The Astrophysical Journal Letters (Jan 2025)
The NANOGrav 15 yr Data Set: Running of the Spectral Index
- Gabriella Agazie,
- Akash Anumarlapudi,
- Anne M. Archibald,
- Zaven Arzoumanian,
- Jeremy G. Baier,
- 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,
- Heling Deng,
- Lankeswar Dey,
- Timothy Dolch,
- David Esmyol,
- Elizabeth C. Ferrara,
- William Fiore,
- Emmanuel Fonseca,
- Gabriel E. Freedman,
- Emiko C. Gardiner,
- Nate Garver-Daniels,
- Peter A. Gentile,
- Kyle A. Gersbach,
- Joseph Glaser,
- Deborah C. Good,
- Kayhan Gültekin,
- Jeffrey S. Hazboun,
- Ross J. Jennings,
- Aaron D. Johnson,
- Megan L. Jones,
- David L. Kaplan,
- Luke Zoltan Kelley,
- Matthew Kerr,
- Joey S. Key,
- Nima Laal,
- Michael T. Lam,
- William G. Lamb,
- Bjorn Larsen,
- T. Joseph W. Lazio,
- Natalia Lewandowska,
- Rafael R. Lino dos Santos,
- 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,
- Patrick M. 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,
- Jessie C. Runnoe,
- Alexander Saffer,
- Shashwat C. Sardesai,
- Ann Schmiedekamp,
- Carl Schmiedekamp,
- Kai Schmitz,
- Tobias Schröder,
- Brent J. Shapiro-Albert,
- Xavier Siemens,
- Joseph Simon,
- Magdalena S. Siwek,
- Sophia V. Sosa Fiscella,
- Ingrid H. Stairs,
- Daniel R. Stinebring,
- Kevin Stovall,
- Abhimanyu Susobhanan,
- Joseph K. Swiggum,
- Stephen R. Taylor,
- Jacob E. Turner,
- Caner Unal,
- Michele Vallisneri,
- Rutger van Haasteren,
- Sarah J. Vigeland,
- Richard von Eckardstein,
- Haley M. Wahl,
- Caitlin A. Witt,
- David Wright,
- Olivia Young
Affiliations
- Gabriella Agazie
- ORCiD
- Center for Gravitation, Cosmology and Astrophysics, Department of Physics, University of Wisconsin–Milwaukee , P.O. Box 413, Milwaukee, WI 53201, USA
- Akash Anumarlapudi
- ORCiD
- Center for Gravitation, Cosmology and Astrophysics, Department of Physics, University of Wisconsin–Milwaukee , P.O. Box 413, Milwaukee, WI 53201, USA
- Anne M. Archibald
- ORCiD
- Newcastle University , NE1 7RU, UK
- Zaven Arzoumanian
- X-Ray Astrophysics Laboratory , NASA Goddard Space Flight Center, Code 662, Greenbelt, MD 20771, USA
- Jeremy G. Baier
- ORCiD
- Department of Physics, Oregon State University , Corvallis, OR 97331, USA
- Paul T. Baker
- ORCiD
- Department of Physics and Astronomy, Widener University , One University Place, Chester, PA 19013, USA
- Bence Bécsy
- ORCiD
- Department of Physics, Oregon State University , Corvallis, OR 97331, USA
- Laura Blecha
- ORCiD
- Physics Department, University of Florida , Gainesville, FL 32611, USA
- Adam Brazier
- ORCiD
- Cornell Center for Astrophysics and Planetary Science and Department of Astronomy, Cornell University , Ithaca, NY 14853, USA; Cornell Center for Advanced Computing, Cornell University , Ithaca, NY 14853, USA
- Paul R. Brook
- ORCiD
- Institute for Gravitational Wave Astronomy and School of Physics and Astronomy, University of Birmingham , Edgbaston, Birmingham B15 2TT, UK
- Sarah Burke-Spolaor
- ORCiD
- Department of Physics and Astronomy, West Virginia University , P.O. Box 6315, Morgantown, WV 26506, USA; Center for Gravitational Waves and Cosmology, West Virginia University , Chestnut Ridge Research Building, Morgantown, WV 26505, USA
- J. Andrew Casey-Clyde
- ORCiD
- Department of Physics, University of Connecticut , 196 Auditorium Road, U-3046, Storrs, CT 06269-3046, USA
- Maria Charisi
