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; Joseph T.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

doi:10.3847/2041-8213/ad99d3

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, Joseph T.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

Physics and Astronomy

University of Wisconsin-Milwaukee
Newcastle University
NASA Goddard Space Flight Center
Oregon State University
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Harvard & Smithsonian
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Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
Middle East Technical University
Ben-Gurion University of the Negev
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Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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, g_run (f ) = g + b ln (f /f_ref ). 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, b Î [-0.80, 2.96], and an inconclusive Bayes factor, B(RPL versus CPL) = 0.69 ± 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.

Original language	English
Article number	L29
Journal	Astrophysical Journal Letters
Volume	978
Issue number	2
DOIs	https://doi.org/10.3847/2041-8213/ad99d3
State	Published - Jan 10 2025

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10.3847/2041-8213/ad99d3

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Agazie, G., Anumarlapudi, A., Archibald, A. M., Arzoumanian, Z., Baier, J. G., 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., ... Young, O. (2025). The NANOGrav 15 yr Data Set: Running of the Spectral Index. Astrophysical Journal Letters, 978(2), Article L29. https://doi.org/10.3847/2041-8213/ad99d3

@article{2f825dae534e47c69b2ec3f3487c3287,

title = "The NANOGrav 15 yr Data Set: Running of the Spectral Index",

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, grun (f ) = g + b ln (f /fref ). 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, b {\^I} [-0.80, 2.96], and an inconclusive Bayes factor, B(RPL versus CPL) = 0.69 ± 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.",

author = "Gabriella Agazie and Akash Anumarlapudi and Archibald, \{Anne M.\} and Zaven Arzoumanian and Baier, \{Jeremy G.\} 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 Heling Deng and Lankeswar Dey and Timothy Dolch and David Esmyol and Ferrara, \{Elizabeth C.\} and William Fiore and Emmanuel Fonseca and Freedman, \{Gabriel E.\} and Gardiner, \{Emiko C.\} and Nate Garver-Daniels and Gentile, \{Peter A.\} and Gersbach, \{Kyle 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 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 Bjorn Larsen and Lazio, \{Joseph T.W.\} and Natalia Lewandowska and \{Lino dos Santos\}, \{Rafael R.\} and Tingting Liu and Lorimer, \{Duncan R.\} and Jing Luo and Lynch, \{Ryan S.\} and Ma, \{Chung Pei\} and Madison, \{Dustin R.\} and Alexander McEwen and McKee, \{James W.\} and McLaughlin, \{Maura A.\} and Natasha McMann and Meyers, \{Bradley W.\} and Meyers, \{Patrick M.\} 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 Runnoe, \{Jessie C.\} and Alexander Saffer and Sardesai, \{Shashwat C.\} and Ann Schmiedekamp and Carl Schmiedekamp and Kai Schmitz and Tobias Schr{\"o}der and Shapiro-Albert, \{Brent J.\} and Xavier Siemens and Joseph Simon and Siwek, \{Magdalena S.\} and \{Sosa Fiscella\}, \{Sophia V.\} 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 \{van Haasteren\}, Rutger and Vigeland, \{Sarah J.\} and \{von Eckardstein\}, Richard and Wahl, \{Haley M.\} and Witt, \{Caitlin A.\} and David Wright and Olivia Young",

