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

142 LISA: A proposed joint ESA–NASA gravitational-wave missionFigure 10.11. Strain amplitudes during the last year before MBH–MBH coalescence. Thecurves are for MBH–MBH binaries at z = 1 with circular orbits, and for one year ofobservations with S/N = 5. For a given mass combination, the first five points from the leftare for 1.0, 0.8, 0.6, 0.4, and 0.2 months before coalescence. The last two points are for0.5 week before and for very roughly the last stable orbit for Schwarzschild MBHs.of the signal strength as a function of frequency during the last year beforecoalescence for events at a redshift of z = 1 and for circular orbits. The squaresymbols show the time at 0.2 year intervals, so the first is one year before, thesecond is 0.8 year before, etc. The last symbol is shifted slightly to be 0.5 weekbefore coalescence, instead of at that time. The cases shown are for equal MBHmasses, and only the spiral-in part of the event before the last stable orbit isreached is considered. However, it should be remembered that the detectability ofthe signal for the spiral-in phase depends mainly on the chirp mass, so the curvesgiven can be used to estimate conditions under which unequal mass coalescenceswould be observable also. The case of possible coalescence of 500M ⊙ seed blackholes during the early growth of MBHs that was discussed earlier is shown forz = 1 for comparison.Since the LISA threshold sensitivity curve and the confusion noise estimateare defined on the assumption that the frequency and signal strength are fixed forthe one year period of the observation, and the MBH–MBH coalescence signalschange dramatically during the year, it is necessary to integrate the square of theamplitude S/N ratio during the year and then take the square root to obtain theeffective S/N ratio. The way in which the effective S/N ratio builds up duringthe year, with the LISA instrumental noise and the confusion noise combinedquadratically, is shown in figure 10.12. What is shown for each of the cases from