The NANOGrav 15 yr Data Set: Harmonic Analysis of the Pulsar Angular Correlations

TL;DR

This paper analyzes 15 years of pulsar timing data to investigate the angular correlations of gravitational wave background signals, confirming the quadrupolar pattern predicted by general relativity while identifying additional monopolar signals.

Contribution

It introduces a flexible Legendre polynomial expansion to analyze pulsar angular correlations and assesses the evidence for quadrupolar versus monopolar signals in the data.

Findings

Significant quadrupolar correlation consistent with general relativity

Detection of a monopolar signal at ~4 nHz

Bayes factor of 200 supporting quadrupolar correlations

Abstract

Pulsar timing array observations have found evidence for an isotropic gravitational wave background with the Hellings-Downs angular correlations, expected from general relativity. This interpretation hinges on the measured shape of the angular correlations, which is predominately quadrupolar under general relativity. Here we explore a more flexible parameterization: we expand the angular correlations into a sum of Legendre polynomials and use a Bayesian analysis to constrain their coefficients with the 15-year pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). When including Legendre polynomials with multipoles $\ell \geq 2$, we only find a significant signal in the quadrupole with an amplitude consistent with general relativity and non-zero at the $\sim 95\%$ confidence level and a Bayes factor of 200. When we include multipoles $\ell \leq 1$, the Bayes factor evidence for quadrupole correlations decreases by more than an order of magnitude due to evidence for a monopolar signal at approximately 4 nHz which has also been noted in previous analyses of the NANOGrav 15-year data. Further work needs to be done in order to better characterize the properties of this monopolar signal and its effect on the evidence for quadrupolar angular correlations.