2004MNRAS.354..443I

The first stars forming in minihaloes at redshifts greater than 20 may have been very massive, and could have left behind massive black hole (MBH) remnants. In a previous paper we investigated the hierarchical merging of these MBHs and their associated haloes, using a semi-analytical approach consisting of a hierarchical merger tree algorithm and explicit prescriptions for the dynamics of merged substructure inside a larger host halo following a merger. One of the results was the prediction of a number of MBHs orbiting throughout present-day galactic haloes. In addition, we estimated the mass-accretion rate of these MBHs, assuming that they retained around them a core of material from the original haloes in which they formed. On the basis of these estimates, in this paper we determine the bolometric, optical and X-ray luminosity functions for accreting MBHs, using thin-disc and advection-dominated accretion-flow models. Our predicted MBH X-ray fluxes are then compared with observations of ultraluminous X-ray sources in galaxies. We find that the slope and normalization of the predicted X-ray luminosity functions are similar to those observed, suggesting that MBHs could account for some fraction of these sources.