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

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 $Γ_{ab}=Γ^{\rm HD}_{ab}+\sum_i ε_i\,Γ^{\rm LSS(i)}_{ab}$, where $ε_i$ 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: $ε_i$ is consistent with zero in both single-bin and two-bin analyses (e.g., $ε_1=0.20^{+1.68}_{-1.66}$ and $ε_2=-0.11^{+2.04}_{-1.83}$; 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.

Figures (6)

• Figure 1: Reconstructed large-scale-structure overdensity maps from spherical-harmonic coefficients $a_{\ell m}$ inferred from the 2MPZ galaxy catalog, truncated to $2 \le \ell \le 12$, for the two redshift bins used in this work. The maps are shown in a Mollweide projection in equatorial coordinates. Red stars mark the sky positions of the 67 pulsars in our PTA sample. The black dashed curves delineate the mask boundary around the Galactic plane, defined using a Galactic latitude cut.
• Figure 2: Pairwise ORF values $\Gamma_{ab}$ versus pulsar angular separation $\zeta_{ab}$ for the model $\Gamma_{ab}=\Gamma^{\rm HD}_{ab}+\epsilon\,\Gamma^{\rm LSS}_{ab}$. The solid black curve shows the HD prediction. Colored points show $\Gamma_{ab}$ evaluated for individual pulsar pairs and are colored by the pair-midpoint right ascension (RA, in hours). Left/right columns correspond to the 2MPZ redshift slices $0<z\le0.1$ and $0.1<z\le0.2$, respectively; top/bottom rows adopt $\epsilon=1$ and $\epsilon=3$.
• Figure 3: Marginalized posterior distribution for $(\epsilon_1,\gamma_{\rm gw},\log_{10}A_{\rm gw})$ in the single-bin model $\Gamma=\Gamma^{\rm HD}+\epsilon_1\,\Gamma^{\rm LSS(1)}$, where $\Gamma^{\rm LSS(1)}$ is derived from the 2MPZ slice $0<z\le0.1$. Diagonal panels show 1D marginalized posteriors and off-diagonal panels show joint credible regions. Titles report the median and $68\%$ credible intervals.
• Figure 4: Same as Figure \ref{['fig:posteriors_bin1']}, but for $(\epsilon_2,\gamma_{\rm gw},\log_{10}A_{\rm gw})$ in the model $\Gamma=\Gamma^{\rm HD}+\epsilon_2\,\Gamma^{\rm LSS(2)}$, where $\Gamma^{\rm LSS(2)}$ is derived from the 2MPZ slice $0.1<z\le0.2$.
• Figure 5: Marginalized posterior distribution for $(\epsilon_1,\epsilon_2,\gamma_{\rm gw},\log_{10}A_{\rm gw})$ in the two-bin model $\Gamma=\Gamma^{\rm HD}+\epsilon_1\Gamma^{\rm LSS(1)}+\epsilon_2\Gamma^{\rm LSS(2)}$. The joint posterior exhibits a strong degeneracy between $\epsilon_1$ and $\epsilon_2$, consistent with partial non-orthogonality of the two LSS templates under the PTA sampling of pulsar pairs. Titles report the median and $68\%$ credible intervals.