The NANOGrav 15 yr data set: Posterior predictive checks for gravitational-wave detection with pulsar timing arrays
Creators: name: Agazie, Gabriella
name: Anumarlapudi, Akash
name: Archibald, Anne M.
name: Arzoumanian, Zaven
name: Baier, Jeremy George
name: Baker, Paul T.
name: Bécsy, Bence
name: Blecha, Laura
name: Brazier, Adam
name: Brook, Paul R.
name: Burke-Spolaor, Sarah
name: Casey-Clyde, J. Andrew
name: Charisi, Maria
name: Chatterjee, Shami
name: Chatziioannou, Katerina
name: Cohen, Tyler
name: Cordes, James M.
name: Cornish, Neil J.
name: Crawford, Fronefield
name: Cromartie, H. Thankful
name: Crowter, Kathryn
name: DeCesar, Megan E.
name: Demorest, Paul B.
name: Deng, Heling
name: Dey, Lankeswar
name: Dolch, Timothy
name: Ferrara, Elizabeth C.
name: Fiore, William
name: Fonseca, Emmanuel
name: Freedman, Gabriel E.
name: Gardiner, Emiko C.
name: Garver-Daniels, Nate
name: Gentile, Peter A.
name: Gersbach, Kyle A.
name: Glaser, Joseph
name: Good, Deborah C.
name: Gültekin, Kayhan
name: Hazboun, Jeffrey S.
name: Jennings, Ross J.
name: Johnson, Aaron D.
name: Jones, Megan L.
name: Kaiser, Andrew R.
name: Kaplan, David L.
name: Kelley, Luke Zoltan
name: Kerr, Matthew
name: Key, Joey S.
name: Laal, Nima
name: Lam, Michael T.
name: Lamb, William G.
name: Larsen, Bjorn
name: Lazio, T. Joseph W.
name: Lewandowska, Natalia
name: Liu, Tingting
name: Lorimer, Duncan R.
name: Luo, Jing
name: Lynch, Ryan S.
name: Ma, Chung-Pei
name: Madison, Dustin R.
name: McEwen, Alexander
name: McKee, James W.
name: McLaughlin, Maura A.
name: McMann, Natasha
name: Meyers, Bradley W.
name: Meyers, Patrick M.
name: Mingarelli, Chiara M. F.
name: Mitridate, Andrea
name: Ng, Cherry
name: Nice, David J.
name: Ocker, Stella Koch
name: Olum, Ken D.
name: Pennucci, Timothy T.
name: Perera, Benetge B. P.
name: Pol, Nihan S.
name: Radovan, Henri A.
name: Ransom, Scott M.
name: Ray, Paul S.
name: Romano, Joseph D.
name: Runnoe, Jessie C.
name: Saffer, Alexander
name: Sardesai, Shashwat C.
name: Schmiedekamp, Ann
name: Schmiedekamp, Carl
name: Schmitz, Kai
name: Shapiro-Albert, Brent J.
name: Siemens, Xavier
name: Simon, Joseph
name: Siwek, Magdalena S.
name: Fiscella, Sophia V. Sosa
name: Stairs, Ingrid H.
name: Stinebring, Daniel R.
name: Stovall, Kevin
name: Susobhanan, Abhimanyu
name: Swiggum, Joseph K.
name: Taylor, Stephen R.
name: Turner, Jacob E.
name: Unal, Caner
name: Vallisneri, Michele
name: Vigeland, Sarah J.
name: Wahl, Haley M.
name: Witt, Caitlin A.
name: Wright, David
name: Young, Olivia
Publisher: name: arXiv
Year: 2024
Subjects: subject: High Energy Astrophysical Phenomena (astro-ph.HE)
subject: General Relativity and Quantum Cosmology (gr-qc)
subject: FOS: Physical sciences
subject: FOS: Physical sciences

description: Pulsar-timing-array experiments have reported evidence for a stochastic background of nanohertz gravitational waves consistent with the signal expected from a population of supermassive--black-hole binaries. Their analyses assume power-law spectra for intrinsic pulsar noise and for the background, as well as a Hellings--Downs cross-correlation pattern among the gravitational-wave--induced residuals across pulsars. These assumptions may not be realized in actuality. We test them in the NANOGrav 15 yr data set using Bayesian posterior predictive checks. After fitting our fiducial model to real data, we generate a population of simulated data-set replications. We use the replications to assess whether the optimal-statistic significance, inter-pulsar correlations, and spectral coefficients are extreme. We recover Hellings--Downs correlations in simulated data sets at significance levels consistent with the correlations measured in the NANOGrav 15 yr data set. A similar test on spectral coefficients shows that their values in real data are not extreme compared to their distributions across replications. We also evaluate the evidence for the stochastic background using posterior-predictive versions of the frequentist optimal statistic and of Bayesian model comparison, and find comparable significance (3.2 $σ$ and 3 $σ$ respectively) to what was previously reported for the standard statistics. We conclude with novel visualizations of the reconstructed gravitational waveforms that enter the residuals for each pulsar. Our analysis strengthens confidence in the identification and characterization of the gravitational-wave background.
description: 20 pages, 14 Figures, accepted to PRD