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The 2012 apocalypse film features a premise that there are neutrinos from the sun that heat the Earth's core and thus leading to the end-of-the-world scenario.

Inspiration

Recently, a paper was published about dark stars - hypothetical objects that heat by the process of WIMP dark matter annihilation with itself instead of traditional nuclear fusion. Their formation relies on energy dissipation of dark matter by weak scattering on normal matter in a gas cloud, permitting its entrapment inside the cloud. When density reaches a critical limit, as the cloud tries to collapse into the star, the annihilation becomes frequent enough to prevent further collapse of the gas cloud preventing fusion. These stars are predicated to form only in regions with sufficient dark matter density, including the early universe and, possibly, centers of galaxies.

Modification

I propose to swap a debatable neutrino heating source from the film for a debatable dark matter annihilation heating source. Dark matter clumps inside the planet, close to its core, and then heats up, securing the end-of-the-world scenario.

The problem, there is not enough dark matter around the Earth.

So, the question is: How close Earth must be to Milky Way's center to undergo such a scenario?

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    $\begingroup$ "The problem, there is not enough dark matter around the Earth.": there isn't enough dark matter anywhere. The proposed dark stars would have the mass of millions of stars and be the diameter of the orbit of Jupiter. The heating of a planet would be negligible. $\endgroup$
    – Christopher James Huff
    Jul 21 at 12:44
  • $\begingroup$ @ChristopherJamesHuff, concerning dark stars, if I am not mistaken, It is proposed that it is possible for dark stars to form near the center of the galaxy in the original paper from same authors. It is unlilkly, sure, but not impossible. So the little heating of the core is not so far fetched either $\endgroup$
    – FrogOfJuly
    Jul 22 at 10:28
  • $\begingroup$ Again, the proposed dark stars are 10 AU across and have masses millions of times that of the sun. Dark stars are not planets, and planets are not dark stars. $\endgroup$
    – Christopher James Huff
    Jul 22 at 12:10

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Irrelevant: your planet is uninhabitable

As best I can determine, the "dark matter heating" mechanism referred to in that paper suggests that there might be a concentration of "dark photons" passing by, each with a mass of around $\mathrm{10^{−14}} eV/c^2$, each of which might be able to impart an energy of around 6 $\mathrm{eV}$ to a nearby atom.

The energy imbalance due to global warming is around $\mathrm{0.5\ Wm^-2}$, or $\mathrm{2.5\times10^{14}\ W}$ total. To match that with interactions delivering 6eV each, you need $2.65\times10^{32}$ of them every second. So you need to concentrate a source of 'radioactive dark matter' with an activity of $10^{32}\ \mathrm{s^{-1}}$ inside your overheated planet. Assuming a uniform distribution, that's $2.5 \times 10^{11}\ \mathrm{s^{-1}m^{-3}}$ activities per unit volume per second.

WIMPs are seriously un-interactive: the interaction cross section for a WIMP with a nucleon is on the order of yoctobarns, or $\mathrm {5\times10^{-52}\ m^2}$. That means crudely you need to have $\mathrm {10^{63}}$ WIMPs passing through each cubic metre of the earth at any given time, to get the activity you need. Unfortunately at $\mathrm {2\times10^{-50}\ kg}$ each those WIMPs have a density of around $\mathrm {10^{13}\ kg\ m^{-3}}$... which means your planet is hosting 5,500 solar masses worth of dark matter. Surface gravity is one billion times earth gravity.

It doesn't matter where in the universe your planet is located, you're not setting a human story there.

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  • $\begingroup$ Can you share the source for dark photon thing? Because I thought that WIMP heating is about annihilation, not radiation. WIMP flux is not the thing I am after, the idea in paper I linked is that through scattering on normal matter dark matter condenses and blobs in the center of Earth, increasing density and thus increasing annihilation rate. No flux here $\endgroup$
    – FrogOfJuly
    Jul 22 at 10:23
  • $\begingroup$ Edit: in the paper matter condences in the center of mass, not Earth's. $\endgroup$
    – FrogOfJuly
    Jul 22 at 10:30
  • $\begingroup$ Also, heating is not produced by interaction with the normal matter, but via annihilation of WIMPs with themselves $\endgroup$
    – FrogOfJuly
    Jul 22 at 10:37
  • $\begingroup$ The dark photons are from physics.aps.org/articles/v15/180, which on further reading of the original paper you linked to is not quite the same thing (your authors are vague about what exactly their dark matter particles are, only that they are their own antiparticles). The key equation in your paper ($Q=m_\chi n^2_χ \sigma$) makes no dimensional sense to me, but I suspect the principle is the same: in order to produce a dangerous amount of heating from barely-interacting dark matter, the density has to be excessively high. $\endgroup$
    – Stephen
    Jul 24 at 7:11

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