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

Gabriella Agazie; Akash Anumarlapudi; Anne M. Archibald; Zaven Arzoumanian; Paul T. Baker; Bence Bécsy; Laura Blecha; Adam Brazier; Paul R. Brook; Sarah Burke-Spolaor; J. Andrew Casey-Clyde; Maria Charisi; Shami Chatterjee; Tyler Cohen; James M. Cordes; Neil J. Cornish; Fronefield Crawford; H. Thankful Cromartie; Kathryn Crowter; Megan E. DeCesar; Paul B. Demorest; Timothy Dolch; Brendan Drachler; Elizabeth C. Ferrara; William Fiore; Emmanuel Fonseca; Gabriel E. Freedman; Emiko Gardiner; Nate Garver-Daniels; Peter A. Gentile; Joseph Glaser; Deborah C. Good; Kayhan Gültekin; Jeffrey S. Hazboun; Ross J. Jennings; Aaron D. Johnson; Megan L. Jones; Andrew R. Kaiser; David L. Kaplan; Luke Zoltan Kelley; Matthew Kerr; Joey S. Key; Nima Laal; Michael T. Lam; William G. Lamb; T. Joseph W. Lazio; Natalia Lewandowska; Tingting Liu; Duncan R. Lorimer; Jing Luo; Ryan S. Lynch; Chung-Pei Ma; Dustin R. Madison; Alexander McEwen; James W. McKee; Maura A. McLaughlin; Natasha McMann; Bradley W. Meyers; Chiara M. F. Mingarelli; Andrea Mitridate; Cherry Ng; David J. Nice; Stella Koch Ocker; Ken D. Olum; Timothy T. Pennucci; Benetge B. P. Perera; 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; Abhimanyu Susobhanan; Joseph K. Swiggum; Stephen R. Taylor; Jacob E. Turner; Caner Unal; Michele Vallisneri; Sarah J. Vigeland; Haley M. Wahl; Caitlin A. Witt; Olivia Young

doi:10.3847/2041-8213/acf4fd

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

Gabriella Agazie, Akash Anumarlapudi, Anne M. Archibald, Zaven Arzoumanian, Paul T. Baker, Bence Bécsy, Laura Blecha, Adam Brazier, Paul R. Brook, Sarah Burke-Spolaor, J. Andrew Casey-Clyde, Maria Charisi, Shami Chatterjee, Tyler Cohen, James M. Cordes, Neil J. Cornish, Fronefield Crawford, H. Thankful Cromartie, Kathryn Crowter, Megan E. DeCesarPaul B. Demorest, Timothy Dolch, Brendan Drachler, Elizabeth C. Ferrara, William Fiore, Emmanuel Fonseca, Gabriel E. Freedman, Emiko Gardiner, Nate Garver-Daniels, Peter A. Gentile, Joseph Glaser, Deborah C. Good, Kayhan Gültekin, Jeffrey S. Hazboun, Ross J. Jennings, Aaron D. Johnson, Megan L. Jones, Andrew R. Kaiser, David L. Kaplan, Luke Zoltan Kelley, Matthew Kerr, Joey S. Key, Nima Laal, Michael T. Lam, William G. Lamb, T. Joseph W. Lazio, Natalia Lewandowska, Tingting Liu, Duncan R. Lorimer, Jing Luo, Ryan S. Lynch, Chung-Pei Ma, Dustin R. Madison, Alexander McEwen, James W. McKee, Maura A. McLaughlin, Natasha McMann, Bradley W. Meyers, Chiara M. F. Mingarelli, Andrea Mitridate, Cherry Ng, David J. Nice, Stella Koch Ocker, Ken D. Olum, Timothy T. Pennucci, Benetge B. P. Perera, 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, Abhimanyu Susobhanan, Joseph K. Swiggum, Stephen R. Taylor, Jacob E. Turner, Caner Unal, Michele Vallisneri, Sarah J. Vigeland, Haley M. Wahl, Caitlin A. Witt, Olivia Young

^*Corresponding author for this work

Physics and Astronomy

Research output: Contribution to journal › Letter › peer-review

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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.

Original language	English
Article number	L3
Number of pages	15
Journal	Astrophysical Journal Letters
Volume	956
Issue number	1
Early online date	5 Oct 2023
DOIs	https://doi.org/10.3847/2041-8213/acf4fd
Publication status	Published - 10 Oct 2023

Bibliographical note

Acknowledgments:
Author 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.

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.

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

Software: 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).

