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The coalescence of massive black hole (BH) binaries due to galaxy mergersprovides a primary source of low-frequency gravitational radiation detectableby pulsar timing measurements and by the proposed LISA (Laser InterferometrySpace Antenna) observatory. We compute the expected gravitational radiationsignal from sources at all redshifts by combining the predicted merger rate ofgalactic halos with recent measurements of the relation between BH mass, M_bh,and the velocity dispersion of its host galaxy, sigma. Our main findings are asfollows: (i) the nHz frequency background is dominated by BH binaries atredshifts z<2, and existing limits from pulsar timing data place tightconstraints on the allowed normalization and power-law slope of the M_bh-sigmarelation or on the fraction of BH binaries that proceed to coalescence; (ii)more than half of all discrete mHz massive BH sources detectable by LISA arelikely to originate at redshifts z>7; (iii) the number of LISA sources per unitredshift per year should drop substantially after reionization as long as BHformation is triggered by gas cooling in galaxies. Studies of the highestredshift sources among the few hundred detectable events per year, will provideunique information about the physics and history of black hole growth ingalaxies.Comment: 31 pages 7 figures, replaced to match version published in Ap

Low‐Frequency Gravitational Waves from Massive Black Hole Binaries: Predictions forLISAand Pulsar Timing Arrays