The gravitational wave signal from massive black hole binaries and its contribution to the LISA data stream

Massive black hole binaries, with masses in the range 10 3-108 M⊙, are expected to be the most powerful sources of gravitational radiation at mHz frequencies, and hence are among the primary targets for the planned Laser Interferometer Space Antenna (LISA). We extend and refine our previous analysis, detailing the gravitational wave signal expected from a cosmological population of massive black hole binaries. As done in our previous paper, we follow the merger history of dark matter halos, the dynamics of the massive black holes they host, and their growth via gas accretion and binary coalescences in a ΛCDM cosmology. Stellar dynamical processes dominates the orbital evolution of black hole binaries at large separations, while gravitational wave emission takes over at small radii, causing the final coalescence of the pairs. We show that the GW signal from this population, in a 3 yr LISA observation, will be resolved into ≃90 discrete events with S/N ≥ 5, among which ≃35 will be observed above threshold until coalescence. These "merging events" involve relatively massive binaries, M ∼ 105 M⊙, in the redshift range 2≲z≲6. The remaining ≃55 events come from higher redshift, less massive binaries (M ∼ 5 × 103 M ⊙ at z ≳ 6) and, although their S/N integrated over the duration of the observation can be substantial, the final coalescence phase is at too high a frequency to be directly observable by space-based interferometeres such as LISA. LISA will be able to detect a fraction ≳90% of all the coalescences of massive black hole binaries occurring at z ≲ 5. The residual confusion noise from unresolved massive black hole binaries is expected to be at least an order of magnitude below the estimated stochastic noise.