Mass Functions of Supermassive Black Holes Across Cosmic Time

The black hole mass function of supermassive black holes describes the evolution of the distribution of black hole mass. It is one of the primary empirical tools available for mapping the growth of supermassive black holes and for constraining theoretical models of their evolution. In this review we discuss methods for estimating the black hole mass function, including their advantages and disadvantages. We also review the results of using these methods for estimating the mass function of both active and inactive black holes. In addition, we review current theoretical models for the growth of supermassive black holes that predict the black hole mass function. We conclude with a discussion of directions for future research which will lead to improvement in both empirical and theoretical determinations of the mass function of supermassive black holes.Comment: 40 pages, 7 figures, review paper accepted for the Advances in Astronomy Special Issue "Seeking for the Leading Actor on the Cosmic Stage: Galaxies versus Supermassive Black Holes

Black Holes, Mergers, and the Entropy Budget of the Universe

Vast amounts of entropy are produced in black hole formation, and the amount of entropy stored in supermassive black holes at the centers of galaxies is now much greater than the entropy free in the rest of the universe. Either mergers involved in forming supermassive black holes are rare,or the holes must be very efficient at capturing nearly all the entropy generated in the process. We argue that this information can be used to constrain supermassive black hole production, and may eventually provide a check on numerical results for mergers involving black holes

Hierarchical build-up of galactic bulges and the merging rate of supermassive binary black holes

The hierarchical build-up of galactic bulges should lead to the build-up of present-day supermassive black holes by a mixture of gas accretion and merging of supermassive black holes. The tight relation between black hole mass and stellar velocity dispersion is thereby a strong argument that the supermassive black holes in merging galactic bulges do indeed merge. Otherwise the ejection of supermassive black holes by gravitational slingshot would lead to excessive scatter in this relation. At high redshift the coalescence of massive black hole binaries is likely to be driven by the accretion of gas in the major mergers signposted by optically bright QSO activity. If massive black holes only form efficiently by direct collapse of gas in deep galactic potential wells with v_c > 100 km/s as postulated in the model of Kauffmann & Haehnelt (2000) LISA expects to see event rates from the merging of massive binary black holes of about 0.1-1 yr^{-1} spread over the redshift range 0 < z < 5. If, however, the hierarchical build-up of supermassive black holes extends to pre-galactic structures with significantly shallower potential wells event rates may be as high as 10-100 yr^{-1} and will be dominated by events from redshift z > 5.Comment: 8 pages, 4 postscript figures. Proceedings of the 4th International LISA Symposium, Penn State University, 19-24 July 2002, ed. L S Fin

Measuring spin of a supermassive black hole at the Galactic centre -- Implications for a unique spin

We determine the spin of a supermassive black hole in the context of discseismology by comparing newly detected quasi-periodic oscillations (QPOs) of radio emission in the Galactic centre, Sagittarius A* (Sgr A*), as well as infrared and X-ray emissions with those of the Galactic black holes. We find that the spin parameters of black holes in Sgr A* and in Galactic X-ray sources have a unique value of $\approx 0.44$ which is smaller than the generally accepted value for supermassive black holes, suggesting evidence for the angular momentum extraction of black holes during the growth of supermassive black holes. Our results demonstrate that the spin parameter approaches the equilibrium value where spin-up via accretion is balanced by spin-down via the Blandford-Znajek mechanism regardless of its initial spin. We anticipate that measuring the spin of black holes by using QPOs will open a new window for exploring the evolution of black holes in the Universe.Comment: 5 pages, 3 figures, accepted by MNRAS LETTE

The Role of Primordial Kicks on Black Hole Merger Rates

Primordial stars are likely to be very massive \geq30\Msun, form in isolation, and will likely leave black holes as remnants in the centers of their host dark matter halos in the mass range 10^{6}-10^{10}\Ms. Such early black holes, at redshifts z\gtsim10, could be the seed black holes for the many supermassive black holes found in galaxies in the local universe. If they exist, their mergers with nearby supermassive black holes may be a prime signal for long wavelength gravitational wave detectors. We simulate formation of black holes in the center of high redshift dark matter halos and explore implications of initial natal kick velocities conjectured by some formation models. The central concentration of early black holes in present day galaxies is reduced if they are born even with moderate kicks of tens of km/s. The modest kicks allow the black holes to leave their parent halo, which consequently leads to dynamical friction being less effective on the lower mass black holes as compared to those still embedded in their parent halos. Therefore, merger rates may be reduced by more than an order of magnitude. Using analytical and illustrative cosmological N--body simulations we quantify the role of natal kicks of black holes formed from massive metal free stars on their merger rates with supermassive black holes in present day galaxies. Our results also apply to black holes ejected by the gravitational slingshot mechanism.Comment: 12 pages, 9 figure