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 sling-shot 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) greater than or similar to 100 km s(-1) as postulated in the model of Kauffmann and Haelmelt (2000 Mon. Not. R. Astron. Soc. 311576) 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 less than or equal to z less than or equal to 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 greater than or similar to 5.