The Supernovae At the End of Time (Script) (Patreon)

Good news everyone: it looks like the universe is going to end with a series of catastrophic explosions.

A little while ago we did a series on the end of the world - I should say “ends” plural, because many very final-seeming fates await the Earth, then solar system, then galaxy, and ultimately the universe. The very very long story short is that the universe ends in heat death, as it approaches maximum entropy, and its eternal exponential expansion drives it to effective utter emptiness and absolute cold. The last interesting thing to happen will be the final explosions as the  last black holes evaporate - and even those will be relatively weak-sauce as far as space explosions go. Just tiny pops scattered across the end of time, before an eternity of perfect boringness.

Well, I have an urgent update for you. New calculations have revealed we may be able to look forward to one last source of astrophysical cataclysms - a new type of supernova that can only happen at the end of the universe. I should also warn you - if you are inclined to ask “why should we care” - then this episode is not for you. This information has literally zero impact on anything humans are ever likely to witness. But for the more long-term thinkers among you, grab your popcorn because your favorite TV show -  AKA the far future of the universe - just got renewed for another season.

Let’s actually start our story at the end. In roughly 10^32000 years from now, give or take several orders of magnitude, the last iron star will be teetering on the edge of catastrophe. The hyperdense crystalline ball of quantum weirdness has supported itself against gravitational collapse by the pressure exerted by its electrons alone. But its electrons have been vanishing for aeons. When one too many vanish, the entire star will undergo catastrophic collapse, and then rebound as a spectacular supernova explosion - a last firework to celebrate the end of time.

So yeah, that’s the end of the story. Much more climactic that the previous version, with black holes fizzling out - at least this one has some decent ka-booms. The update is due to new work by astrophysicist Matt Caplan, and I’ll get to the details of that finding.

First, there are many questions to be answered - how does the Sun end up as one of these “iron stars” in the first place? What’s happening to its electrons? To get to the bottom of these mysteries we’ll need to rewind to the beginning of the story. Well not quite the very beginning, but on the timescales of iron stars pretty close to it. We’re a mere 13.7 billion years after the big bang, when one of these iron stars was in its extremely brief phase as a bright ball of hydrogen, bathing a young planetary systems in the energy produced by its fusion engine. On one of those planets - the third one out - a steamship is making its slow journey to a place that the local carbon based lifeforms call “England”.

On that ship - the SS Pilsna - Subrahmanyan Chandrasekhar - Chandra to his friends - was pondering the far future of the star whose warm light now bathed the deck. Chandra was one of very few in the world who knew that fate. In fact, he was on his way to Cambridge to begin his graduate studies with Ralph Fowler, the guy who had just discovered what that fate would be. This was in 1930, and while everyone else enjoyed a period of relative peace between the world wars, the scientific world was in the midst of a revolution.

The new science of quantum mechanics had shattered our classical understanding of the world in many ways. Fowler, for example, had discovered a new, theoretical state of ultra-dense matter - degenerate matter - in which atoms are stripped of their electrons, and then those electrons are crammed so close together that all possible quantum states are occupied. Now electrons can’t overlap - can’t occupy identical quantum states - a weird quantum fact that had also been recently discovered. Unable to get any closer, the electrons in this degenerate matter exert a powerful outward pressure - electron degeneracy pressure.

Fowler’s finding solved a great mystery of the time. A new type of star had been discovered - white dwarfs. These faint but searing-hot stars appeared to have densities so high that a single cubic centimeter of their material weighed a literal ton. Fowler realized they could be composed of his degenerate matter, and that degeneracy pressure alone would be enough to stop them from collapsing under their own intense gravitational field.

It had become clear that this must be the Sun’s fate. Once its nuclear fuel supply runs out, there would be no outward flow of energy to resist the gravitational crush. Its core would collapse until halted by electron degeneracy pressure. Meanwhile the outer layers would have been ejected, leaving its exposed core as a white dwarf. The most eminent physicists of the era were coming to believe that the white dwarf should be the fate of all stars.

Chandrasekhar, pondering the problem on the SS Pilsna, realized that the most eminent physicists were wrong. He realized that, while Fowler’s calculations for the state of the degenerate plasma were brilliant, they were also incomplete. They failed to incorporate the effects of Albert Einstein’s relativity theory, which predicted that the world looks very different to things traveling close to the speed of light. And in the extreme heat of a white dwarf, electrons would indeed be traveling fast enough for relativity to change the physics. Chandra redid Fowler’s calculation and discovered something wild. Although this degeneracy pressure could support a dead star up to a point - if that stellar remnant’s mass was too high then a new process would take over. The star’s own electrons would be driven into it nuclei in a process called electron capture. And fewer electrons means less electron degeneracy pressure, which means the star begins to collapse, which means more electrons driven into nuclei, and so in in a runaway process.

