Paper: The NANOGrav 15 yr Data Set: Evidence for a 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, Rand Burnette, Robin Case, Maria Charisi, Shami Chatterjee, Katerina Chatziioannou, Belinda D. Cheeseboro, Siyuan Chen, Tyler Cohen, James M. Cordes, Neil J. Cornish, Fronefield Crawford, H. Thankful Cromartie, Kathryn Crowter, Curt J. Cutler, Megan E. DeCesar, Dallas DeGan, Paul B. Demorest, Heling Deng, Timothy Dolch, Brendan Drachler, Justin A. Ellis, Elizabeth C. Ferrara, William Fiore, Emmanuel Fonseca, Gabriel E. Freedman, Nate Garver-Daniels, Peter A. Gentile, Kyle A. Gersbach, Joseph Glaser, Deborah C. Good, Kayhan Gültekin, Jeffrey S. Hazboun, Sophie Hourihane, Kristina Islo, Ross J. Jennings, Aaron D. Johnson, Megan L. Jones, Andrew R. Kaiser, David L. Kaplan, Luke Zoltan Kelley, Matthew Kerr, Joey S. Key, Tonia C. Klein, Nima Laal, Michael T. Lam, William G. Lamb, T. Joseph W. Lazio, Natalia Lewandowska, Tyson B. Littenberg, Tingting Liu, Andrea Lommen, Duncan R. Lorimer, Jing Luo, Ryan S. Lynch, Chung-Pei Ma, Dustin R. Madison, Margaret A. Mattson, Alexander McEwen, James W. McKee, Maura A. McLaughlin, Natasha McMann, Bradley W. Meyers, Patrick M. Meyers, Chiara M. F. Mingarelli, Andrea Mitridate, Priyamvada Natarajan, Cherry Ng, David J. Nice, Stella Koch Ocker, Ken D. Olum, Timothy T. Pennucci, Benetge B. P. Perera, Polina Petrov, Nihan S. Pol, Henri A. Radovan, Scott M. Ransom, Paul S. Ray, Joseph D. Romano, Shashwat C. Sardesai, Ann Schmiedekamp, Carl Schmiedekamp, Kai Schmitz, Levi Schult, Brent J. Shapiro-Albert, Xavier Siemens, Joseph Simon, Magdalena S. Siwek, Ingrid H. Stairs, Daniel R. Stinebring, Kevin Stovall, Jerry P. Sun, Abhimanyu Susobhanan, Joseph K. Swiggum, Jacob Taylor, Stephen R. Taylor, Jacob E. Turner, Caner Unal, Michele Vallisneri, Rutger van Haasteren, Sarah J. Vigeland, Haley M. Wahl, Qiaohong Wang, Caitlin A. Witt, Olivia Young
Figure caption: Summary of the main Bayesian and optimal-statistic analyses presented in this paper, which establish multiple lines of evidence for the presence of Hellings–Downs correlations in the 15 yr NANOGrav data set. Throughout we refer to the 68.3%, 95.4%, and 99.7% regions of distributions as 1σ/2σ/3σ regions, even in two dimensions. (a) Bayesian “free-spectrum” analysis, showing posteriors (gray violins) of independent variance parameters for a Hellings–Downs-correlated stochastic process at frequencies i/T, with T the total data set time span. The blue represents the posterior median and 1σ/2σ posterior bands for a power-law model; the dashed black line corresponds to a γ = 13/3 (SMBHB-like) power law, plotted with the median posterior amplitude. See Section 3 for more details. (b) Posterior probability distribution of GWB amplitude and spectral exponent in an HD power-law model, showing 1σ/2σ/3σ credible regions. The value γ GWB = 13/3 (dashed black line) is included in the 99% credible region. The amplitude is referenced to f ref = 1 yr−1 (blue) and 0.1 yr−1 (orange). The dashed blue and orange curves in the ﹩{\mathrm{log}}_{10}{A}_{\mathrm{GWB}}﹩ subpanel show its marginal posterior density for a γ = 13/3 model, with f ref = 1 yr−1 and f ref = 0.1 yr−1, respectively. See Section 3 for more details. (c) Angular-separation-binned interpulsar correlations, measured from 2211 distinct pairings in our 67-pulsar array using the frequentist optimal statistic, assuming maximum-a-posteriori pulsar noise parameters and γ = 13/3 common-process amplitude from a Bayesian inference analysis. The bin widths are chosen so that each includes approximately the same number of pulsar pairs, and central bin locations avoid zeros of the Hellings–Downs curve. This binned reconstruction accounts for correlations between pulsar pairs (Romano et al. 2021; Allen & Romano 2022). The dashed black line shows the Hellings–Downs correlation pattern, and the binned points are normalized by the amplitude of the γ = 13/3 common process to be on the same scale. Note that we do not employ binning of interpulsar correlations in our detection statistics; this panel serves as a visual consistency check only. See Section 4 for more frequentist results. (d) Bayesian reconstruction of normalized interpulsar correlations, modeled as a cubic spline within a variable-exponent power-law model. The violins plot the marginal posterior densities (plus median and 68% credible values) of the correlations at the knots. The knot positions are fixed and are chosen on the basis of features of the Hellings–Downs curve (also shown as a dashed black line for reference): they include the maximum and minimum angular separations, the two zero-crossings of the Hellings–Downs curve, and the position of minimum correlation. See Section 3 for more details.