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 binaries, that is, binaries containing a black hole in the mass range 10 -- 100 Msun orbiting a black hole in the mass range 100 -- 1000 Msun. For one-year integrations leading up to the innermost stable orbit, and a signal-to-noise ratio of 10, we estimate a detection rate of only 1 per million years for 10 Msun/100 Msun 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 (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 years before merger, none can be detected there earlier than 400 years before merger. An extended LISA mission that enabled 10-year integrations could detect IMBH systems at the Virgo cluster 1000 years before merger, and systems in galactic globular clusters a million years before merger. We compare and contrast these estimates with earlier estimates by Miller (2002).