Keywords

Supermassive black holes
Gravitational wave astronomy
Pulsars
Gravitational waves

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AgazieG2023NANOGravFinal published version, 1.86 MBLicence: Creative Commons: Attribution (CC BY)

Cite this

Agazie, G., Anumarlapudi, A., Archibald, A. M., Arzoumanian, Z., Baker, P. T., Bécsy, B., Blecha, L., Brazier, A., Brook, P. R., Burke-Spolaor, S., Casey-Clyde, J. A., Charisi, M., Chatterjee, S., Cohen, T., Cordes, J. M., Cornish, N. J., Crawford, F., Cromartie, H. T., Crowter, K., ... Young, O. (2023). The NANOGrav 15 yr Data Set: Search for Anisotropy in the Gravitational-wave Background. Astrophysical Journal Letters, 956(1), Article L3. https://doi.org/10.3847/2041-8213/acf4fd

@article{e43c9440636541daab3613cc65ca820c,

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

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 (Cl=1/Cl=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.",

keywords = "Supermassive black holes, Gravitational wave astronomy, Pulsars, Gravitational waves",

author = "Gabriella Agazie and Akash Anumarlapudi and Archibald, {Anne M.} and Zaven Arzoumanian and Baker, {Paul T.} and Bence B{\'e}csy and Laura Blecha and Adam Brazier and Brook, {Paul R.} and Sarah Burke-Spolaor and Casey-Clyde, {J. Andrew} and Maria Charisi and Shami Chatterjee and Tyler Cohen and Cordes, {James M.} and Cornish, {Neil J.} and Fronefield Crawford and Cromartie, {H. Thankful} and Kathryn Crowter and DeCesar, {Megan E.} and Demorest, {Paul B.} and Timothy Dolch and Brendan Drachler and Ferrara, {Elizabeth C.} and William Fiore and Emmanuel Fonseca and Freedman, {Gabriel E.} and Emiko Gardiner and Nate Garver-Daniels and Gentile, {Peter A.} and Joseph Glaser and Good, {Deborah C.} and Kayhan G{\"u}ltekin and Hazboun, {Jeffrey S.} and Jennings, {Ross J.} and Johnson, {Aaron D.} and Jones, {Megan L.} and Kaiser, {Andrew R.} and Kaplan, {David L.} and Kelley, {Luke Zoltan} and Matthew Kerr and Key, {Joey S.} and Nima Laal and Lam, {Michael T.} and Lamb, {William G.} and {W. Lazio}, {T. Joseph} and Natalia Lewandowska and Tingting Liu and Lorimer, {Duncan R.} and Jing Luo and Lynch, {Ryan S.} and Chung-Pei Ma and Madison, {Dustin R.} and Alexander McEwen and McKee, {James W.} and McLaughlin, {Maura A.} and Natasha McMann and Meyers, {Bradley W.} and Mingarelli, {Chiara M. F.} and Andrea Mitridate and Cherry Ng and Nice, {David J.} and Ocker, {Stella Koch} and Olum, {Ken D.} and Pennucci, {Timothy T.} and Perera, {Benetge B. P.} and Pol, {Nihan S.} and Radovan, {Henri A.} and Ransom, {Scott M.} and Ray, {Paul S.} and Romano, {Joseph D.} and Sardesai, {Shashwat C.} and Ann Schmiedekamp and Carl Schmiedekamp and Kai Schmitz and Levi Schult and Shapiro-Albert, {Brent J.} and Xavier Siemens and Joseph Simon and Siwek, {Magdalena S.} and Stairs, {Ingrid H.} and Stinebring, {Daniel R.} and Kevin Stovall and Abhimanyu Susobhanan and Swiggum, {Joseph K.} and Taylor, {Stephen R.} and Turner, {Jacob E.} and Caner Unal and Michele Vallisneri and Vigeland, {Sarah J.} and Wahl, {Haley M.} and Witt, {Caitlin A.} and Olivia Young",

note = "Acknowledgments: Author 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. 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. M{\'e}ndez (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 E{\"o}tv{\"o}s Lor{\'a}nd University, funded by the E{\"o}tv{\"o}s Lor{\'a}nd 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. Facilities: Arecibo - Arecibo observatory, GBT - Green Bank Telescope, VLA - Very Large Array. Software: 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).",

year = "2023",

month = oct,

day = "10",

doi = "10.3847/2041-8213/acf4fd",

language = "English",

volume = "956",

journal = "Astrophysical Journal Letters",

issn = "2041-8205",

publisher = "Institute of Physics Publishing Ltd",

number = "1",

}

Agazie, G, Anumarlapudi, A, Archibald, AM, Arzoumanian, Z, Baker, PT, Bécsy, B, Blecha, L, Brazier, A, Brook, PR, Burke-Spolaor, S, Casey-Clyde, JA, Charisi, M, Chatterjee, S, Cohen, T, Cordes, JM, Cornish, NJ, Crawford, F, Cromartie, HT, Crowter, K, DeCesar, ME, Demorest, PB, Dolch, T, Drachler, B, Ferrara, EC, Fiore, W, Fonseca, E, Freedman, GE, Gardiner, E, Garver-Daniels, N, Gentile, PA, Glaser, J, Good, DC, Gültekin, K, Hazboun, JS, Jennings, RJ, Johnson, AD, Jones, ML, Kaiser, AR, Kaplan, DL, Kelley, LZ, Kerr, M, Key, JS, Laal, N, Lam, MT, Lamb, WG, W. Lazio, TJ, Lewandowska, N, Liu, T, Lorimer, DR, Luo, J, Lynch, RS, Ma, C-P, Madison, DR, McEwen, A, McKee, JW, McLaughlin, MA, McMann, N, Meyers, BW, Mingarelli, CMF, Mitridate, A, Ng, C, Nice, DJ, Ocker, SK, Olum, KD, Pennucci, TT, Perera, BBP, Pol, NS, Radovan, HA, Ransom, SM, Ray, PS, Romano, JD, Sardesai, SC, Schmiedekamp, A, Schmiedekamp, C, Schmitz, K, Schult, L, Shapiro-Albert, BJ, Siemens, X, Simon, J, Siwek, MS, Stairs, IH, Stinebring, DR, Stovall, K, Susobhanan, A, Swiggum, JK, Taylor, SR, Turner, JE, Unal, C, Vallisneri, M, Vigeland, SJ, Wahl, HM, Witt, CA & Young, O 2023, 'The NANOGrav 15 yr Data Set: Search for Anisotropy in the Gravitational-wave Background', Astrophysical Journal Letters, vol. 956, no. 1, L3. https://doi.org/10.3847/2041-8213/acf4fd

