The NANOGrav 15 yr Data Set: Search for Anisotropy in the Gravitational-wave Background
Authors: Agazie Gabriella , Anumarlapudi Akash , Archibald Anne M. , Arzoumanian Zaven , Baker Paul T. , Bécsy Bence , Blecha Laura , Brazier Adam , Brook Paul R. , Burke-Spolaor Sarah , Casey-Clyde J. Andrew , Charisi Maria , Chatterjee Shami , Cohen Tyler , Cordes James M. , Cornish Neil J. , Crawford Fronefield , Cromartie H. Thankful , Crowter Kathryn , DeCesar Megan E. , Demorest Paul B. , Dolch Timothy , Drachler Brendan , Ferrara Elizabeth C. , Fiore William , Fonseca Emmanuel , Freedman Gabriel E. , Gardiner Emiko , Garver-Daniels Nate , Gentile Peter A. , Glaser Joseph , Good Deborah C. , Gültekin Kayhan , Hazboun Jeffrey S. , Jennings Ross J. , Johnson Aaron D. , Jones Megan L. , Kaiser Andrew R. , Kaplan David L. , Kelley Luke Zoltan , Kerr Matthew , Key Joey S. , Laal Nima , Lam Michael T. , Lamb William G. , W. Lazio T. Joseph , Lewandowska Natalia , Liu Tingting , Lorimer Duncan R. , Luo Jing , Lynch Ryan S. , Ma Chung-Pei , Madison Dustin R. , McEwen Alexander , McKee James W. , McLaughlin Maura A. , McMann Natasha , Meyers Bradley W. , Mingarelli Chiara M. F. , Mitridate Andrea , Ng Cherry , Nice David J. , Ocker Stella Koch , Olum Ken D. , Pennucci Timothy T. , Perera Benetge B. P. , Pol Nihan S. , Radovan Henri A. , Ransom Scott M. , Ray Paul S. , Romano Joseph D. , Sardesai Shashwat C. , Schmiedekamp Ann , Schmiedekamp Carl , Schmitz Kai , Schult Levi , Shapiro-Albert Brent J. , Siemens Xavier , Simon Joseph , Siwek Magdalena S. , Stairs Ingrid H. , Stinebring Daniel R. , Stovall Kevin , Susobhanan Abhimanyu , Swiggum Joseph K. , Taylor Stephen R. , Turner Jacob E. , Unal Caner , Vallisneri Michele , Vigeland Sarah J. , Wahl Haley M. , Witt Caitlin A. , Young Olivia 
Published: October 2023

Abstract
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 yr data set. However, if the GWB is produced by a population of inspiraling supermassive black hole binary (SMBHB) systems, then the background is predicted to be anisotropic, depending on the distribution of these systems in the local Universe and the statistical properties of the SMBHB population. In this work, we search for anisotropy in the GWB using multiple methods and bases to describe the distribution of the GWB power on the sky. We do not find significant evidence of anisotropy. By modeling the angular power distribution as a sum over spherical harmonics (where the coefficients are not bound to always generate positive power everywhere), we find that the Bayesian 95% upper limit on the level of dipole anisotropy is (C

l=1/C

l=0) < 27%. This is similar to the upper limit derived under the constraint of positive power everywhere, indicating that the dipole may be close to the data-informed regime. By contrast, the constraints on anisotropy at higher spherical-harmonic multipoles are strongly prior dominated. We also derive conservative estimates on the anisotropy expected from a random distribution of SMBHB systems using astrophysical simulations conditioned on the isotropic GWB inferred in the 15 yr data set and show that this data set has sufficient sensitivity to probe a large fraction of the predicted level of anisotropy. We end by highlighting the opportunities and challenges in searching for anisotropy in pulsar timing array data.