On the rate of detectability of intermediate-mass black hole binaries using LISA

We estimate the rate at which the proposed space gravitational-wave interferometer LISA could detect intermediate-mass black hole (IMBH) binaries, that is, binaries containing a black hole in the mass range 10 100 M-circle dot orbiting a black hole in the mass range 100-1000 M-circle dot. For 1 yr integrations leading up to the innermost stable circular orbit and a signal-to-noise ratio of 10, we estimate a detection rate of only 1 per million years for 10 M-circle dot/100 M-circle dot binaries. The estimate uses the method of parameter estimation via matched filtering, incorporates a noise curve for LISA established by the LISA Science Team that is available online, and employs an IMBH formation rate model used by Miller in 2002. We find that the detectable distance is relatively insensitive to LISA arm lengths or acceleration noise but is roughly inversely proportional to LISA position errors and varies roughly as T-1/2, where T is the integration time in years. We also show that while all IMBH systems in this mass range may be detected in the Virgo cluster up to 40 yr before merger, none can be detected there earlier than 400 yr before merger. An extended LISA mission that enabled 10 yr integrations could detect IMBH systems at the Virgo cluster 1000 yr before merger, and systems in Galactic globular clusters 1 million yr before merger. We compare and contrast these estimates with earlier estimates by Miller.