We now know that the end result is either a neutron star or a black hole, accompanied by a powerful supernova explosion. But on the HM. Pilsner, Chandra just knew that no white dwarf could exist above that mass limit - what we now call the Chandrasekhar limit, which for a stellar core made of the degenerate carbon should be 1.44 times the mass of the Sun. Not a bad start to graduate school - showing up on your professor’s doorstep having already improved on one of your prof’s major life achievements.

So let’s fast forward our story a little - to the very long, boring future of a stellar remnant below the Chandrasekhar limit. They start out hot and bright, but with no capacity to generate  new energy, they slowly radiate away the heat of their youth. As they cool, the once-searing plasma changes state. It freezes. The star crystalizes. In regular crystals, atoms or molecules are bonded into a lattice by sharing their electrons. In a white dwarf, the nuclei can never recapture their electrons to become atoms again. The electrons remain as a hot, degenerate plasma and continue their work of keeping the star from collapsing. Meanwhile the nuclei stop interacting with the electrons and slow down as they cool. They become almost motionless within the star, and slip into a regular grid pattern.

Eventually, all white dwarfs must cool to the temperature of ambient space - now a frigid 3 Kelvin, but in the future even colder as the universe expands and the cosmic background radiation disperses. Eventually, all white dwarf must fade to near-invisible nuggets we call black dwarfs.

To continue our story from here we need to enter an entirely new temporal regime. Deep inside the crystalized black dwarf that our Sun will become, a single carbon nucleus has been sitting neatly in its assigned column and row for many times the age of the universe. Suddenly it’ll find itself one row over - teleported due to fundamental quantum uncertainty it its position. This quantum tunneling lands the nucleus close enough to its neighbor that the two fuse into a heavier element. This process is called pycnonuclear fusion - and it will very VERY slowly convert the Sun’s core from carbon into the most stable form of matter - iron - over around 10^1500 years. The result is an iron star - or an iron black dwarf - the hypothetical fate of all stars whose cores are beneath the Chandrasekhar limit.

I should add here that there’s an alternative ending. All of this depends on protons themselves being fundamentally stable. If protons can decay, then the entire white dwarf will vaporize into a subatomic mist in a mere 10^32 or so years, long before it could become an iron star.

But assuming protons are stable, we’ll reach a point where the universe consists of only iron stars and radiation. And those iron stars are also doomed - they’ll quietly become black holes through countless aeons of more quantum tunneling - something like 10^10^75 years. And those black hole will evaporate rather quickly by comparison - leaking away as pure radiation in 10^60 years.

This absurdly long and dull future may have been given a little more sparkle. Matt Caplan, in a paper published in August this year, has found a way for some of these iron stars to end on a brighter note - as black dwarf supernovae.

Remember that the Chandresekhar limit gives the largest mass possible for a stellar remnant to be supported by this pressure. It depends on the number of electrons relative to the mass of the star. But Caplan performed a detailed analysis of the nuclear reactions that lead to an iron star, and found that the delicate balance is threatened. In the last stage of the pycnonuclear fusion process, two silicon nuclei fuse to produce nickel, and then one of the nickel’s protons emits a positron to become a neutron. The result is iron-56 - the most stable element in the universe. But that emitted positron is the antimatter counterpart of the electrons that are supporting the star from the collapse. It immediately annihilates with one of those electrons, depleting the star’s supply. By the time the iron star is fully formed, its Chandresekhar mass has dropped from around 1.44 to less than 1.2. times the Sun’s mass.

That means that a white dwarf - or now iron black dwarf - that was initially stable with a mass below the original Chandrasekhar limit could become unstable if it’s mass is greater than 1.16 solar masses. When that happens, catastrophic collapse should result in a new types of supernova that will only happen in that distant future - a black dwarf supernova. They’ll leave behind smaller iron cores or a neutron stars. For the largest such stars, you should expect the first explosions to begin in 10^1100 years from now, while those at the lower limit will take up to 10^32000 years to pop. And the remnants of our solar system get to see all of this - our Sun will stay a black dwarf - probably of crystalized iron - through all of this.

I know this is a relief to many of you - the prospect of an anticlimactic end of time weighed on my mind also. But we can rest a little easier - there’ll be at least one more interesting thing to look forward to - Iron stars exploding in unimaginably distant future of space time.