- ORCiD
- Department of Physics and Astronomy, Vanderbilt University , 2301 Vanderbilt Place, Nashville, TN 37235, USA
- Shami Chatterjee
- ORCiD
- Cornell Center for Astrophysics and Planetary Science and Department of Astronomy, Cornell University , Ithaca, NY 14853, USA
- Tyler Cohen
- ORCiD
- Department of Physics, New Mexico Institute of Mining and Technology , 801 Leroy Place, Socorro, NM 87801, USA
- James M. Cordes
- ORCiD
- Cornell Center for Astrophysics and Planetary Science and Department of Astronomy, Cornell University , Ithaca, NY 14853, USA
- Neil J. Cornish
- ORCiD
- Department of Physics, Montana State University , Bozeman, MT 59717, USA
- Fronefield Crawford
- ORCiD
- Department of Physics and Astronomy, Franklin & Marshall College , P.O. Box 3003, Lancaster, PA 17604, USA
- H. Thankful Cromartie
- ORCiD
- National Research Council Research Associate, National Academy of Sciences , Washington, DC 20001, USA
- Kathryn Crowter
- ORCiD
- Department of Physics and Astronomy, University of British Columbia , 6224 Agricultural Road, Vancouver, BC V6T 1Z1, Canada
- Megan E. DeCesar
- ORCiD
- George Mason University , Fairfax, VA 22030, USA
- Paul B. Demorest
- ORCiD
- National Radio Astronomy Observatory , 1003 Lopezville Road, Socorro, NM 87801, USA
- Heling Deng
- Department of Physics, Oregon State University , Corvallis, OR 97331, USA
- Lankeswar Dey
- ORCiD
- Department of Physics and Astronomy, West Virginia University , P.O. Box 6315, Morgantown, WV 26506, USA; Center for Gravitational Waves and Cosmology, West Virginia University , Chestnut Ridge Research Building, Morgantown, WV 26505, USA
- Timothy Dolch
- ORCiD
- Department of Physics, Hillsdale College , 33 East College Street, Hillsdale, MI 49242, USA; Eureka Scientific , 2452 Delmer Street, Suite 100, Oakland, CA 94602-3017, USA
- David Esmyol
- Institute for Theoretical Physics, University of Münster , 48149 Münster, Germany ; [email protected]
- Elizabeth C. Ferrara
- ORCiD
- Department of Astronomy, University of Maryland , College Park, MD 20742, USA; Center for Research and Exploration in Space Science and Technology , NASA/GSFC, Greenbelt, MD 20771, USA; NASA Goddard Space Flight Center , Greenbelt, MD 20771, USA
- William Fiore
- ORCiD
- Department of Physics and Astronomy, West Virginia University , P.O. Box 6315, Morgantown, WV 26506, USA; Center for Gravitational Waves and Cosmology, West Virginia University , Chestnut Ridge Research Building, Morgantown, WV 26505, USA
- Emmanuel Fonseca
- ORCiD
- Department of Physics and Astronomy, West Virginia University , P.O. Box 6315, Morgantown, WV 26506, USA; Center for Gravitational Waves and Cosmology, West Virginia University , Chestnut Ridge Research Building, Morgantown, WV 26505, USA
- Gabriel E. Freedman
- ORCiD
- Center for Gravitation, Cosmology and Astrophysics, Department of Physics, University of Wisconsin–Milwaukee , P.O. Box 413, Milwaukee, WI 53201, USA
- Emiko C. Gardiner
- ORCiD
- Department of Astronomy, University of California , Berkeley, 501 Campbell Hall #3411, Berkeley, CA 94720, USA
- Nate Garver-Daniels
- ORCiD
- Department of Physics and Astronomy, West Virginia University , P.O. Box 6315, Morgantown, WV 26506, USA; Center for Gravitational Waves and Cosmology, West Virginia University , Chestnut Ridge Research Building, Morgantown, WV 26505, USA
