Paper
A Template-Based Search for Large-Scale-Structure--Correlated Anisotropy in the Nanohertz Gravitational-Wave Background Using the Public NANOGrav 15-Year Data Set
Authors
Yun Fang
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.
Metadata
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.02110v1</id>\n <title>A Template-Based Search for Large-Scale-Structure--Correlated Anisotropy in the Nanohertz Gravitational-Wave Background Using the Public NANOGrav 15-Year Data Set</title>\n <updated>2026-03-02T17:26:06Z</updated>\n <link href='https://arxiv.org/abs/2603.02110v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.02110v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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 $Γ_{ab}=Γ^{\\rm HD}_{ab}+\\sum_i ε_i\\,Γ^{\\rm LSS(i)}_{ab}$,\n 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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='astro-ph.CO'/>\n <category scheme='http://arxiv.org/schemas/atom' term='astro-ph.HE'/>\n <published>2026-03-02T17:26:06Z</published>\n <arxiv:comment>15 pages,6 figures</arxiv:comment>\n <arxiv:primary_category term='astro-ph.CO'/>\n <author>\n <name>Yun Fang</name>\n </author>\n </entry>"
}