Prospects for gravitational-wave detection and supermassive black hole astrophysics with pulsar timing arrays

Large-area sky surveys show that massive galaxies undergo at least one major merger in a Hubble time. Ongoing pulsar timing array (PTA) experiments are aimed at measuring the gravitational wave (GW) emission from binary supermassive black holes (SMBHs) at the centres of galaxy merger remnants. In this paper, using the latest observational estimates for a range of galaxy properties and scaling relations, we predict the amplitude of the GW background generated by the binary SMBH population. We also predict the numbers of individual binary SMBH GW sources. We predict the characteristic strain amplitude of the GW background to lie in the range $5.1\times10^{-16}<A_{\rm yr}<2.4\times10^{-15}$ at a frequency of $(1\,{\rm yr})^{-1}$, with 95% confidence. Higher values within this range, which correspond to the more commonly preferred choice of galaxy merger timescale, will fall within the expected sensitivity ranges of existing PTA projects in the next few years. In contrast, we find that a PTA consisting of at least 100 pulsars observed with next-generation radio telescopes will be required to detect continuous-wave GWs from binary SMBHs. We further suggest that GW memory bursts from coalescing SMBH pairs are not viable sources for PTAs. Both the GW background and individual GW source counts are dominated by binaries formed in mergers between early-type galaxies of masses $\gtrsim5\times10^{10}M_{\odot}$ at redshifts $\lesssim 1.5$. Uncertainties in the galaxy merger timescale and the SMBH mass - galaxy bulge mass relation dominate the uncertainty in our predictions.