- Peter A. Gentile
- ORCiD
- Department of Physics and Astronomy, West Virginia University , P.O. Box 6315, Morgantown, WV 26506, USA; Center for Gravitational Waves and Cosmology, West Virginia University , Chestnut Ridge Research Building, Morgantown, WV 26505, USA
- Kyle A. Gersbach
- Department of Physics and Astronomy, Vanderbilt University , 2301 Vanderbilt Place, Nashville, TN 37235, USA
- Joseph Glaser
- ORCiD
- Department of Physics and Astronomy, West Virginia University , P.O. Box 6315, Morgantown, WV 26506, USA; Center for Gravitational Waves and Cosmology, West Virginia University , Chestnut Ridge Research Building, Morgantown, WV 26505, USA
- Deborah C. Good
- ORCiD
- Department of Physics and Astronomy, University of Montana , 32 Campus Drive, Missoula, MT 59812, USA
- Kayhan Gültekin
- ORCiD
- Department of Astronomy and Astrophysics, University of Michigan , Ann Arbor, MI 48109, USA
- Jeffrey S. Hazboun
- ORCiD
- Department of Physics, Oregon State University , Corvallis, OR 97331, USA
- Ross J. Jennings
- ORCiD
- Department of Physics and Astronomy, West Virginia University , P.O. Box 6315, Morgantown, WV 26506, USA; Center for Gravitational Waves and Cosmology, West Virginia University , Chestnut Ridge Research Building, Morgantown, WV 26505, USA
- Aaron D. Johnson
- ORCiD
- Center for Gravitation, Cosmology and Astrophysics, Department of Physics, University of Wisconsin–Milwaukee , P.O. Box 413, Milwaukee, WI 53201, USA; Division of Physics, Mathematics, and Astronomy, California Institute of Technology , Pasadena, CA 91125, USA
- Megan L. Jones
- ORCiD
- Center for Gravitation, Cosmology and Astrophysics, Department of Physics, University of Wisconsin–Milwaukee , P.O. Box 413, Milwaukee, WI 53201, USA
- David L. Kaplan
- ORCiD
- Center for Gravitation, Cosmology and Astrophysics, Department of Physics, University of Wisconsin–Milwaukee , P.O. Box 413, Milwaukee, WI 53201, USA
- Luke Zoltan Kelley
- ORCiD
- Department of Astronomy, University of California , Berkeley, 501 Campbell Hall #3411, Berkeley, CA 94720, USA
- Matthew Kerr
- ORCiD
- Space Science Division, Naval Research Laboratory , Washington, DC 20375-5352, USA
- Joey S. Key
- ORCiD
- University of Washington Bothell , 18115 Campus Way NE, Bothell, WA 98011, USA
- Nima Laal
- ORCiD
- Department of Physics, Oregon State University , Corvallis, OR 97331, USA
- Michael T. Lam
- ORCiD
- SETI Institute , 339 North Bernardo Avenue Suite 200, Mountain View, CA 94043, USA; School of Physics and Astronomy, Rochester Institute of Technology , Rochester, NY 14623, USA; Laboratory for Multiwavelength Astrophysics, Rochester Institute of Technology , Rochester, NY 14623, USA
- William G. Lamb
- ORCiD
- Department of Physics and Astronomy, Vanderbilt University , 2301 Vanderbilt Place, Nashville, TN 37235, USA
- Bjorn Larsen
- Department of Physics, Yale University , New Haven, CT 06520, USA
- T. Joseph W. Lazio
- Jet Propulsion Laboratory, California Institute of Technology , 4800 Oak Grove Drive, Pasadena, CA 91109, USA
- Natalia Lewandowska
- ORCiD
- Department of Physics and Astronomy, State University of New York at Oswego , Oswego, NY 13126, USA
- Rafael R. Lino dos Santos
- ORCiD
- National Centre for Nuclear Research , Pasteura 7, 02-093 Warsaw, Poland ; [email protected]
- Tingting Liu
- ORCiD
