(ed.). Gravitational waves (IOP, 2001)(422s).

Expected gravitational-wave results from LISA 141distances by interaction with the black holes. If so, the estimated observable eventrate for white dwarfs and neutron stars from [65] could be drastically reduced.10.2.4 Structure formation and massive black hole coalescenceThe third of the important astrophysical questions that LISA has a good chance ofgiving new information on concerns the development of structure in the universe.It is currently believed that objects considerably smaller than galaxies formedfirst, and that continuing sequences of interactions and mergers led to the presentdistribution of galaxy types and sizes, and to galaxy clusters and superclusters. IfMBHs were already present in pre-galactic structures that merged, this could leadto the MBHs sinking down to the centre of the new structure by dynamical frictionand getting close enough together to coalesce due to gravitational radiation beforethe next merger [58, 69].The above scenario is quite attractive, and could give a high event rate forLISA. If so, valuable new constraints on the merger process and on the conditionsafter mergers would be obtained. However, there are a number of issues that affectthe event rate that have to be considered.One question is how effective dynamical friction will be in bringing MBHsof a given size to the centre of the new structure in less than the time betweenmergers. For galaxies like ours, the time required is less than the Hubble time forMBHs of roughly 3×10 6 M ⊙ or larger (see, e.g., Zhu and Ostriker [70]). However,the stars in the cusp around a MBH before merger will stay with it for some time,and will affect the dynamics. Thus, whether the mergers of pre-galactic structuresin galaxies like ours with fairly modest spheroid and MBH masses are likely tohave produced coalescences of perhaps 10 5 or 10 6 M ⊙ MBHs appears to be anopen one.There also is a question about whether the MBHs will modify the stardistribution near the centre of the new structure enough so that the dynamicalfriction will be decreased considerably. Calculations indicate that this may occurwhen the MBHs are fairly close together, but not yet close enough to coalesce bygravitational radiation in less than a Hubble time (see, e.g., Makino [71]. On theother hand, conditions such as Brownian motion of the MBH and tri-axiality in thestructure may affect the results, and there also may be complex enough motionsgoing on soon after a merger to change the conclusions. Thus the effectiveness ofthis ‘hang-up’ in the coalescence process is not known.Another question arises if another merger occurs before the MBHs from anearlier merger have coalesced. In principle, one, two or all three of the MBHscould be thrown out of the new structure by the slingshot effect. However, thenew merger could even have a beneficial effect, if the resulting disturbances inthe central star density overcame the possible hang-up for the earlier two MBHsand allowed them to coalesce.The signals arising from MBH coalescences after mergers of galaxies or ofpre-galactic structures would be very large. Figure 10.11 shows several cases