TY - JOUR

T1 - The NANOGrav 15 yr Data Set

T2 - Search for Anisotropy in the Gravitational-wave Background

AU - Agazie, Gabriella

AU - Anumarlapudi, Akash

AU - Archibald, Anne M.

AU - Arzoumanian, Zaven

AU - Baker, Paul T.

AU - Bécsy, Bence

AU - Blecha, Laura

AU - Brazier, Adam

AU - Brook, Paul R.

AU - Burke-Spolaor, Sarah

AU - Casey-Clyde, J. Andrew

AU - Charisi, Maria

AU - Chatterjee, Shami

AU - Cohen, Tyler

AU - Cordes, James M.

AU - Cornish, Neil J.

AU - Crawford, Fronefield

AU - Cromartie, H. Thankful

AU - Crowter, Kathryn

AU - DeCesar, Megan E.

AU - Demorest, Paul B.

AU - Dolch, Timothy

AU - Drachler, Brendan

AU - Ferrara, Elizabeth C.

AU - Fiore, William

AU - Fonseca, Emmanuel

AU - Freedman, Gabriel E.

AU - Gardiner, Emiko

AU - Garver-Daniels, Nate

AU - Gentile, Peter A.

AU - Glaser, Joseph

AU - Good, Deborah C.

AU - Gültekin, Kayhan

AU - Hazboun, Jeffrey S.

AU - Jennings, Ross J.

AU - Johnson, Aaron D.

AU - Jones, Megan L.

AU - Kaiser, Andrew R.

AU - Kaplan, David L.

AU - Kelley, Luke Zoltan

AU - Kerr, Matthew

AU - Key, Joey S.

AU - Laal, Nima

AU - Lam, Michael T.

AU - Lamb, William G.

AU - W. Lazio, T. Joseph

AU - Lewandowska, Natalia

AU - Liu, Tingting

AU - Lorimer, Duncan R.

AU - Luo, Jing

AU - Lynch, Ryan S.

AU - Ma, Chung-Pei

AU - Madison, Dustin R.

AU - McEwen, Alexander

AU - McKee, James W.

AU - McLaughlin, Maura A.

AU - McMann, Natasha

AU - Meyers, Bradley W.

AU - Mingarelli, Chiara M. F.

AU - Mitridate, Andrea

AU - Ng, Cherry

AU - Nice, David J.

AU - Ocker, Stella Koch

AU - Olum, Ken D.

AU - Pennucci, Timothy T.

AU - Perera, Benetge B. P.

AU - Pol, Nihan S.

AU - Radovan, Henri A.

AU - Ransom, Scott M.

AU - Ray, Paul S.

AU - Romano, Joseph D.

AU - Sardesai, Shashwat C.

AU - Schmiedekamp, Ann

AU - Schmiedekamp, Carl

AU - Schmitz, Kai

AU - Schult, Levi

AU - Shapiro-Albert, Brent J.

AU - Siemens, Xavier

AU - Simon, Joseph

AU - Siwek, Magdalena S.

AU - Stairs, Ingrid H.

AU - Stinebring, Daniel R.

AU - Stovall, Kevin

AU - Susobhanan, Abhimanyu

AU - Swiggum, Joseph K.

AU - Taylor, Stephen R.

AU - Turner, Jacob E.

AU - Unal, Caner

AU - Vallisneri, Michele

AU - Vigeland, Sarah J.

AU - Wahl, Haley M.

AU - Witt, Caitlin A.

AU - Young, Olivia

N1 - Acknowledgments: Author 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. 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. Facilities: Arecibo - Arecibo observatory, GBT - Green Bank Telescope, VLA - Very Large Array. Software: 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).

PY - 2023/10/10

Y1 - 2023/10/10

N2 - 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 (Cl=1/Cl=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.

AB - 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 (Cl=1/Cl=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.

KW - Supermassive black holes

KW - Gravitational wave astronomy

KW - Pulsars

KW - Gravitational waves

U2 - 10.3847/2041-8213/acf4fd

DO - 10.3847/2041-8213/acf4fd

M3 - Letter

SN - 2041-8205

VL - 956

JO - Astrophysical Journal Letters

JF - Astrophysical Journal Letters

IS - 1

M1 - L3

ER -

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

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