Massive black hole evolution models confronting the n-Hz amplitude of the stochastic gravitational wave background

ABSTRACT We estimate the amplitude of nano-Hz stochastic gravitational wave background (GWB) resulting from an unresolved population inspiralling massive black hole binaries (MBHBs). To this aim, we use L-Galaxies semi-analytical model applied on top Millennium merger trees. The dynamical evolution MBHBs includes friction, stellar and gas binary hardening, (GW) feedback. At frequencies proved by Pulsar Timing Array experiments, our predicts ${\sim }1.2 \times 10^{-15}$ at }3 10^{-8}\, \rm Hz$ in agreement with current estimations. contribution to comes primarily equal-mass chirp masses above $\rm 10^{8}\, M_{\odot }$. then consider recently detected common red noise NANOGrav, PPTA, EPTA data, working under hypothesis that it is indeed a GWB coming MBHBs. By boosting growth via accretion, show can produce signal $A\approx (2\!-\!3) 10^{-15}$. There are, however, difficulties predicting level without mismatching key observational constraints such as quasar bolometric luminosity functions or local mass function. This highlights how forthcoming GW observations can, for first time, confront galaxy models.