- Department of Physics and Astronomy, West Virginia University , P.O. Box 6315, Morgantown, WV 26506, USA; Center for Gravitational Waves and Cosmology, West Virginia University , Chestnut Ridge Research Building, Morgantown, WV 26505, USA
- Duncan R. Lorimer
- ORCiD
- Department of Physics and Astronomy, West Virginia University , P.O. Box 6315, Morgantown, WV 26506, USA; Center for Gravitational Waves and Cosmology, West Virginia University , Chestnut Ridge Research Building, Morgantown, WV 26505, USA
- Jing Luo
- ORCiD
- Department of Astronomy & Astrophysics, University of Toronto , 50 St. George Street, Toronto, ON M5S 3H4, Canada
- Ryan S. Lynch
- ORCiD
- Green Bank Observatory , P.O. Box 2, Green Bank, WV 24944, USA
- Chung-Pei Ma
- ORCiD
- Department of Astronomy, University of California , Berkeley, 501 Campbell Hall #3411, Berkeley, CA 94720, USA; Department of Physics, University of California , Berkeley, CA 94720, USA
- Dustin R. Madison
- ORCiD
- Department of Physics, University of the Pacific , 3601 Pacific Avenue, Stockton, CA 95211, USA
- Alexander McEwen
- ORCiD
- Center for Gravitation, Cosmology and Astrophysics, Department of Physics, University of Wisconsin–Milwaukee , P.O. Box 413, Milwaukee, WI 53201, USA
- James W. McKee
- ORCiD
- E.A. Milne Centre for Astrophysics, University of Hull , Cottingham Road, Kingston-upon-Hull, HU6 7RX, UK; Centre of Excellence for Data Science, Artificial Intelligence and Modelling (DAIM), University of Hull , Cottingham Road, Kingston-upon-Hull, HU6 7RX, UK
- Maura A. McLaughlin
- ORCiD
- Department of Physics and Astronomy, West Virginia University , P.O. Box 6315, Morgantown, WV 26506, USA; Center for Gravitational Waves and Cosmology, West Virginia University , Chestnut Ridge Research Building, Morgantown, WV 26505, USA
- Natasha McMann
- ORCiD
- Department of Physics and Astronomy, Vanderbilt University , 2301 Vanderbilt Place, Nashville, TN 37235, USA
- Bradley W. Meyers
- ORCiD
- Department of Physics and Astronomy, University of British Columbia , 6224 Agricultural Road, Vancouver, BC V6T 1Z1, Canada; International Centre for Radio Astronomy Research, Curtin University , Bentley, WA 6102, Australia
- Patrick M. Meyers
- ORCiD
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology , Pasadena, CA 91125, USA
- Chiara M. F. Mingarelli
- ORCiD
- Department of Physics, Yale University , New Haven, CT 06520, USA
- Andrea Mitridate
- ORCiD
- Deutsches Elektronen-Synchrotron DESY , Notkestr. 85, 22607 Hamburg, Germany
- Cherry Ng
- ORCiD
- Dunlap Institute for Astronomy and Astrophysics, University of Toronto , 50 St. George Street, Toronto, ON M5S 3H4, Canada
- David J. Nice
- ORCiD
- Department of Physics, Lafayette College , Easton, PA 18042, USA
- Stella Koch Ocker
- ORCiD
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology , Pasadena, CA 91125, USA; The Observatories of the Carnegie Institution for Science , Pasadena, CA 91101, USA
- Ken D. Olum
- ORCiD
- Institute of Cosmology, Department of Physics and Astronomy, Tufts University , Medford, MA 02155, USA
- Timothy T. Pennucci
- ORCiD
- Institute of Physics and Astronomy, Eötvös Loránd University , Pázmány P. s. 1/A, 1117 Budapest, Hungary
- Benetge B. P. Perera
- ORCiD
- Arecibo Observatory , HC3 Box 53995, Arecibo, PR 00612, USA
- Nihan S. Pol
- ORCiD
