In the Dark

There’s a recent paper on arXiv with the title A direct black hole mass measurement in a Little Red Dot at the Epoch of Reionizationon by Juodžbalis et al. that is causing a lot of interest. The paper is here and the abstract is:

There is a discussion of this in the Grauniad here and in several other places on the interwebs. It comes hard on the heels of the theoretical paper announced here.

I only saw this paper yesterday and, now that I’ve read it, it isn’t really all that clear to me what this object is. No doubt there’ll be considerable follow-up. One possibility – and it is just a possibility – is that we are seeing evidence of a primordial black hole, called a PBH for short. These are black holes formed by direct collapse in the early Universe rather than by merging of stellar black holes. Note the use of the word “naked” is rather misleading. It does not mean a naked singularity, in the sense of a singularity without an event horizon around it. In this case it just means that it appears not to be surrounded by accreting material or even a host galaxy.

A PBH of mass M would form at a particular cosmic time t if a region of radiius ~ct (the cosmological horizon scale) collapses into a black hole. Obviously this would require a large fluctuation in density on that scale but if a PBH does form then its mass will be roughly the mass contained within the horizon, i.e. M ~ ρ(t) (ct)³ (ignoring dimensionless factors). The sort of mass required (~10⁶ M_☉) corresponds to a time when the Universe was radiation-dominated and before matter and radiation decoupled. What would be inside such a black hole is therefore predominantly trapped radiation, which is Quite Interesting, but as far as the outside universe is considered it’s just a massive black hole.

Anyway, during radiation domination, the mass-energy density of the Universe ρ(t) ∝ t^-2, so the horizon mass increases linearly with t. According to the standard cosmology, the epoch of radiation domination lasts for approximately 50,000 years after the Big Bang, i.e. of order 10¹² seconds, and at the end of it the horizon mass is of order 10¹⁴ M_☉. Assuming that the universe is completely radiation-dominated before that the time at which a PBH of mass 10⁶ M_☉ would form is about 10⁴ seconds, i.e. getting on for 3 hours after the Big Bang. This is after the end of cosmological nucleosynthesis, but not by much. Primordial black holes of lower mass than this would form earlier, with a stellar mass PBH having to collapse around the time of the quark-hadron transition. Lighter PBHs would form even earlier.

The numbers I’ve quoted are very approximate, back-of-the-envelope, ballpark guesstimates. For one thing not all of the horizon mass will end up in a PBH: energy may well be released during the collapse. Moreover, some PBHs on one scale will subsequently be subsumed within objects of larger mass. Also I’ve ignored quite a lot of numerical factors. All this will have to be worked out properly, but there are potential constraints on any physical processes that might give rise to PBHs on the relevant scale if they involve a release of significant amount of energy as there may not be time for this excess to be thermalized by scattering or they may intefere with the element abundances predicted by nucleosynthesis.

That is all assuming it is a primordial black hole in the first place…