Low-frequency gravitational waves from massive black hole binaries: Predictions for LISA and pulsar timing arrays

The coalescence of massive black hole (BH) binaries due to galaxy mergers provides a primary source of low-frequency gravitational radiation detectable by pulsar timing measurements and by the proposed the Laser Interferometry Space Antenna (LISA) observatory. We compute the expected gravitational radiation signal from sources at all redshifts by combining the predicted merger rate of galactic halos with recent measurements of the relation between BH mass, M_BH, and the velocity dispersion of its host galaxy, σ. Our main findings are as follows: (1) the nHz frequency background is dominated by BH binaries at redshifts z≲,2, and existing limits from pulsar timing data place tight constraints on the allowed normalization and power-law slope of the M_BH-σ relation or on the fraction of BH binaries that proceed to coalescence; (2) more than half of all discrete mHz massive BH sources detectable by LISA are likely to originate at redshifts z≳7; (3) the number of LISA sources per unit redshift per year should drop substantially after reionization as long as BH formation is triggered by gas cooling in galaxies. Studies of the highest redshift sources among the few hundred detectable events per year will provide unique information about the physics and history of black hole growth in galaxies.