How to Detect an Astrophysical Nanohertz Gravitational Wave Background
Authors: Bécsy Bence , Cornish Neil J. , Meyers Patrick M. , Kelley Luke Zoltan , Agazie Gabriella , Anumarlapudi Akash , Archibald Anne M. , Arzoumanian Zaven , Baker Paul T. , Blecha Laura , Brazier Adam , Brook Paul R. , Burke-Spolaor Sarah , Casey-Clyde J. Andrew , Charisi Maria , Chatterjee Shami , Chatziioannou Katerina , Cohen Tyler , Cordes James M. , Crawford Fronefield , Cromartie H. Thankful , Crowter Kathryn , DeCesar Megan E. , Demorest Paul B. , Dolch Timothy , Ferrara Elizabeth C. , Fiore William , Fonseca Emmanuel , Freedman Gabriel E. , Garver-Daniels Nate , Gentile Peter A. , Glaser Joseph , Good Deborah C. , Gültekin Kayhan , Hazboun Jeffrey S. , Hourihane Sophie , Jennings Ross J. , Johnson Aaron D. , Jones Megan L. , Kaiser Andrew R. , Kaplan David L. , Kerr Matthew , Key Joey S. , Laal Nima , Lam Michael T. , Lamb William G. , W. Lazio T. Joseph , Lewandowska Natalia , Littenberg Tyson B. , 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 , Shapiro-Albert Brent J. , Siemens Xavier , Simon Joseph , Siwek Magdalena S. , Sosa Fiscella Sophia V. , Stairs Ingrid H. , Stinebring Daniel R. , Stovall Kevin , Susobhanan Abhimanyu , Swiggum Joseph K. , Taylor Stephen R. , Turner Jacob E. , Unal Caner , Vallisneri Michele , van Haasteren Rutger , Vigeland Sarah J. , Wahl Haley M. , Witt Caitlin A. , Young Olivia 
Published: November 2023

Abstract
Analyses of pulsar timing data have provided evidence for a stochastic gravitational wave background in the nanohertz frequency band. The most plausible source of this background is the superposition of signals from millions of supermassive black hole binaries. The standard statistical techniques used to search for this background and assess its significance make several simplifying assumptions, namely (i) Gaussianity, (ii) isotropy, and most often, (iii) a power-law spectrum. However, a stochastic background from a finite collection of binaries does not exactly satisfy any of these assumptions. To understand the effect of these assumptions, we test standard analysis techniques on a large collection of realistic simulated data sets. The data-set length, observing schedule, and noise levels were chosen to emulate the NANOGrav 15 yr data set. Simulated signals from millions of binaries drawn from models based on the Illustris cosmological hydrodynamical simulation were added to the data. We find that the standard statistical methods perform remarkably well on these simulated data sets, even though their fundamental assumptions are not strictly met. They are able to achieve a confident detection of the background. However, even for a fixed set of astrophysical parameters, different realizations of the universe result in a large variance in the significance and recovered parameters of the background. We also find that the presence of loud individual binaries can bias the spectral recovery of the background if we do not account for them.