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.