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 ($0<z\le 0.1$ and $0.1<z\le 0.2$) and model PTA cross-correlations as ${\mathrm{\Gamma }}_{ab}={\mathrm{\Gamma }}_{ab}^{\mathrm{H}\mathrm{D}}+{\sum }_i{\epsilon }_i{\mathrm{\Gamma }}_{ab}^{\mathrm{L}\mathrm{S}\mathrm{S}(\mathrm{i})}$, 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., ${\epsilon }_1=0.20_{-1.66}^{+1.68}$ and ${\epsilon }_2=-0.11_{-1.83}^{+2.04}$; 68% credible intervals), and Bayes factors favor the isotropic Hellings–Downs hypothesis (${\mathcal{B}}_{{\mathrm{H}\mathrm{D}+\mathrm{L}\mathrm{S}\mathrm{S}}_1,\mathrm{H}\mathrm{D}}=0.40$, ${\mathcal{B}}_{{\mathrm{H}\mathrm{D}+\mathrm{L}\mathrm{S}\mathrm{S}}_2,\mathrm{H}\mathrm{D}}=0.43$, ${\mathcal{B}}_{{\mathrm{H}\mathrm{D}+\mathrm{L}\mathrm{S}\mathrm{S}}_{1+2},\mathrm{H}\mathrm{D}}=0.11$). 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.