Joint Angular-Power Distributions of Interfering Nanohertz Gravitational Waves
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 χ2 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.
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BibTeX
@misc{bi2026joint,
title = {{Joint Angular-Power Distributions of Interfering Nanohertz Gravitational Waves}},
author = {Yan-Chen Bi and Yu-Mei Wu and Qing-Guo Huang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32809},
eprint = {2610.32809},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32809},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Joint Angular-Power Distributions of Interfering Nanohertz Gravitational Waves
AU - Yan-Chen Bi
AU - Yu-Mei Wu
AU - Qing-Guo Huang
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32809
UR - https://arxiv.org/abs/2610.32809
AB - 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.
ER -