The nightmare scenario: measuring the stochastic gravitational wave background from stalling massive black hole binaries with pulsar timing arrays

Abstract

Massive black-hole binaries, formed when galaxies merge, are among the\nprimary sources of gravitational waves targeted by ongoing Pulsar Timing Array\n(PTA) experiments and the upcoming space-based LISA interferometer. However,\ntheir formation and merger rates are still highly uncertain. Recent upper\nlimits on the stochastic gravitational-wave background obtained by PTAs are\nstarting being in marginal tension with theoretical models for the pairing and\norbital evolution of these systems. This tension can be resolved by assuming\nthat these binaries are more eccentric or interact more strongly with the\nenvironment (gas and stars) than expected, or by accounting for possible\nselection biases in the construction of the theoretical models. However,\nanother (pessimistic) possibility is that these binaries do not merge at all,\nbut stall at large ($\\sim$ pc) separations. We explore this extreme scenario by\nusing a galaxy-formation semi-analytic model including massive black holes\n(isolated and in binaries), and show that future generations of PTAs will\ndetect the stochastic gravitational-wave background from the massive black-hole\nbinary population within $10-15$ years of observations, even in the "nightmare\nscenario" in which all binaries stall at the hardening radius. Moreover, we\nargue that this scenario is too pessimistic, because our model predicts the\nexistence of a sub-population of binaries with small mass ratios ($q \\lesssim\n10^{-3}$) that should merge within a Hubble time simply as a result of\ngravitational-wave emission. This sub-population will be observable with large\nsignal-to-noise ratios by future PTAs thanks to next-generation radio\ntelescopes such as SKA or FAST, and possibly by LISA.\n