of air, or water, or atomic nuclei, all throughout. What would they think of us now?

• John Baez says:

Indeed, it can be perfectly jolly if the temperature gradually drops to absolute zero and life continues ever more slowly, for example thinking at a rate inversely proportional to time, so the total amount of thinking done is proportional to the logarithm of time: the total amount of thinking done will still increase without bound as t → ∞. This point was made very vividly by Freeman Dyson.

Unfortunately if the Universe expands exponentially there will probably be a heat death at a low but nonzero temperature, due to the radiation from the cosmological horizon—so thinking will really grind to a halt.

This issue is discussed here:

• L. M. Krauss and G. D. Starkman, Life, the universe, and nothing: life and death in an ever-expanding universe, Astrophys. J. 531, (2000) 22-30.

Abstract. Current evidence suggests that the cosmological constant is not zero, or that we live in an open universe. We examine the implications for the future under these assumptions, and find that they are striking. If the Universe is cosmological constant-dominated, our ability to probe the evolution of large scale structure will decrease with time —presently observable distant sources will disappear on a time-scale comparable to the period of stellar burning. Moreover, while the Universe might expand forever, the integrated conscious lifetime of any civilization will be finite, although it can be astronomically long. We find that this latter result is far more general. In the absence of possible exotic and uncertain strong gravitational effects, the total information recoverable by any civilization over the entire history of our universe is finite, and assuming that consciousness has a physical computational basis, life cannot be eternal.

Also here:

• Katherine Freese and William Kinney, The ultimate fate of life in an accelerating universe, Physics Letters B 558 (2003), 1–8.

• When the entire observable universe was the density of nuclear matter, how large was it? Smaller than the solar system!

• Toby Bartels says:

They'd probably think about us the same as I'm thinking about those post-dwarf people. Fortunately, we still have a lot to explore around here. But at some point, if we don't die off but we also don't discover a way to go beyond the predictions in John's post, then we'll regret that we weren’t born earlier.

• Joel says:

This assumes a single universe. Today the common belief is more towards a multiverse which would change this completely. What changes may be seen in a multiverse?

• John Baez says:

I don’t think “the common belief is more towards a multiverse”. A lot of good physicists think the multiverse idea is untestable and not really scientific.

But anyway: in sufficently diverse multiverse, anything whatsoever can happen.

• True, but some very prominent physicists think that it is a very important idea.

Hundreds of years ago, someone not believing in divine intervention might have wondered why the Earth is just at the right distance from the Sun for life to exist. Claiming that stars are also suns and have planets at more or less random distances solves the problem. At the time, that was not testable, but it is now.

The multiverse is in a similar status.

(To be sure, there are some who claim that the multiverse follows from other theories. If true, then it doesn’t have to be testable directly; we believe what GR says happens inside black holes, for instance. However, those theories such as eternal inflation which more or less predict a multiverse are themselves somewhat speculative.)

• John Baez says:

At the time, that was not testable, but it is now. The multiverse is in a similar status.

One difference is that it’s easier to look around inside the universe than to look around at different universes.

Anyway, I’m very uninterested in the topic of the multiverse, so I should probably have not responded. I would much rather talk about Schur functors, the polyphony of Ockeghem, how plants respond to an excess of magnesium in the ground water, or any number of other topics.

Phillip – since you seem to understand the multiverse discussion – would a quantized space-time also count as a “multiverse”?

• Probably not, but the question is too vague. The general problem of comment-box conversations is even more difficult with topics like the multiverse, where there are actually several similar but quite distinct ideas. I recommend Max Tegmark’s Our Mathematical Universe, which is mostly about different types of multiverses. Even if you don’t agree with Max on all points, he himself is consistent and clear and it is a good introduction to the topic.

Probably not, but the question is too vague.

By quantized space-time I had mostly in mind the replacement of the algebra of commutative functions on a “phase-space” by a non-commutative algebra and its representations.

The general problem of comment-box conversations is even more difficult with topics like the multiverse, where there are actually several similar but quite distinct ideas.

Yes, I agree.
It seems a quantized space-time would be classified as a multiverse if one makes further assumptions about the “existence of quantum states”, like in particular if – I understand <a href=”https://en.wikipedia.org/wiki/MultiverseWikipedia correctly- if one adopts the Many-worlds interpretation.

I recommend Max Tegmark’s Our Mathematical Universe, which is mostly about different types of multiverses. Even if you don’t agree with Max on all points, he himself is consistent and clear and it is a good introduction to the topic.

Thanks for the recommendation. Yes I had seen that Max Tegmark is a distinguished scientist. Wikipedia writes:

He was awarded the Royal Swedish Academy of Engineering Science’s Gold Medal in 2019 for, according to the citation, “his contributions to our understanding of humanity’s place in the cosmos and the opportunities and risks associated with artificial intelligence. He has courageously tackled these existential questions in his research and, in a commendable way, succeeded in communicating the issues to a wider public.”

Unfortunately I think I have not enough time for reading about multiverses. I just wanted to confirm my understanding about the terminology that is involved with quantum gravity approaches.

2. The evolution of the world can be compared to a display of fireworks that has just ended: some few red wisps, ashes and smoke. Standing on a well-chilled cinder, we see the slow fading of suns, and we try to recall the vanishing brilliance of the origin of the worlds.

