Red noise and evolving signals: a complete frequentist approach to supermassive black hole binary searches with pulsar timing arrays
Abstract
Searches for gravitational waves (GWs) from isolated supermassive black hole binaries (SMBHBs) in pulsar timing array (PTA) data require simultaneous estimation of signal and noise parameters, so the dimensionality of the fit scales with the number of observed pulsars. This computational difficulty is exacerbated when source evolution from GW emission is included, since retaining both Earth and pulsar terms introduces the unknown pulsar distances. Existing frequentist methods such as the ℱ-statistic are restricted to non-evolving sources. In addition, they often rely on a noise covariance estimated from the same data and then held fixed during the signal search, which can bias parameter estimates. We present a Generalized Likelihood Ratio Test and the associated 𝒯-statistic that overcomes the aforementioned limitations. This formulation extends earlier work in which the dimensionality of the fitting problem was drastically reduced by semi-analytical maximization of the likelihood over the pulsar phase parameters, followed by efficient global optimization over the remaining parameters using Particle Swarm Optimization. Our simulations demonstrate that for an evolving SMBHB signal with chirp mass ℳ=109.2 M⊙ and signal-to-noise ratio $20$, this detection statistic achieves a 100% detection probability at a false-alarm probability of $0.06$ in a 30-pulsar timing array, which is characterized by a 100 ns root-mean-square white noise residual and pulsar-specific red noise. For the 30-pulsar timing array at signal-to-noise ratio $10$ and false-alarm probability $0.06$, 𝒯 detects 99/100 realizations, outperforming the ℱp statistic evaluated with the H0-fitted covariance, which detects 71/100 realizations.
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BibTeX
@misc{tao2026noise,
title = {{Red noise and evolving signals: a complete frequentist approach to supermassive black hole binary searches with pulsar timing arrays}},
author = {Xuan Tao and Boris Goncharov and Yiqian Qian and Yan Wang and Soumya D. Mohanty},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.07330},
eprint = {2606.07330},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.07330},
}
RIS
TY - UNPB
TI - Red noise and evolving signals: a complete frequentist approach to supermassive black hole binary searches with pulsar timing arrays
AU - Xuan Tao
AU - Boris Goncharov
AU - Yiqian Qian
AU - Yan Wang
AU - Soumya D. Mohanty
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2606.07330
UR - https://arxiv.org/abs/2606.07330
AB - Searches for gravitational waves (GWs) from isolated supermassive black hole binaries (SMBHBs) in pulsar timing array (PTA) data require simultaneous estimation of signal and noise parameters, so the dimensionality of the fit scales with the number of observed pulsars. This computational difficulty is exacerbated when source evolution from GW emission is included, since retaining both Earth and pulsar terms introduces the unknown pulsar distances. Existing frequentist methods such as the ℱ-statistic are restricted to non-evolving sources. In addition, they often rely on a noise covariance estimated from the same data and then held fixed during the signal search, which can bias parameter estimates. We present a Generalized Likelihood Ratio Test and the associated 𝒯-statistic that overcomes the aforementioned limitations. This formulation extends earlier work in which the dimensionality of the fitting problem was drastically reduced by semi-analytical maximization of the likelihood over the pulsar phase parameters, followed by efficient global optimization over the remaining parameters using Particle Swarm Optimization. Our simulations demonstrate that for an evolving SMBHB signal with chirp mass ℳ=10^9.2 M_⊙ and signal-to-noise ratio $20$, this detection statistic achieves a 100% detection probability at a false-alarm probability of $0.06$ in a 30-pulsar timing array, which is characterized by a 100 ns root-mean-square white noise residual and pulsar-specific red noise. For the 30-pulsar timing array at signal-to-noise ratio $10$ and false-alarm probability $0.06$, 𝒯 detects 99/100 realizations, outperforming the ℱ_p statistic evaluated with the H_0-fitted covariance, which detects 71/100 realizations.
ER -