A Template-Based Search for Large-Scale-Structure--Correlated Anisotropy in the Nanohertz Gravitational-Wave Background Using the Public NANOGrav 15-Year Data Set

TL;DR

This paper introduces a Bayesian analysis framework embedding galaxy survey data into pulsar timing array (PTA) data to search for anisotropic gravitational-wave background correlations with large-scale structure, finding no significant evidence but setting upper limits.

Contribution

The paper presents the first Bayesian PTA likelihood method incorporating external galaxy survey templates directly into the analysis for LSS-correlated anisotropy detection.

Findings

No significant LSS-correlated component detected in NANOGrav data.

Bayes factors favor isotropic Hellings--Downs hypothesis over LSS-correlated models.

Upper limits placed on LSS contribution to the gravitational-wave background.

Abstract

Recent PTA analyses reporting evidence for a nanohertz common-spectrum process motivate targeted tests of whether any anisotropic component of the stochastic gravitational-wave background (SGWB) is correlated with the nearby large-scale structure (LSS), as anticipated for an astrophysical background dominated by supermassive black hole binaries. We present the first Bayesian PTA likelihood analysis that embeds an externally observed, full-sky galaxy-survey LSS template directly as an overlap-reduction-function (ORF) component. Using the 2MASS Photometric Redshift (2MPZ) galaxy catalog, we construct low-multipole LSS--correlated ORF templates in two redshift slices ($0<z\le0.1$ and $0.1<z\le0.2$) and model PTA cross-correlations as $\Gamma_{ab}=\Gamma^{\rm HD}_{ab}+\sum_i \epsilon_i\,\Gamma^{\rm LSS(i)}_{ab}$, where $\epsilon_i$ quantifies the amplitude of an SGWB component whose angular correlations project onto the fixed 2MPZ LSS templates. Applying this framework to the NANOGrav 15-year dataset, we find no statistically significant evidence for an LSS-correlated component: $\epsilon_i$ is consistent with zero in both single-bin and two-bin analyses (e.g., $\epsilon_1=0.20^{+1.68}_{-1.66}$ and $\epsilon_2=-0.11^{+2.04}_{-1.83}$; 68\% credible intervals), and Bayes factors favor the isotropic Hellings--Downs hypothesis ($\mathcal{B}_{{\rm HD+LSS}_1,{\rm HD}}=0.40$, $\mathcal{B}_{{\rm HD+LSS}_2,{\rm HD}}=0.43$, $\mathcal{B}_{{\rm HD+LSS}_{1+2},{\rm HD}}=0.11$). We therefore place upper limits on any 2MPZ-traced, LSS-correlated contribution to the SGWB at $z<0.2$. More broadly, our framework provides a reproducible pathway for incorporating observed LSS information into PTA anisotropy searches and naturally motivates extensions to finer redshift tomography and next-generation PTA datasets.