The Supermassive Black Hole Binary Population Behind the Measured Amplitude

This paper asks a single question: What comoving merger rate and characteristic chirp mass are required for supermassive binaries to produce the measured nanohertz amplitude? Working from the published common-process amplitude of 2.4e-15 in characteristic strain at one cycle per year and the standard binary spectral index of thirteen thirds, the study computes the relevant quantities by the Phinney integral relating background energy density to the merger rate per chirp-mass interval. The headline computed values are omega_gw_at_10nHz = 3.4232658889151874e-09, rate_at_1e9_Msun = 12.0. These values are compared throughout with the published pulsar-timing values from the North American, European, Parkes and Chinese arrays. The calculation is fully reproducible from the deposited code, and every headline number appears in the accompanying results file. This study is simulated and computed from stated assumptions; it is not a measurement, and no new timing data are presented.