# Mass distribution in the early universe

The latest big quasar find at ~12.8 bn LJ with an estimated mass of 12 bn M☉ (see e.g. http://www.newscientist.com/article/mg22530104.000-ancient-black-hole-had-an-inexplicable-growth-spurt.html) puts current black-hole-forming hypotheses into question. As the linked article explains, scientist doubt that most of the matter could pass into the hole in such a short time due to the outward pushing force of the radiation created by the material falling into it.

My question is rather, was there enough matter in such a close vicinity of a BH that it could grow to this size? At 900 million years from the big bang I have the feeling that there is hardly enough time for the required matter to even pass through the volume around the BH where accretion can happen.

One way of assessing the feasibility would be just to ask what a freefall timescale would be. If you have say $10^{11}\ M_{\odot}$ in a sphere of radius 10 kpc (I am just using typical sorts of numbers for a big galaxy), then the average density is $5\times 10^{-22} kg/m^{3}$ and has a freefall time $\sim (G\rho)^{-1/2}$ of 200 million years. Of course there are other problems, like shedding angular momentum, but it looks like this timescale is short enough for gravity to do its thing (in the absence of radiation pressure).