Low-frequency gravitational radiation from coalescing massive black hole binaries in hierarchical cosmologies

Abstract

We compute the expected gravitational wave signal from coalescing massive black hole (MBH) binaries at the center of galaxies in a hierarchical structure formation scenario in which seed holes of intermediate mass form far up in the dark halo merger tree. The merger history of DM halos and MBHs is followed from z=20 to the present in a LCDM cosmology. MBHs get incorporated through halo mergers into larger and larger structures, sink to the center owing to dynamical friction against the DM background, accrete cold material in the merger remnant, and form MBH binary systems. Stellar dynamical interactions cause the hardening of the binary at large separations, while gravitational wave emission takes over at small radii and leads to the final coalescence of the pair. The integrated emission from inspiraling MBH binaries results in a gravitational wave background (GWB). The characteristic strain spectrum has the standard h_c(f)\propto f^{-2/3} behavior only in the range 1E-9<f<1E-6 Hz. At lower frequencies the orbital decay of MBH binaries is driven by the ejection of background stars, and h_c(f) \propto f. At higher frequencies, f>1E-6 Hz, the strain amplitude is shaped by the convolution of last stable circular orbit emission. We discuss the observability of inspiraling MBH binaries by the planned LISA. Over a 3-year observing period LISA should resolve this GWB into discrete sources, detecting ~60 (~250) individual events above a S/N=5 (S/N=1) confidence level. (Abridged)