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

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 0.1 and 0.1<z 0.2) and model PTA cross-correlations as ab= HD ab+ sum i epsilon i, 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 (B HD+LSS 1, HD=0.40, B HD+LSS 2, HD=0.43, B HD+LSS 1+2, 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.