- Department of Physics, Texas Tech University , Box 41051, Lubbock, TX 79409, USA
- Henri A. Radovan
- ORCiD
- Department of Physics, University of Puerto Rico , Mayagüez, PR 00681, USA
- Scott M. Ransom
- ORCiD
- National Radio Astronomy Observatory , 520 Edgemont Road, Charlottesville, VA 22903, USA
- Paul S. Ray
- ORCiD
- Space Science Division, Naval Research Laboratory , Washington, DC 20375-5352, USA
- Joseph D. Romano
- ORCiD
- Department of Physics, Texas Tech University , Box 41051, Lubbock, TX 79409, USA
- Jessie C. Runnoe
- ORCiD
- Department of Physics and Astronomy, Vanderbilt University , 2301 Vanderbilt Place, Nashville, TN 37235, USA
- Alexander Saffer
- ORCiD
- National Radio Astronomy Observatory , 520 Edgemont Road, Charlottesville, VA 22903, USA
- Shashwat C. Sardesai
- ORCiD
- Center for Gravitation, Cosmology and Astrophysics, Department of Physics, University of Wisconsin–Milwaukee , P.O. Box 413, Milwaukee, WI 53201, USA
- Ann Schmiedekamp
- ORCiD
- Department of Physics, Penn State Abington , Abington, PA 19001, USA
- Carl Schmiedekamp
- ORCiD
- Department of Physics, Penn State Abington , Abington, PA 19001, USA
- Kai Schmitz
- ORCiD
- Institute for Theoretical Physics, University of Münster , 48149 Münster, Germany ; [email protected]
- Tobias Schröder
- ORCiD
- Institute for Theoretical Physics, University of Münster , 48149 Münster, Germany ; [email protected]
- Brent J. Shapiro-Albert
- ORCiD
- Department of Physics and Astronomy, West Virginia University , P.O. Box 6315, Morgantown, WV 26506, USA; Center for Gravitational Waves and Cosmology, West Virginia University , Chestnut Ridge Research Building, Morgantown, WV 26505, USA; Giant Army , 915A 17th Avenue, Seattle, WA 98122, USA
- Xavier Siemens
- ORCiD
- Center for Gravitation, Cosmology and Astrophysics, Department of Physics, University of Wisconsin–Milwaukee , P.O. Box 413, Milwaukee, WI 53201, USA; Department of Physics, Oregon State University , Corvallis, OR 97331, USA
- Joseph Simon
- ORCiD
- Department of Astrophysical and Planetary Sciences, University of Colorado , Boulder, CO 80309, USA
- Magdalena S. Siwek
- ORCiD
- Center for Astrophysics, Harvard University , 60 Garden Street, Cambridge, MA 02138, USA
- Sophia V. Sosa Fiscella
- ORCiD
- School of Physics and Astronomy, Rochester Institute of Technology , Rochester, NY 14623, USA; Laboratory for Multiwavelength Astrophysics, Rochester Institute of Technology , Rochester, NY 14623, USA
- Ingrid H. Stairs
- ORCiD
- Department of Physics and Astronomy, University of British Columbia , 6224 Agricultural Road, Vancouver, BC V6T 1Z1, Canada
- Daniel R. Stinebring
- ORCiD
- Department of Physics and Astronomy, Oberlin College , Oberlin, OH 44074, USA
- Kevin Stovall
- ORCiD
- National Radio Astronomy Observatory , 1003 Lopezville Road, Socorro, NM 87801, USA
- Abhimanyu Susobhanan
- ORCiD
- Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut) , Callinstrasse 38, D-30167, Hannover, Germany
- Joseph K. Swiggum
- ORCiD
- Department of Physics, Lafayette College , Easton, PA 18042, USA
- Stephen R. Taylor
- ORCiD
- Department of Physics and Astronomy, Vanderbilt University , 2301 Vanderbilt Place, Nashville, TN 37235, USA
- Jacob E. Turner
- ORCiD
- Green Bank Observatory , P.O. Box 2, Green Bank, WV 24944, USA
- Caner Unal
- ORCiD
