Galaxy Tomography with the Gravitational Wave Background from Supermassive Black Hole Binaries

The detection of a stochastic gravitational wave background by pulsar timing arrays suggests the presence of a supermassive black hole binary population. Although the observed spectrum generally matches predictions for orbital evolution driven by gravitational-wave emission in circular orbits, there is a preference for a spectral turnover at the lowest observed frequencies, which may point to a significant hardening phase transitioning from early environmental influences to later stages dominated by gravitational-wave emission. In the vicinity of these binaries, the ejection of stars or dark matter particles through gravitational three-body slingshots efficiently extracts orbital energy, leading to a low-frequency turnover in the spectrum. We model how the gravitational-wave spectrum depends on the initial inner galactic profile prior to scouring by binary ejections, accounting for a range of initial binary eccentricities. By analyzing the NANOGrav 15-year data, we find that a parsec-scale galactic center density of around $10^6\,M_\odot/\mathrm{pc}^3$ is favored across most of the parameter space, shedding light on environmental effects that shape black hole evolution and the combined matter density near galaxy centers.