# The NANOGrav 15-year Data Set: Search for Anisotropy in the Gravitational-Wave Background

**Authors:** Gabriella Agazie, Akash Anumarlapudi, Anne M. Archibald, Zaven Arzoumanian, Paul T. Baker, Bence Bécsy, Laura Blecha, Adam Brazier, Paul R. Brook, Sarah Burke-Spolaor, J. Andrew Casey-Clyde, Maria Charisi, Shami Chatterjee, Tyler Cohen, James M. Cordes, Neil J. Cornish, Fronefield Crawford, H. Thankful Cromartie, Kathryn Crowter, Megan E. DeCesar  
**arXiv:** [2306.16221](https://arxiv.org/abs/2306.16221)  
**Date:** 2023-06-28  
**Summary page:** https://www.summarizepaper.com/en/paper/2306.16221v1/

## Key points

- The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has found evidence of an isotropic nanohertz gravitational wave background (GWB) in their 15-year dataset.
- Anisotropy in the GWB would indicate a distribution of inspiraling supermassive black hole binary (SMBHB) systems.
- Researchers used multiple methods to search for anisotropy in the GWB but did not find significant evidence.
- They placed a Bayesian 95% upper limit on anisotropy level at $(C_{l>0} / C_{l=0}) < 20\%$, suggesting any potential anisotropy is likely to be small.
- Astrophysical simulations conditioned on the isotropic GWB were performed to investigate expected levels of anisotropy from a random distribution of SMBHB systems.
- Various techniques were discussed for modeling and inferring GWB anisotropy with Pulsar Timing Array (PTA) data, including weighted spherical harmonics, analytic forms for basis functions, square root expressions, polarization mapping, and data-driven bases.
- Previous studies had limited data and struggled to detect any potential anisotropies.
- This study contributes significantly to our understanding of both isotropic and anisotropic nanohertz GWBs and provides insights into future studies.

## Summary

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has reported evidence for the presence of an isotropic nanohertz gravitational wave background (GWB) in its 15-year dataset. However, if the GWB is produced by a population of inspiraling supermassive black hole binary (SMBHB) systems, then the background is expected to be anisotropic, depending on the distribution of these systems in the local Universe and the statistical properties of the SMBHB population. In this study, researchers aimed to search for anisotropy in the GWB using multiple methods and bases to describe its power on the sky. They did not find significant evidence of anisotropy and placed a Bayesian 95% upper limit on its level such that $(C_{l>0} / C_{l=0}) < 20\%$, indicating that any potential anisotropy is likely to be small. To further investigate expected levels of anisotropy from a random distribution of SMBHB systems, astrophysical simulations conditioned on the isotropic GWB inferred from the 15-year dataset were performed. The results showed that this dataset has sufficient sensitivity to probe a large fraction of predicted levels of anisotropy. The authors also discussed various techniques used to model and infer GWB anisotropy with Pulsar Timing Array (PTA) data. These techniques include expressing angular power as a linear expansion of weighted spherical harmonics, computing analytic forms for basis functions, imposing positive behavior on GWB through square root expressions, mapping polarization content, and using data-driven bases for efficient modeling. Prior to this study only one dedicated PTA search for GWB anisotropy had been conducted by another collaboration; however due to limited data from only six high-quality pulsars it was difficult to detect any potential anisotropies. Overall this study contributes significantly to our understanding of both isotropic and anisotropic nanohertz GWBs and highlights opportunities and challenges associated with searching for such signals in pulsar timing array data. The findings provide valuable insights into future studies aiming to probe nature and origin of gravitational waves.