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The recent evidence of a stochastic background of gravitational waves in thenHz band by pulsar-timing array (PTA) experiments has shed new light on theformation and evolution of massive black hole binaries with masses $\sim10^8$--$10^9 M_\odot$. The PTA data are consistent with a population of suchbinaries merging efficiently after the coalescence of their galactic hosts, andpresenting masses slightly larger than previously expected. This momentousdiscovery calls for investigating the prospects of detecting the smaller ($\sim10^5$--$10^7 M_\odot$) massive black hole binaries targeted by the LaserInterferometer Space Antenna (LISA). By using semi-analytic models for theformation and evolution of massive black hole binaries calibrated against thePTA results, we find that LISA will observe at least a dozen and up tothousands of black hole binaries during its mission duration. The minimumnumber of detections rises to $\sim 70$ if one excludes models that onlymarginally reproduce the quasar luminosity function at $z=6$. We also assessLISA's parameter estimation capabilities with state-of-the-art waveformsincluding higher modes and realistic instrumental response, and find that themasses, sky position, and distance will typically be estimated to withinrespectively 1%, 10 square degrees, and 10% for the detected systems (assuminga 4-year mission).

Implications of the pulsar timing array detections for massive black hole mergers in the LISA band