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

138 LISA: A proposed joint ESA–NASA gravitational-wave missionstationary non-relativistic equilibrium state that can be supported for very long.Under the cloud collapse scenario, an important question is whether signalsare likely to be produced that LISA could see. For example, if a supermassivestar forms and then evolves to the relativistic instability, the final collapse to aMBH could be slow enough that most of the gravitational-wave radiation wouldbe at such low frequencies that LISA would have poor sensitivity. Also, ifthe collapse were nearly spherically symmetric, the radiative efficiency wouldbe poor. However, recent fully relativistic calculations by Baumgarte andShapiro [59] of the evolution of a rotating supermassive star up to the onset ofcollapse provide some basis for a more optimistic view. The later evolution canbe determined reliably only by a numerical, three-dimensional hydrodynamicssimulation in general relativity. However, estimates of what will happen indicatethat most of the mass will go into a MBH, and that a bar instability which radiatesefficiently at frequencies observable by LISA may form.Even if the supermassive black holes in quasars at high redshifts are formedinitially by cloud collapse, it still seems quite possible that the collisional growthscenario may contribute substantially to the formation of seed black holes formore modest sized MBHs, like the one in our galaxy. Under the collisionalgrowth scenario, if a number of 500M ⊙ seed black holes are formed beforerunaway growth occurs and the largest has already swallowed the others, thenthe coalescence of two of these seeds could be seen by LISA even at a substantialredshift. For such a coalescence at z = 5, it can be shown that the signal strengthas a function of frequency during the last year before coalescence, for a circularorbit, would stay just about at the LISA threshold sensitivity curve level, so theevent would be detectable with S/N = 5.A remaining question, even if many intermediate sized MBHs are producedby the collisional growth of seeds, is whether the time of runaway growth ofthe largest seed black hole would be delayed to high enough mass for LISA toobserve the coalescences. As pointed out by Lee [60], the calculations of Quinlanand Shapiro are based on the Fokker–Planck approach, and that approach doesnot allow for the proper statistical treatment of a runaway instability. This is truefor the calculations of Lee [55] also. In considering this issue, it should be notedthat only the chirp mass for the binary is important for determining the signalstrength and frequency as a function of time. Thus the coalescence of a 100M ⊙black hole with a 4000M ⊙ one would be as observable as for two 500M ⊙ blackholes. Further work on the runaway growth question, as well as on the overallcollisional growth and cloud collapse scenarios, certainly would be valuable.10.2.3 Massive black holes in normal galaxiesAnother important astrophysical question concerns the abundance of intermediatesize MBHs of roughly 10 5 –10 6 M ⊙ . From observations based almost entirely ongalaxies containing larger MBHs and SMBHs, various authors have estimatedthat the mass of the central object is about 500 times smaller than the mass of the