Anisotropies in the PTA gravitational wave background: what can they teach us about supermassive black hole binaries?

Abstract

The gravitational wave background detected by pulsar timing arrays is sourced by a finite population of supermassive black hole binaries, and is therefore anisotropic. We ask what measuring that anisotropy can teach us about the population, using models that span a wide range of effective source counts, all normalized to the measured background amplitude. We find four things. First, the expected anisotropy is produced by the single brightest binary: a dipole at the level of the published NANOGrav 95% upper limit would require one source to supply about 60% of the power in the band. Second, no model that also reproduces the measured strain spectrum contains a source that bright. In every case the loudest binary stays below the NANOGrav continuous-wave upper limit at every frequency it covers, consistent with the joint search of the 15-year data, which finds no resolved source. Third, because the anisotropy is produced by one source, compressing the sky to an angular power spectrum discards the phase information that locates it. Such a search is never more sensitive than looking for the source directly, and is strictly worse once more than a dipole is kept. Fourth, the published upper limits on the angular power spectrum therefore reflect the analysis prior rather than the data: they coincide with the 95th percentile of the prior induced by the square-root spherical harmonic basis adopted in the analysis. What does constrain the population today is the shape of the strain spectrum. Rare, bright sources depress the median spectrum below its mean, and fitting the measured spectrum already disfavors mass functions dominated by binaries above about 10^10 solar masses.