Astrophysical Population Coordinates for Supermassive Black Hole Binaries in Pulsar Timing Array Inference

Abstract

Pulsar timing arrays can probe the population physics of supermassive black-hole binaries through the nanohertz gravitational-wave background. We construct a phenomenological forward model that follows source abundance, binary residence time, the high-mass population, finite-source strain moments, and the pulsar timing response. The simulated observables constrain three standardized population coordinates: ${\hat{I}}^2$, which controls the residence-time and spectral response; $\ddot{I}{•}_{eff}$, which describes source normalization after accounting for its covariance with ${\hat{I}}^2$; and $m_{eff}$, which is dominated by the high-mass cutoff. In the evaluation ensemble, the posterior-mean correlations with the simulated values are $0.928$, $0.926$, and $0.884$, with central 90 per cent coverages of $0.938\pm 0.015$, $0.871\pm 0.021$, and $0.898\pm 0.019$, respectively. Frequency-resolved observables are most important for ${\hat{I}}^2$, and strain moments beyond a common-process power law provide sensitivity to the normalization and high-mass coordinates; the fourth strain moment identifies $m_{eff}$ with rare, massive binaries. These coordinates quantify the relative sensitivity of the adopted PTA summaries within this population model, for which nearby population realizations retain substantial posterior overlap.

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