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Inspiraling massive black-hole binaries (MBHBs) forming in the aftermath ofgalaxy mergers are expected to be the loudest gravitational-wave (GW) sourcesrelevant for pulsar-timing arrays (PTAs) at nHz frequencies. The incoherentoverlap of signals from a cosmic population of MBHBs gives rise to a stochasticGW background (GWB) with characteristic strain around $h_c\sim10^{-15}$ at areference frequency of 1 yr$^{-1}$, although uncertainties around this valueare large. Current PTAs are piercing into the GW amplitude range predicted byMBHB-population models, but no detection has been reported so far. To assessthe future success prospects of PTA experiments, it is therefore important toestimate the minimum GWB level consistent with our current understanding of theformation and evolution of galaxies and massive black holes (MBHs). To thispurpose, we couple a semianalytic model of galaxy evolution and an extensivestudy of the statistical outcome of triple MBH interactions. We show that evenin the most pessimistic scenario where all MBHBs stall before entering theGW-dominated regime, triple interactions resulting from subsequent galaxymergers inevitably drive a considerable fraction of the MBHB population tocoalescence. At frequencies relevant for PTA, the resulting GWB is only afactor of 2-to-3 suppressed compared to a fiducial model where binaries areallowed to merge over Gyr timescales. Coupled with current estimates of theexpected GWB amplitude range, our findings suggest that the minimum GWB fromcosmic MBHBs is unlikely to be lower than $h_c\sim 10^{-16}$ (at $f = 1$yr$^{-1}$), well within the expected sensitivity of projected PTAs based onfuture observations with FAST, MeerKAT and SKA.

monthly notices of the royal astronomical society

Post-Newtonian evolution of massive black hole triplets in galactic  nuclei -- III. A robust lower limit to the nHz stochastic background of  gravitational waves