The mass function of high-redshift seed black holes

In this Letter we derive the mass function of seed black holes that result from the central mass concentrated via disc accretion in collapsed haloes at redshift z approximate to 15. Using standard arguments including stability, we show that these pregalactic discs can assemble a significant mass concentration in the inner regions, providing fuel for the formation and initial growth of supermassive black holes. Assuming that these mass concentrations do result in central seed black holes, we determine the mass distribution of these seeds as a function of key halo properties. The seed mass distribution determined here turns out to be asymmetric and skewed to higher masses. Starting with these initial seeds, building up to 109 solar masses by z = 6 to power the bright quasars is not a problem in the standard Lambda cold dark matter cosmogony. These seed black holes in gas-rich environments are likely to grow into the supermassive black holes at later times via mergers and accretion. Gas accretion on to these seeds at high redshift will produce miniquasars that likely play an important role in the reionization of the Universe. Some of these seed black holes, on the other hand, could be wandering in galaxy haloes as a consequence of frequent mergers, powering the off-nuclear ultra-luminous X-ray sources detected in nearby galaxies.