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So as I mentioned in my previous question in the series, the parent red dwarf star of a one-planet system, Eridanus, has frozen over due to an unknown reason. By a "frozen red dwarf star", I mean, that the hydrogen and helium and other trace elements of the star have been frozen down to near CMB temperature. Literally "frozen". The red dwarf star is now just solid hydrogen and solid helium (formed by the crushing pressures inside the star), with lakes of liquid helium on the surface. The orbiting planet, Taurus, now witnesses a 10,000 year long era of freezing darkness. The inhabitants of the planet Taurus, the Villagers have to survive this eon. Characteristics of Eridanus pre-freeze:

  • Mass - 0.0898 M☉

  • Radius - 0.1192 R☉

  • Bolometric luminosity - 0.000553 L☉

  • Age - 6.8 BY

  • Temperature - 2600 K

Characteristics of Taurus:

  • Mass - 2.4 Earth masses

  • Radius - 9,780.83 KM

  • Gravity - 10 m/s2

  • Axial tilt - 19.8 degrees

  • Mean Temperature - 12.8°C

  • Day length - 23h 39min

  • Semi-Major axis - 3,200,000 KM

I cannot calculate the final size of the red dwarf as it contracts from the sudden cooling, as I am not a physics nerd, however, I can say with some certainty that the frozen star would be really, really small, somewhere along the size of Neptune, if my estimates are correct.

In my scenario, Eridanus, is not frozen forever. As is slowly contracts, it liberates heat from the compression of matter. Eventually after 10,000 years, Eridanus relights back into a full-fledged red dwarf star, bathing the planet Taurus, and its inhabitants, the Villagers, with warmth and sunlight.

However, certain comments say the exact opposite. The red dwarf would basically supernova. The reason is that, because I cooled the star too quickly, the star just collapses at a fraction of lightspeed and rebounds back from the shockwaves and explodes into a supernova. The supernova, then rips apart the orbiting planet, Taurus, into dust, incinerating the Villagers. The Villagers have barely enough time to register any decrease in output, before they are ripped apart by the supernova

Basically, instead of witnessing a dark 10,000 year long freezing night, the Villagers instead witness a blinding flash of light in the sky, as the star collapsed from the freeze, and soon be incinerated. Again, I cannot calculate the brightness of a red dwarf going supernova from just freezing it, however if a certain XKCD article describes the Sun going supernova at 1 AU would be a billion times brighter than the Tsar Bomba detonating against your eyeball, Taurus being located just 3.2 million km from Eridanus, would most likely witness a similar apparent brightness.

Basically, I cannot figure out how, a red dwarf can go supernova from just cooling it down, so here I come up with this question:

Would a Red dwarf star actually go supernova from just cooling it down to near absolute zero suddenly?

(P.S Nevermind how the star cooled down so quickly. I will handwave away the issue of how I cooled a star so quickly, because for now, I am focused on the question on how a star can explode from just cooling down)

EDIT 1: To fraxinus:

The habitable zone of a red dwarf is a tidal nightmare. Your planet will not rotate for long.

As I described in a previous question (the First question in the series, in fact), Taurus is not tidally locked to Eridanus. Since I haven't found any papers about the possibility of non-tidally locked rotating planets around red dwarfs, for now, I'll just handwave tidal locking for now.

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    $\begingroup$ I didn't read your other question so I might have missed someone else saying this, but I'd just like to point out that there is pretty much no way to survive for that period of time with no sun except for high technology and nuclear power, no other powersource will allow a largish population to survive even a year at that temperature, your atmosphere would also collapse without the energy invested. Does remind me of an old story though--I think it was called "Bucket of Air" $\endgroup$
    – Bill K
    Commented May 24, 2023 at 0:02
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    $\begingroup$ @BillK its "Pail of Air" $\endgroup$
    – Alastor
    Commented May 24, 2023 at 3:08
  • $\begingroup$ The CMB is around 3K, not 0K. The difference might actually be significant given that we'd be talking about superfluids and other weird states of matter at that kind of temperature. $\endgroup$
    – N. Virgo
    Commented May 24, 2023 at 9:33
  • $\begingroup$ @N.Virgo I said "near 0K" not exactly "0K". $\endgroup$
    – Alastor
    Commented May 24, 2023 at 9:44
  • $\begingroup$ @FuriousArcturus sure, but whether 3K is "near" 0K or not is a matter of perspective. $\endgroup$
    – N. Virgo
    Commented May 24, 2023 at 10:02

4 Answers 4

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It isn't going to be quite as bad as it would be in a larger star, because a little red dwarf isn't held up by radiation pressure... it simply isn't hot enough to do that sort of thing so it is actually a fair bit more dense than a hotter star, on average. It won't collapse as far or as fast as a larger star would, and it doesn't have nearly as much matter to go skoom either.

