Year: 2026
Type: preprint
Abstract: Finite populations of supermassive black-hole binaries produce fluctuations in both gravitational-wave power and pulsar timing correlations. We characterize the realization-dependent, orientation-averaged Earth-term angular correlation through its frequency-resolved Legendre coefficients. A hybrid model of bright sources and a Gaussian faint background extends the conditional Gamma distribution in the many-weak-source limit to non-central $χ^2$ statistics, yielding correlated multipoles after population marginalization. Our analytical variance decomposition and SMBHB population simulations reveal a population-dependent transition from interference dominated variance at low frequencies to population-power-dominated variance at high frequencies. In the many-weak-source regime, a multivariate lognormal approximation captures the main features of the joint distribution using only the first two log-cumulants. These results provide statistical benchmarks for fluctuations in both the overall amplitude and angular structure of the realized correlation.
Source: arXiv (Cornell University)
Authors: Bi, Yan-Chen, Wu, Yu-Mei, Huang, Qing-Guo
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223652667