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Massive black-hole binaries, formed when galaxies merge, are among theprimary sources of gravitational waves targeted by ongoing Pulsar Timing Array(PTA) experiments and the upcoming space-based LISA interferometer. However,their formation and merger rates are still highly uncertain. Recent upperlimits on the stochastic gravitational-wave background obtained by PTAs arestarting being in marginal tension with theoretical models for the pairing andorbital evolution of these systems. This tension can be resolved by assumingthat these binaries are more eccentric or interact more strongly with theenvironment (gas and stars) than expected, or by accounting for possibleselection biases in the construction of the theoretical models. However,another (pessimistic) possibility is that these binaries do not merge at all,but stall at large ($\sim$ pc) separations. We explore this extreme scenario byusing a galaxy-formation semi-analytic model including massive black holes(isolated and in binaries), and show that future generations of PTAs willdetect the stochastic gravitational-wave background from the massive black-holebinary population within $10-15$ years of observations, even in the "nightmarescenario" in which all binaries stall at the hardening radius. Moreover, weargue that this scenario is too pessimistic, because our model predicts theexistence of a sub-population of binaries with small mass ratios ($q \lesssim10^{-3}$) that should merge within a Hubble time simply as a result ofgravitational-wave emission. This sub-population will be observable with largesignal-to-noise ratios by future PTAs thanks to next-generation radiotelescopes such as SKA or FAST, and possibly by LISA.

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