So, using my powers of being largely ignorant of physics and mathematics but being prepared to assemble some latex markup anyway:

The gravitational potential energy of an isothermal cloud of gas which has a $\frac{1}{R^2}$ density profile, which is a not-totally-unreasonable model of your star, is $-\frac{GM^2}{R}$ (see this relevant astronomy.SE answer). This isn't a perfect model, but it'll do as a first approximation. The gas cloud therefore has an initial potential energy of approximately -2.5x1040 J. As the cloud shrinks, it trades potential energy for kinetic energy which will heat the cloud up again.

Now, you can use the virial theorem to show that when the gas cloud was a star with the given gravitational potential and radius, it must have had a thermal energy of ~1.25x1040 J in order to remain stable (less and it would shrink under gravity, more and it would expand due to its own heat). My guess is, then, by the time it has converted that much gravitational potential energy to kinetic energy it basically has to reignite, at which point it'll be hot enough to support its own weight again and it'll re-expand. You'll get to this point when the cloud has shrunk to 2/3rd of its original radius.

The free-fall timescale of your gas cloud is just a few minutes, which implies reignition in pretty short order. Exactly what happens at the point of reignition is unclear to me... the star should start fusing again, and will in due course re-expand, but I'm not sure how long that re-expansion would take and how quickly the outer layers of the gas cloud would return to their original temperatures. I'm also not sure if you'd end up with a pulse of more energetic fusion because the average density of the star has increased significantly (by a factor of ~3.4) which implies that reignition will be Quite Energetic. This doesn't seem like it might be a supernova-type situation... I don't think the collapse can continue long enough or fast enough to release that much energy, but you might still end up with a lot of exciting stellar activity up to and maybe including superflares which is still going to be pretty bad news for anyone nearby. Given the near-magical circumstances involve here, there's room to handwave in either direction as you see fit; no-one is going to run a simulation to prove you wrong because it is much too much like hard work for no gain.

Anyway, even if your freezing process involved a direct translation of your star to black dwarf status, in order to avoid unfortunately gravitational incidents of this kind, it isn't obvious to me that fusion would spontaneously restart anyway given that there's plenty of pressure available and given a bit of time it'll start cooking off. Your freezing has to be a much more magical effect in order to keep the star quiescent for long enough.

Short note on the use of the term "supernova": the unit of boom for supernovae is sometimes the FOE, meaning ten to the fifty-one ergs, equivalent to 1044 J. That's several orders of magnitude more energy than is required to reignite your star, so there's much too little energy here for anyone to reasonably call the effects a "supernova" even if there was a boom. Given that much of the energy released by the gravitational collapse will be absorbed by the very dense cloud of cold gas that's doing the collapsing, it might not even visibly nova. A parallel might be drawn with helium flashes in red giants which involve an incredible release of energy that barely registers on the surface of the star.

