The First Upper Bound on the Nano-Hertz Gravitational Waves and Galaxy Cross-Correlation signal using 15-year NANOGrav Data and DESI Galaxy Survey

TL;DR

This paper presents the first upper bound on the cross-correlation between nanohertz gravitational waves and galaxy distribution using 15-year PTA data and DESI survey, providing new constraints on SMBHBs and large-scale structure.

Contribution

Developed a novel analysis pipeline to study the cross-correlation of nHz GW signals with galaxy surveys, and established the first observational upper limit on this correlation.

Findings

No significant correlation detected between SGWB and DESI galaxies.

Set an upper bound on the cross-correlation coefficient at $\, ext{ell}=8$.

Provides groundwork for future multi-tracer analyses combining PTA and galaxy survey data.

Abstract

The recent detection of a common-spectrum stochastic signal by multiple pulsar timing array (PTA) collaborations has provided tentative evidence for a nanohertz (nHz) stochastic gravitational-wave background (SGWB). This signal can be widely interpreted as originating from a cosmic population of inspiraling supermassive black hole binaries (SMBHBs). Current PTA analyses primarily constrain the SGWB power spectrum and its auto-angular power spectrum. However, the supermassive black holes will produce an underlying correlation with the large-scale structure of the Universe, which can help in understanding the formation and evolution of the binaries. In this work, we develop a new analysis pipeline PyGxGW-PTA for studying the cross-correlation of nHz GW signal with galaxy surveys ($C^{\rm g\, GW}_\ell$) and obtain the first constraint on the SGWB and galaxy distribution cross-correlation using the NANOGrav 15-year dataset in combination with the DESI galaxy catalog. We find no statistically significant correlation between the SGWB and the large-scale distribution of DESI galaxies and using an optimal estimator we put an upper bound on $C^{\rm g\, GW}_{\ell=8} < 0.0083$ at $95\%$ C.I. This yields the first observational upper limit on the spatial correlation between the nHz SGWB and the large-scale structure of the Universe, establishing the observational groundwork for future multi-tracer analyses that will combine PTA data with next-generation galaxy surveys to unveil the SMBHB-galaxy correlation.