Fingerprints of individual supermassive black hole binaries in pulsar timing arrays
Phys. Rev. D 114, 044055 – Published 17 August, 2026
DOI: https://doi.org/10.1103/ql8b-7q8v
Abstract
With evidence for a nanohertz gravitational-wave background now established by pulsar timing arrays, the search focuses on identifying individual supermassive black hole binaries. We show that these binaries produce a distinct spatial correlation pattern across the array, acting as a deterministic analog to the stochastic Hellings and Downs curve. We derive a closed analytic expression for this single-source overlap reduction function, , factorizing the signal into a source-dependent amplitude and a purely geometric fingerprint. Using simulated datasets, we demonstrate that this fingerprint breaks the degeneracy between an individual binary and a stochastic background. Including these cross-correlations yields Bayes factors of 1611 favoring the continuous-wave model over a Hellings and Downs correlated background model and 159 favoring the continuous-wave model over an uncorrelated red-noise model. Furthermore, these new cross-correlations improve sky localization by a factor of over an uncorrelated search. Finally, while coherent matched filtering offers higher theoretical sensitivity, we argue that a cross-correlation-based search for individual binaries provides a robust alternative that hedges against the possibility of overfitting to noise fluctuations by focusing on the evidence for the correlations. Indeed, the geometric fingerprints we present here show that spatial correlations can also be used to identify the first nanohertz gravitational-wave sources.