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    $\begingroup$ Thanks for the math, Starfish. Re-ignition at the core would be quick, but the heat generated would have no way to propagate to the non-core bits of the star, and the momentum of the falling frozen bits would prevent it from expanding. Pressure in the middle would easily reach red giant levels before the core had enough force to push through the non-ignited frozen parts. At minimum, the star would release centuries of fusion energy in a few minutes. $\endgroup$
    – Robert Rapplean
    Commented May 24, 2023 at 15:43
  • $\begingroup$ @RobertRapplean fusion in the core would reignite pretty promptly, I think... it is already very dense, much more so than the Sun. There's limited scope for it to collapse much further. The layer around the core will be the interesting bit. There will be a big energy release (and the star will necessarily be much hotter than normal at the point at which it expands) but the stupendous amount of energy required to reignite the star and reinflate it should go some way to absorbing the unrequested fusion surplus. $\endgroup$
    – Starfish Prime
    Commented May 25, 2023 at 8:11
  • $\begingroup$ @RobertRapplean remember also that the outer layers must necessarily be warming too... their density is increasing whilst they're still infalling, and they're also getting heated by the hotter and denser layers below them even before anything starts really cooking off. $\endgroup$
    – Starfish Prime
    Commented May 25, 2023 at 8:13
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    $\begingroup$ @RobertRapplean yeah, the whole thing is hideously difficult. The answer seems to be either "core possibly goes degenerate, everything else fuses promptlybut in an unstable and messy manner, you get a mini-version of a type-1a supernova" or "everything warms up promptly, star goes a bit wobbly, largely stays intact". Without access to an idle astrophysics postdoc and a compute cluster, I don't think there's an easy way to resolve it. $\endgroup$
    – Starfish Prime
    Commented May 26, 2023 at 9:03
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    $\begingroup$ @StarfishPrime The core has to go degenerate unless it reignites first as it has no other way of standing up to that pressure. And a fusion burn in a degenerate core goes wild for a little bit. It won't go type 1a because the burn is in the core rather than on the surface but it's going to be incredibly nasty. $\endgroup$
    – Loren Pechtel
    Commented Sep 25, 2023 at 15:08
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Gravitational accel. at the surface is about 2.5 km/s/s. Equation for final velocity given accel. & distance (radius) is: $v_{f}^2 = 2ax$. Plugging it in, I get 590 km/s, or 0.002 c. The rebound would be pretty gnarly, but not supernova levels. The speed of gas is below the escape velocity of the star (as all things dropping into a gravity well from less than infinity are), so maybe more like a nebula.

This doesn't address how the gas will reheat as it collapses and converts gravitational potential energy into kinetic energy of the particles. That energy all tallied up is probably very significant. I'll edit my answer later to look at that.

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  • $\begingroup$ The issue is not the energy release of the falling material, but that that energy release initiates a very intense pulse of fusion because the star is now way, way past the equilibrium point and will rebound. $\endgroup$
    – Loren Pechtel
    Commented Sep 25, 2023 at 15:10
  • $\begingroup$ @LorenPechtel Funny, I was just at another Q being critical of a Newtonian approach to a very complex scenario and yet here I am, doing the exact same thing lol. Yeah, now that you mention it, the fusion pulse would probably blow off much of the star. Maybe several times as it oscillates back and forth to equilibrium. It definitely won't be the same star afterwards. $\endgroup$
    – BMF
    Commented Sep 25, 2023 at 17:51
  • $\begingroup$ It's not that you used Newton, but that you missed the source of the problem. The infall energy can't explode the star but the reignition can. $\endgroup$
    – Loren Pechtel
    Commented Sep 25, 2023 at 23:07
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Some speculation:

If you manage to cool down the whole star to some manageable temperature of the core, yes it will stop fusing hydrogen.

On the other hand, you will have to actively cool it after the initial cooling down because it contains a some amount of radioactive elements (Uranium, Thorium, Potassium) that will heat it back from the inside.

This is slow enough and I am not sure it will work on 10ka timespan for a solar-metallicity star. On the other hand, you can make your star chemically peculiar and enrich it in heat-generating stuff.

In regard to the planet:

The habitable zone of a red dwarf is a tidal nightmare. Your planet will not rotate for long.

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What your describing doesn't happen in reality, of course, so we don't have a word for it.

What is the largest thing you can imagine getting dropped on your head? A meteor? If the thing being dropped gets big enough, we're really dropping our entire planet on that other thing. Let's start with a Mars-sized planetoid. The energy from that would easily melt our crust, sending us back to the pre-Cambrian.

Let's scale this up to where you're dropping half a star on the other half of the star. Stars are balls of super-hot gas, and the outer layers aren't very dense. Post-freezing, there's zero air pressure. There's nothing to slow the star-stuff down as it freefalls into itself.

We have numbers for what happens when a small chunk of a star falls onto another star. It's called a nova. It's not enough to fuse extra elements, but it's a burst of 10x radiation that would roast our planet pretty quickly.

This, however, does sound like enough energy to fuse the higher elements. Maybe up to Iron, but definitely well above Oxygen. It wouldn't actually be a supernova, but would definitely shred the solar system. Maybe a few orders of magnitude less powerful than a supernova. We'd probably just mis-classify it if we saw it.

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