Post a Comment On: Backreaction

Black holes seem to be the most obvious explanation for the finding that galaxies harbor “dark” matter that doesn’t emit light but that makes itself noticeable by its gravitational pull. While the simplicity of the idea is appealing, we know that it is wrong. Black holes are so compact that they cause noticeable gravitational lensing, and our observations of gravitational lensing events allow to estimate that black holes are not enough to explain dark matter. Ruling out this option works well for black holes with masses about that of the Sun, 1033 grams, or heavier, and down to about 1024 grams. Gravitational lensing however cannot tell us much about lighter black holes because the lensing effect isn’t strong enough to be observable. Black holes lighter than about a solar mass cannot be created by stellar collapse; they must be created in the very early universe from extreme density fluctuations. These “primordial” black holes can be very light and the lightest of them could be decaying right now due to Hawking radiation. That we have not seen any evidence for such a decay tells us that primordial black holes, if they exist at all, exist only in an intermediate mass range, somewhere between 1017 and 1024 grams. It has turned out difficult to say anything about the prevalence of primordial black holes in this intermediate mass regime.

In a recent paper now three researchers from Berkeley and Stanford point out that these primordial black holes, and probably also other types of massive compact dark matter, should make themselves noticeable by igniting supernovae:
Dark Matter Triggers of Supernovae
Peter W. Graham, Surjeet Rajendran, Jaime Varela
arXiv:1505.04444 [hep-ph] The authors note that white dwarfs are lingering close by nuclear fusion and their idea is that a black hole passing through the white dwarf could initiate a runaway fusion process.

A white dwarf is what you get when a star has exhausted its supply of hydrogen but isn’t heavy enough to create a neutron star or even black hole. After a star has used up the hydrogen in its core, the core starts collapsing and hydrogen fusion to helium continuous for some while in the outer shell, creating a red giant. The core contracts under gravitational pressure, which increases the temperature and allows fusion of heavier elements. What happens further depends on the initial star’s total mass which determines how high the core pressure can get.

If the star was very light, fusion into elements heavier than carbon and oxygen is not possible. The remaining object - the “white dwarf” - is first very hot and dense but, since it has no energy supply, it will go on to cool. In a white dwarf, electrons are not bound to nuclei but instead form a uniformly distributed gas. The pressure counteracting the gravitational pull and thereby stabilizing the white dwarf is the degeneracy pressure of this electron gas, caused by the Fermi exclusion principle. In contrast to the pressure that we are used to from ideal gases, the degeneracy pressure does not change much with the temperature.

In their paper the authors study under which circumstances it is possible to ignite nuclear fusion in a white dwarf. Each fusion reaction between two of the white dwarf’s carbon nuclei produces enough energy to cause more fusion, thereby creating the possibility for a runaway process. Whether or not a fusion reaction can be sustained depends on how quickly the temperature spreads into the medium away from site of fusion. The authors estimate that white dwarfs might fail under fairly general circumstances to spread out the temperature quickly enough, thereby enabling a continuously feed fusion process.

Igniting such a runaway fusion in white dwarfs is possible only because in these stellar objects an increase in temperature does not lead to an increase of pressure. If it did, then the matter would expand locally and the density decrease, thereby effectively stalling the fusion. This is what would happen if you tried to convince our Sun to fuse heavier elements. The process would not run away, but stop very quickly.

Now if dark matter was constituted of small black holes, then the black holes should hit other stellar objects every now and then, especially towards the center of galaxies where the dark matter density is highest. A small black hole passing through a white dwarf at a velocity larger than the escape velocity would eat out a tunnel from the white dwarf’s matter. The black hole would slightly slow down as its mass increases but, more important, the black hole’s gravitational pull would accelerate the white dwarf’s matter towards it, which locally heats up the temperature.

In the paper the authors estimate that for black holes in a certain mass regime this acceleration would be sufficient to ignite nuclear fusion. If the black hole is too light, then the acceleration isn’t high enough. If the black hole is too heavy, then the tunnel in the white dwarf is too large and the matter doesn’t remain dense enough. But for black holes in the mass range of about 1022 gram, the conditions are just right for nuclear fusion to be ignited.

I find this interesting for two reasons. First, because it allows the authors to put constraints on the prevalence of primordial black holes from the number of white dwarfs and supernovae we observe, and these are constraints in a mass regime that we don’t know much about. Second, because it suggests a potential new mechanism to ignite supernovae.

[Image] Figure 3 from arxiv:1505.04444. The expected rate of additional 1a supernovae from primordial black holes igniting white dwarfs. Assumed is here that the primordial black holes make up most of the dark matter in galaxies.

The paper is based on rough analytical estimates and does not contain a detailed numerical study of a supernova explosion, which is a computationally very hard problem. One should thus remain somewhat skeptic as to whether the suggested ignition process will actually succeed in blowing up the whole white dwarf, or if it maybe will just blast off a piece or rip apart the whole thing into quickly cooling pieces. I would love to see a visual simulation of this and hope that one will come by in the soon future. Meanwhile, I’ve summed up my imagination in 30 frames :)

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