Prior volume effect inflates the gravitational-wave background in pulsar timing arrays
Abstract
Pulsar timing arrays (PTAs) have found evidence for a nanohertz gravitational-wave background (GWB) whose amplitude exceeds most predictions based on supermassive black hole binaries (SMBHBs). Using NANOGrav 15-year data, we show that a substantial part of this excess arises from a prior volume effect. The GWB amplitude is constrained mainly by the pulsars' auto-correlations, where the GWB is degenerate with each pulsar's intrinsic red noise. By decomposing the GWB posterior, we find that marginalizing over the standard log-uniform red-noise priors introduces a prior volume term that favors a stronger GWB, pulling the inferred amplitude more than 2σ above the maximum-likelihood estimate. The Hellings-Downs (HD) cross-correlations, which measure the GWB alone, are not strong enough to counter the volume term. The profile likelihood, a cross-correlation-only estimator, and priors that are uniform in power or informed by the pulsar population all avoid or reduce this effect and lower the amplitude into agreement with SMBHBs. The revised priors also yield a steeper GWB spectrum closer to the SMBHB predictions, strengthen the evidence for HD correlations, and weaken the preference for new-physics sources over SMBHBs.
Related
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BibTeX
@misc{dai2026prior,
title = {{Prior volume effect inflates the gravitational-wave background in pulsar timing arrays}},
author = {Biwei Dai and Matias Zaldarriaga and Yacine Ali-Ha\"ımoud},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28739},
eprint = {2610.28739},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28739},
}
RIS
TY - UNPB
TI - Prior volume effect inflates the gravitational-wave background in pulsar timing arrays
AU - Biwei Dai
AU - Matias Zaldarriaga
AU - Yacine Ali-Ha\"ımoud
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28739
UR - https://arxiv.org/abs/2610.28739
AB - Pulsar timing arrays (PTAs) have found evidence for a nanohertz gravitational-wave background (GWB) whose amplitude exceeds most predictions based on supermassive black hole binaries (SMBHBs). Using NANOGrav 15-year data, we show that a substantial part of this excess arises from a prior volume effect. The GWB amplitude is constrained mainly by the pulsars' auto-correlations, where the GWB is degenerate with each pulsar's intrinsic red noise. By decomposing the GWB posterior, we find that marginalizing over the standard log-uniform red-noise priors introduces a prior volume term that favors a stronger GWB, pulling the inferred amplitude more than 2σ above the maximum-likelihood estimate. The Hellings-Downs (HD) cross-correlations, which measure the GWB alone, are not strong enough to counter the volume term. The profile likelihood, a cross-correlation-only estimator, and priors that are uniform in power or informed by the pulsar population all avoid or reduce this effect and lower the amplitude into agreement with SMBHBs. The revised priors also yield a steeper GWB spectrum closer to the SMBHB predictions, strengthen the evidence for HD correlations, and weaken the preference for new-physics sources over SMBHBs.
ER -