Bonus points if you recognize the author without googling!

• Supernaut says:

I’m guessing perhaps either O. Stapledon or H. G. Wells?

• Nope, though having read some stuff by both, that’s not a bad guess. Those two are up at the top for the combination of s.f. and literary skill. While Star Maker is great (even anticipating Max Tegmark’s various Multiverses), I liked Last and First Men even more.

The quote is from a famous cosmologist:
https://en.wikipedia.org/wiki/Georges_Lemaître

3. Pedro says:

Will Boltzmann brains form past that?

• John Baez says:

According to this paper, which I have not checked:

• Don Page, The lifetime of the Universe.

the probability that a 10 cm × 10 cm × 10 cm volume of vacuum will undergo quantum fluctuations creating a brain that lasts for 0.1 seconds is roughly

$\displaystyle{ e^{-10^{50}} }$

So, I believe this sort of Boltzmann brain only becomes likely in the observable Universe at time scales much longer than I’m talking about in my blog article.

• linasv says:

The very naughty question is, of course, “how can I know that I am not a Boltzmann brain, right now?”

• John Baez says:

Yes. And another question: what would it even mean to “know you are a Boltzmann brain” or “know you are not a Boltzmann brain”?

• Toby Bartels says:

I know I’m a Boltzmann brain, but heck if I know what you all are. 😁

4. Peter Erwin says:

Stars become white dwarfs—and eventually black dwarfs when they cool—if they have mass less than 1.4 solar masses.

That’s the limit on the mass of the degenerate core that forms at the heart of the star, late in its life. Any star with a total initial masses of less than 8 solar masses will end as a white dwarf, with most of the mass lost to stellar winds and the planetary nebula phase. (The Sun itself will end up as a white dwarf with a mass of about 0.5 solar masses.)

• John Baez says:

Thanks. I will correct my wording! In this black dwarf story we care about the mass of the star’s degenerate core.

5. I’ve started reading the Toby Ord paper – is there a timescale at which no particle anywhere is observable by any other, in the various senses he speaks of? It seems that with no remaining way to measure time passing, a Poincaire recurrence of our exact Universe, or something else cool, will occur ‘immediately’!

• John Baez says:

Hi, Allan! Great question!

I’ve never seen estimates on how long it takes black dwarf stars or neutron stars to ‘sublimate’—that is, disappear due to the loss of particles that randomly happen to acquire enough energy to be flung off. This process is very slow, but I think it’s inevitable since it decreases free energy! You see, it decreases entropy by an arbitrarily large amount as the density of gas in the surrounding interstellar space approaches zero, and the temperature is bounded below by about 10-30 kelvin if the ΛCDM model is correct, so this process will eventually decrease the free energy E – TS, no matter how much it increases the energy.

Since I don’t know how long this process takes, I don’t know if this is the limiting factor for reaching the time when “no particle anywhere is observable by any other”.

People calculating black dwarf lifetimes seem to be assuming that this process takes more than 1032000 years, because they’re not worrying that the black dwarfs may sublimate before they collapse. I would not myself assume that without doing some calculations. A lot can happen in 1032000 years.

However, once every particle become unbound to every other, it won’t take long for each one to become causally disconnected from every other, because the distance between them will double every 12 billion years, and 12 billion years is peanuts compared to the time scales we’re talking about here, or even the 10100 years it’ll take for supermassive black holes to evaporate.

In short, when it comes to answering your question, the expansion of the Universe is not the limiting factor. It’s the amount of time it takes for all particles to become unbound.

I should probably re-emphasize that at these long times, physics that we don’t understand yet will probably become important. It’s just fun to try to guess what will happen given the physics we know.

• arch1 says:

Wouldn’t the thing that occurs ‘immediately’ usually be a just another particle or two appearing – super uninteresting, but enough to measure time as it drags on, until they decay or get acausally distant?

If so (and even if we ignore the intervening timeless stretches) it seems the truly interesting configurations would still separated by vast stretches of measurable time.

6. Peter Erwin says:

Iron is more dense than lighter elements, so as this happens the black dwarf will shrink. It may eventually shrink down to being so dense that electron pressure will no longer hold it up.

That’s not quite what happens. The white dwarf is indeed held up against gravity by electron degeneracy pressure.The problem with converting the white dwarf to iron is that this involves fusing silicon-28 to form nickel-56, which decays to form cobalt-56, which in turn decays to (stable) iron-56. Each such decay removes an electron, and removing electrons reduces the electron degeneracy pressure. This in turn lowers the Chandrasekhar limit, so a massive enough C+O or O+Ne+Mg white dwarf can start out below the Chandrasekhar limit (for normal electron abundance) and then eventually find, once enough of its nuclei have been fused to iron-peak elements, that the limit has gone down to the point where it’s no longer stable.

• John Baez says:

Hmm! So it’s really just the decrease in electron number that does it? Would the maximum mass of a white dwarf made of iron nuclei and electrons be equal to the maximum mass of a white dwarf made of silicon nuclei and electrons? (Assume they’re both electrically neutral.)

• Peter Erwin says:

Yes, the maximum mass of a silicon (or lower-mass nuclei) white dwarf is the usual ∼1.4 solar masses; the maximum mass for an iron white dwarf is closer to 1.2 solar masses.

This site uses Akismet to reduce spam. Learn how your comment data is processed.