The NANOGrav 15 yr Data Set: Search for Anisotropy in the Gravitational-wave Background

Creators: Agazie, Gabriella¹; Anumarlapudi, Akash¹; Archibald, Anne M.²; Arzoumanian, Zaven³; Baker, Paul T.⁴; Bécsy, Bence⁵; Blecha, Laura⁶; Brazier, Adam⁷; Brook, Paul R.⁸; Burke-Spolaor, Sarah⁹; Casey-Clyde, J. Andrew¹⁰; Charisi, Maria¹¹; Chatterjee, Shami⁷; Cohen, Tyler¹²; Cordes, James M.⁷; Cornish, Neil J.¹³; Crawford, Fronefield¹⁴; Cromartie, H. Thankful^{7, 15}; Crowter, Kathryn¹⁶; DeCesar, Megan E.^{17, 18}; Demorest, Paul B.¹⁹; Dolch, Timothy^{20, 21}; Drachler, Brendan²²; Ferrara, Elizabeth C.^{23, 3}; Fiore, William⁹; Fonseca, Emmanuel⁹; Freedman, Gabriel E.¹; Gardiner, Emiko²⁴; Garver-Daniels, Nate⁹; Gentile, Peter A.⁹; Glaser, Joseph⁹; Good, Deborah C.^{10, 25}; Gültekin, Kayhan²⁶; Hazboun, Jeffrey S.⁵; Jennings, Ross J.^{9, 27}; Johnson, Aaron D.^{1, 28}; Jones, Megan L.¹; Kaiser, Andrew R.⁹; Kaplan, David L.¹; Kelley, Luke Zoltan²⁴; Kerr, Matthew¹⁸; Key, Joey S.²⁹; Laal, Nima⁵; Lam, Michael T.²²; Lamb, William G.¹¹; W. Lazio, T. Joseph³⁰; Lewandowska, Natalia³¹; Liu, Tingting⁹; Lorimer, Duncan R.⁹; Luo, Jing^{32, 33}; Lynch, Ryan S.³⁴; Ma, Chung-Pei²⁴; Madison, Dustin R.³⁵; McEwen, Alexander¹; McKee, James W.³⁶; McLaughlin, Maura A.⁹; McMann, Natasha¹¹; Meyers, Bradley W.^{16, 37}; Mingarelli, Chiara M. F.^{10, 25, 38}; Mitridate, Andrea³⁹; Ng, Cherry³²; Nice, David J.⁴⁰; Ocker, Stella Koch⁷; Olum, Ken D.⁴¹; Pennucci, Timothy T.⁴²; Perera, Benetge B. P.⁴³; Pol, Nihan S.¹¹; Radovan, Henri A.⁴⁴; Ransom, Scott M.¹⁹; Ray, Paul S.¹⁸; Romano, Joseph D.⁴⁵; Sardesai, Shashwat C.¹; Schmiedekamp, Ann⁴⁶; Schmiedekamp, Carl⁴⁶; Schmitz, Kai⁴⁷; Schult, Levi¹¹; Shapiro-Albert, Brent J.^{9, 48}; Siemens, Xavier^{1, 5}; Simon, Joseph^{49, 50}; Siwek, Magdalena S.⁵¹; Stairs, Ingrid H.¹⁶; Stinebring, Daniel R.⁵²; Stovall, Kevin¹⁹; Susobhanan, Abhimanyu¹; Swiggum, Joseph K.^{40, 27}; Taylor, Stephen R.¹¹; Turner, Jacob E.⁹; Unal, Caner^{53, 54}; Vallisneri, Michele^{28, 30}; Vigeland, Sarah J.¹; Wahl, Haley M.⁹; Witt, Caitlin A.^{55, 56}; Young, Olivia²²