note = "Publisher Copyright: {\textcopyright} 2025. The Author(s)",

year = "2025",

month = jan,

day = "10",

doi = "10.3847/2041-8213/ad99d3",

language = "English",

volume = "978",

journal = "Astrophysical Journal Letters",

issn = "2041-8205",

publisher = "American Astronomical Society",

number = "2",

}

Agazie, G, Anumarlapudi, A, Archibald, AM, Arzoumanian, Z, Baier, JG, 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, Deng, H, Dey, L, Dolch, T, Esmyol, D, Ferrara, EC, Fiore, W, Fonseca, E, Freedman, GE, Gardiner, EC, Garver-Daniels, N, Gentile, PA, Gersbach, KA, Glaser, J, Good, DC, Gültekin, K, Hazboun, JS, Jennings, RJ, Johnson, AD, Jones, ML, Kaplan, DL, Kelley, LZ, Kerr, M, Key, JS, Laal, N, Lam, MT, Lamb, WG, Larsen, B, Lazio, JTW, Lewandowska, N, Lino dos Santos, RR, Liu, T, Lorimer, DR, Luo, J, Lynch, RS, Ma, CP, Madison, DR, McEwen, A, McKee, JW, McLaughlin, MA, McMann, N, Meyers, BW, Meyers, PM, 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, Runnoe, JC, Saffer, A, Sardesai, SC, Schmiedekamp, A, Schmiedekamp, C, Schmitz, K, Schröder, T, Shapiro-Albert, BJ, Siemens, X, Simon, J, Siwek, MS, Sosa Fiscella, SV, Stairs, IH, Stinebring, DR, Stovall, K, Susobhanan, A, Swiggum, JK, Taylor, SR, Turner, JE, Unal, C, Vallisneri, M, van Haasteren, R, Vigeland, SJ, von Eckardstein, R, Wahl, HM, Witt, CA, Wright, D & Young, O 2025, 'The NANOGrav 15 yr Data Set: Running of the Spectral Index', Astrophysical Journal Letters, vol. 978, no. 2, L29. https://doi.org/10.3847/2041-8213/ad99d3

TY - JOUR

T1 - The NANOGrav 15 yr Data Set

T2 - Running of the Spectral Index

AU - Agazie, Gabriella

AU - Anumarlapudi, Akash

AU - Archibald, Anne M.

AU - Arzoumanian, Zaven

AU - Baier, Jeremy G.

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 - Deng, Heling

AU - Dey, Lankeswar

AU - Dolch, Timothy

AU - Esmyol, David

AU - Ferrara, Elizabeth C.

AU - Fiore, William

AU - Fonseca, Emmanuel

AU - Freedman, Gabriel E.

AU - Gardiner, Emiko C.

AU - Garver-Daniels, Nate

AU - Gentile, Peter A.

AU - Gersbach, Kyle 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 - 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 - Larsen, Bjorn

AU - Lazio, Joseph T.W.

AU - Lewandowska, Natalia

AU - Lino dos Santos, Rafael R.

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 - Meyers, Patrick M.

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 - Runnoe, Jessie C.

AU - Saffer, Alexander

AU - Sardesai, Shashwat C.

AU - Schmiedekamp, Ann

AU - Schmiedekamp, Carl

AU - Schmitz, Kai

AU - Schröder, Tobias

AU - Shapiro-Albert, Brent J.

AU - Siemens, Xavier

AU - Simon, Joseph

AU - Siwek, Magdalena S.

AU - Sosa Fiscella, Sophia V.

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 - van Haasteren, Rutger

AU - Vigeland, Sarah J.

AU - von Eckardstein, Richard

AU - Wahl, Haley M.

AU - Witt, Caitlin A.

AU - Wright, David

AU - Young, Olivia

PY - 2025/1/10

Y1 - 2025/1/10

N2 - 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, grun (f ) = g + b ln (f /fref ). 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, b Î [-0.80, 2.96], and an inconclusive Bayes factor, B(RPL versus CPL) = 0.69 ± 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.

AB - 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, grun (f ) = g + b ln (f /fref ). 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, b Î [-0.80, 2.96], and an inconclusive Bayes factor, B(RPL versus CPL) = 0.69 ± 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.

UR - https://www.scopus.com/pages/publications/85214714193

U2 - 10.3847/2041-8213/ad99d3

DO - 10.3847/2041-8213/ad99d3

M3 - Article

AN - SCOPUS:85214714193

SN - 2041-8205

VL - 978

JO - Astrophysical Journal Letters

JF - Astrophysical Journal Letters

IS - 2

M1 - L29

ER -

The NANOGrav 15 yr Data Set: Running of the Spectral Index

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