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

Expected gravitational-wave results from LISA 139spheroid (central bulge) of the galaxy. An even tighter relationship to the velocitydispersion in the spheroid has been reported recently [61]. However, the reasonsfor these relationships are not yet known [56, 62–64]. It appears likely that LISAdata can address whether a relation something like this extends to galaxies withsmaller spheroids, which constitute the majority of all galaxies.MBHs in galactic centres are expected to usually have an increased densityof stars around them in the region where the potential of the MBH dominates thatof the galaxy. This density cusp is usually taken to be a power law cusp, with a−7/4 power dependence on radius if the distribution of stellar motions is relaxedand a −3/2 power for some unrelaxed cusps. It is generally expected that therewill be large numbers of compact stars, i.e. white dwarfs and neutron stars, in thecusp. Occasionally, one of them that is on a nearly radial orbit and passes closeto the MBH may be deflected enough by the other stars so that it comes withinfive or so gravitational radii of the MBH and loses significant amounts of energyand angular momentum by gravitational radiation. If so, and if further deflectionsby the other stars are not important, the compact star orbit will continue to shrinkgradually until coalescence with the MBH occurs.Unfortunately, in almost all cases for white dwarfs and neutron stars, theabove gradual approach scenario is interferred with by interactions with otherstars. Hils and Bender [65] have simulated what happens for a particular modelwhich assumes 1M ⊙ for both the compact stars and the normal stars in the cusp.After the first pass near the MBH, the orbit of the compact star is modified byinteractions with the other stars more rapidly than by the gravitational radiation,unless the compact star is bound very tightly to the MBH initially. Thus thecompact star usually will plunge rapidly into the MBH, or its point of closestapproach will wander far enough away to not give appreciable interaction. A rapidplunge will not provide enough integration time for detection. In the remainingfavourable cases, the signal typically will be observable by LISA from a one yeardata record starting up to roughly 100 years before coalescence.Despite a loss of several orders of magnitude in the event rate due toplunging, the study by Hils and Bender [65] gave some hope of LISA seeing suchsignals. However, studies by Sigurdsson and Rees [66] and by Sigurdsson [67],plus an unpublished extension of the above study by Hils and Bender, indicatedthat the prospects were considerably better for observing gradual approaches tocoalescence with galactic centre MBHs for roughly 5 or 10M ⊙ black holes. Theeffect of mass segregation was included. Such events would be detectable at aredshift of z = 1 during the last year before coalescence for MBH masses from5 × 10 4 to 2 × 10 6 M ⊙ .Estimates of the event rate are certainly model dependent, but still offerencouragment that multiple signals of this kind will be observed. As an example,results obtained by Hils and Bender for one particular model are shown infigure 10.10. About 1% of the mass in the cusp was assumed to be in 7M ⊙black holes, and mass segregation was included. For each factor two range inthe mass of the central MBH about a nominal value M, and for each factor two