1. University of Wisconsin–Milwaukee
2. Newcastle University
3. Goddard Space Flight Center
4. Widener University
5. Oregon State University
6. University of Florida
7. Cornell University
8. University of Birmingham
9. West Virginia University
10. University of Connecticut
11. Vanderbilt University
12. New Mexico Institute of Mining and Technology
13. Montana State University
14. Franklin & Marshall College
15. NASA Hubble Fellowship: Einstein Postdoctoral Fellow.
16. University of British Columbia
17. George Mason University
18. United States Naval Research Laboratory
19. National Radio Astronomy Observatory
20. Hillsdale College
21. Eureka Scientific
22. Rochester Institute of Technology
23. University of Maryland, College Park
24. University of California, Berkeley
25. Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, USA
26. University of Michigan–Ann Arbor
27. NANOGrav Physics Frontiers Center Postdoctoral Fellow.
28. California Institute of Technology
29. University of Washington
30. Jet Propulsion Lab
31. State University of New York at Oswego
32. University of Toronto
33. Deceased.
34. Green Bank Observatory, P.O. Box 2, Green Bank, WV 24944, USA
35. University of the Pacific
36. University of Hull
37. International Centre for Radio Astronomy Research
38. Yale University
39. Deutsches Elektronen-Synchrotron DESY
40. Lafayette College
41. Tufts University
42. Eötvös Loránd University
43. Arecibo Observatory
44. University of Puerto Rico System
45. Texas Tech University
46. Pennsylvania State University
47. University of Münster
48. Giant Army, 915A 17th Avenue, Seattle WA 98122, USA
49. University of Colorado Boulder
50. NSF Astronomy and Astrophysics Postdoctoral Fellow.
51. Harvard-Smithsonian Center for Astrophysics
52. Oberlin College
53. Ben-Gurion University of the Negev
54. Feza Gürsey Institute
55. Northwestern University
56. Adler Planetarium

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.

Copyright and License

Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Acknowledgement

The NANOGrav collaboration receives support from National Science Foundation (NSF) Physics Frontiers Center award numbers 1430284 and 2020265, the Gordon and Betty Moore Foundation, NSF AccelNet award number 2114721, an NSERC Discovery Grant, and CIFAR. The Arecibo Observatory is a facility of the NSF operated under cooperative agreement (AST-1744119) by the University of Central Florida (UCF) in alliance with Universidad Ana G. Méndez (UAGM) and Yang Enterprises (YEI), Inc. The Green Bank Observatory is a facility of the NSF operated under cooperative agreement by Associated Universities, Inc. The National Radio Astronomy Observatory is a facility of the NSF operated under cooperative agreement by Associated Universities, Inc. This work was conducted in part using the resources of the Advanced Computing Center for Research and Education (ACCRE) at Vanderbilt University, Nashville, TN.