- Department of Physics, Middle East Technical University , 06531 Ankara, Turkey; Department of Physics, Ben-Gurion University of the Negev , Be’er Sheva 84105, Israel; Feza Gursey Institute, Bogazici University , Kandilli, 34684, Istanbul, Turkey
- Michele Vallisneri
- ORCiD
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology , Pasadena, CA 91125, USA; Jet Propulsion Laboratory, California Institute of Technology , 4800 Oak Grove Drive, Pasadena, CA 91109, USA
- Rutger van Haasteren
- ORCiD
- Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut) , Callinstrasse 38, D-30167, Hannover, Germany
- Sarah J. Vigeland
- ORCiD
- Center for Gravitation, Cosmology and Astrophysics, Department of Physics, University of Wisconsin–Milwaukee , P.O. Box 413, Milwaukee, WI 53201, USA
- Richard von Eckardstein
- ORCiD
- Institute for Theoretical Physics, University of Münster , 48149 Münster, Germany ; [email protected]
- Haley M. Wahl
- ORCiD
- Department of Physics and Astronomy, West Virginia University , P.O. Box 6315, Morgantown, WV 26506, USA; Center for Gravitational Waves and Cosmology, West Virginia University , Chestnut Ridge Research Building, Morgantown, WV 26505, USA
- Caitlin A. Witt
- ORCiD
- Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Northwestern University , Evanston, IL 60208, USA; Adler Planetarium , 1300 South DuSable Lake Shore Drive, Chicago, IL 60605, USA
- David Wright
- ORCiD
- Department of Physics, Oregon State University , Corvallis, OR 97331, USA
- Olivia Young
- ORCiD
- School of Physics and Astronomy, Rochester Institute of Technology , Rochester, NY 14623, USA; Laboratory for Multiwavelength Astrophysics, Rochester Institute of Technology , Rochester, NY 14623, USA
- DOI
- https://doi.org/10.3847/2041-8213/ad99d3
- Journal volume & issue
-
Vol. 978,
no. 2
p. L29
Abstract
The NANOGrav 15 yr data provide compelling evidence for a stochastic gravitational-wave (GW) background at nanohertz frequencies. The simplest model-independent approach to characterizing the frequency spectrum of this signal consists of a simple power-law fit involving two parameters: an amplitude A and a spectral index γ . In this Letter, we consider the next logical step beyond this minimal spectral model, allowing for a running (i.e., logarithmic frequency dependence) of the spectral index, ${\gamma }_{{\rm{run}}}(f)=\gamma +\beta \mathrm{ln}\left(f/{f}_{{\rm{ref}}}\right)$ . We fit this running-power-law (RPL) model to the NANOGrav 15 yr data and perform a Bayesian model comparison with the minimal constant-power-law (CPL) model, which results in a 95% credible interval for the parameter β consistent with no running, $\beta \in \left[-0.80,2.96\right]$ , and an inconclusive Bayes factor, ${ \mathcal B }\left({\rm{RPL}}\,{\rm{versus}}\,{\rm{CPL}}\right)=0.69\pm 0.01$ . We thus conclude that, at present, the minimal CPL model still suffices to adequately describe the NANOGrav signal; however, future data sets may well lead to a measurement of nonzero β . Finally, we interpret the RPL model as a description of primordial GWs generated during cosmic inflation, which allows us to combine our results with upper limits from Big Bang nucleosynthesis, the cosmic microwave background, and LIGO–Virgo–KAGRA.
Keywords
- Pulsar timing method
- Gravitational waves
- Bayesian statistics
- Cosmic inflation
- Cosmology
- Cosmic microwave background radiation