L.B. acknowledges support from the National Science Foundation under award AST-1909933 and from the Research Corporation for Science Advancement under Cottrell Scholar Award No. 27553. P.R.B. is supported by the Science and Technology Facilities Council, grant number ST/W000946/1. S.B. gratefully acknowledges the support of a Sloan Fellowship, and the support of NSF under award #1815664. M.C. and S.R.T. acknowledge support from NSF AST-2007993. M.C. and N.S.P. were supported by the Vanderbilt Initiative in Data Intensive Astrophysics (VIDA) Fellowship. Support for this work was provided by the NSF through the Grote Reber Fellowship Program administered by Associated Universities, Inc./National Radio Astronomy Observatory. Support for H.T.C. is provided by NASA through the NASA Hubble Fellowship Program grant #HST-HF2-51453.001 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. Pulsar research at UBC is supported by an NSERC Discovery Grant and by CIFAR. K.C. is supported by a UBC Four Year Fellowship (6456). M.E.D. acknowledges support from the Naval Research Laboratory by NASA under contract S-15633Y. T.D. and M.T.L. are supported by an NSF Astronomy and Astrophysics Grant (AAG) award number 2009468. E.C.F. is supported by NASA under award number 80GSFC21M0002. G.E.F., S.C.S., and S.J.V. are supported by NSF award PHY-2011772. The Flatiron Institute is supported by the Simons Foundation. A.D.J. and M.V. acknowledge support from the Caltech and Jet Propulsion Laboratory President's and Director's Research and Development Fund. A.D.J. acknowledges support from the Sloan Foundation. The work of N.La. and X.S. is partly supported by the George and Hannah Bolinger Memorial Fund in the College of Science at Oregon State University. N.La. acknowledges the support from Larry W. Martin and Joyce B. O'Neill Endowed Fellowship in the College of Science at Oregon State University. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004). D.R.L. and M.A.M. are supported by NSF #1458952. M.A.M. is supported by NSF #2009425. C.M.F.M. was supported in part by the National Science Foundation under grant Nos. NSF PHY-1748958 and AST-2106552. A.Mi. is supported by the Deutsche Forschungsgemeinschaft under Germany's Excellence Strategy—EXC 2121 Quantum Universe—390833306. The Dunlap Institute is funded by an endowment established by the David Dunlap family and the University of Toronto. K.D.O. was supported in part by NSF grant No. 2207267. T.T.P. acknowledges support from the Extragalactic Astrophysics Research Group at Eötvös Loránd University, funded by the Eötvös Loránd Research Network (ELKH), which was used during the development of this research. S.M.R. and I.H.S. are CIFAR Fellows. Portions of this work performed at NRL were supported by ONR 6.1 basic research funding. J.D.R. also acknowledges support from start-up funds from Texas Tech University. J.S. is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-2202388, and acknowledges previous support by the NSF under award 1847938. S.R.T. acknowledges support from an NSF CAREER award #2146016. C.U. acknowledges support from BGU (Kreitman fellowship), and the Council for Higher Education and Israel Academy of Sciences and Humanities (Excellence fellowship). C.A.W. acknowledges support from CIERA, the Adler Planetarium, and the Brinson Foundation through a CIERA-Adler postdoctoral fellowship. O.Y. is supported by the National Science Foundation Graduate Research Fellowship under grant No. DGE-2139292.

Contributions

An alphabetical-order author list was used for this Letter in recognition of the fact that a large, decade-timescale project such as NANOGrav is necessarily the result of the work of many people. All authors contributed to the activities of the NANOGrav collaboration leading to the work presented here, and reviewed the manuscript, text, and figures prior to the Letter's submission. Additional specific contributions to this Letter are as follows. N.S.P., S.R.T., and J.D.R. proposed and planned this analysis. N.S.P. coordinated the execution of the analysis and writing of this Letter. N.S.P., S.R.T., E.C.G., L.Z.K., J.D.R., K.D.O., P.M., and N.L. contributed text to the Letter. N.S.P. led the frequentist analyses, N.L. and L.S. led the Bayesian analyses, and E.C.G. led the holodeck-based astrophysical simulation analyses, all of which had input from S.R.T, J.D.R, L.Z.K., K.O., and P.M. The NANOGrav 15 yr data set was developed by G.A., A.A., A.M.A., Z.A., P.T.B., P.R.B., H.T.C., K.C., M.E.D., P.B.D., T.D., E.C.F., W.F., E.F., G.E.F., N.G., P.A.G., J.G., D.C.G., J.S.H., R.J.J., M.L.J., D.L.K., M.K., M.T.L., D.R.L., J.L., R.S.L., A.M., M.A.M., N.M., B.W.M., C.N., D.J.N., T.T.P., B.B.P.P., N.S.P., H.A.R., S.M.R., P.S.R., A.S., C.S., B.J.S., I.H.S., K.S., A.S., J.K.S., and H.M.W. through a combination of observations, arrival time calculations, data checks and refinements, and timing model development and analysis; additional specific contributions to the data set are summarized in NG15dataset.

Facilities

Arecibo - Arecibo observatory, GBT - Green Bank Telescope, VLA - Very Large Array.

Software References

astropy (Astropy Collaboration et al. 2022), ENTERPRISE (Ellis et al. 2020), enterprise_extensions (Taylor et al. 2021), healpy (Zonca et al. 2019), holodeck (Agazie et al. 2023d), Jupyter (Kluyver et al. 2016), MAPS (Pol et al. 2022), matplotlib (Hunter 2007), numpy (Harris et al. 2020), PTMCMC (Ellis & van Haasteren 2017), scipy (Virtanen et al. 2020).

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