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arxiv: 2606.28554 · v1 · pith:EJLDWXHZnew · submitted 2026-06-26 · 🌌 astro-ph.CO · astro-ph.HE

The NANOGrav 15 yr Data Set: Impacts of Customized Chromatic Noise Models on Gravitational Wave Analyses

Nikita Agarwal , Gabriella Agazie , Alessandra Amosso , Akash Anumarlapudi , Anne M. Archibald , Zaven Arzoumanian , Anjana Ashok , Jeremy G. Baier
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Paul T. Baker Bence Becsy Laura Blecha Adam Brazier Paul R. Brook Sarah Burke-Spolaor Rand Burnette Robin Case J. Andrew Casey-Clyde Yu-Ting Chang 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 Graham M. Doskoch 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 Gultekin Aiden Gundersen C. J. Harris Doa Hashemi Asl Jeffrey S. Hazboun Ross J. Jennings Aaron D. Johnson Megan L. Jones David L. Kaplan Anala K. Sreekumar Luke Zoltan Kelley Matthew Kerr Joey S. Key Nima Laal Michael T. Lam William G. Lamb Bjorn Larsen T. Joseph W. Lazio Natalia Lewandowska Tingting Liu Duncan R. Lorimer Jing Luo Ryan S. Lynch Chung-Pei Ma Dustin R. Madison Ashley Martsen Cayenne Matt Alexander McEwen James W. McKee Maura A. McLaughlin Natasha McMann Bradley W. Meyers Patrick M. Meyers Matthew T. Miles Chiara M. F. Mingarelli Andrea Mitridate Cherry Ng David J. Nice Shania Nichols Stella K. Ocker Daniel J. Oliver Ken D. Olum Timothy T. Pennucci Benetge B. P. Perera Polina Petrov 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 Levi Schult Brent J. Shapiro-Albert Xavier Siemens Joseph Simon Sophia V. Sosa Fiscella Ingrid H. Stairs Daniel R. Stinebring Kevin Stovall Robin Strahler Abhimanyu Susobhanan Joseph K. Swiggum Jacob Taylor Stephen R. Taylor Mercedes S. Thompson Jacob E. Turner Michele Vallisneri Rutger van Haasteren Joris P. W. Verbiest Sarah J. Vigeland Haley M. Wahl Kalista Wayt Kevin P. Wilson Caitlin A. Witt David Wright Olivia Young
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Pith reviewed 2026-06-30 00:39 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.HE
keywords pulsar timing arraysstochastic gravitational wave backgroundHellings-Downs correlationchromatic noisenanohertz gravitational wavessupermassive black hole binariescontinuous wave searches
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The pith

Customized chromatic noise models raise the Bayes factor for Hellings-Downs correlations eightfold in pulsar timing data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies specialized models for frequency-dependent noise to the fifteen-year pulsar timing dataset. These models produce substantially stronger statistical evidence that the observed timing residuals contain the spatial correlations predicted for a stochastic gravitational wave background. The same models shift the inferred background to lower amplitude while permitting a steeper spectrum in a free fit. Searches for individual continuous-wave sources gain a larger effective volume, and support for nonstandard gravity modes declines. Reinterpretations under both supermassive black hole binary and cosmological source hypotheses show only small adjustments to model parameters.

Core claim

Use of the customized chromatic noise models on the fifteen-year dataset increases the Bayes factor for Hellings-Downs correlations over an uncorrelated red-noise process to 1571 using a power-law spectrum with fourteen Fourier modes, an eightfold rise over earlier results, while lowering the background amplitude to 2.1 times 10 to the minus fifteen at fixed index and raising the free spectral index to 3.5.

What carries the argument

Customized chromatic noise models that isolate frequency-dependent noise processes in pulsar timing residuals from a potential gravitational wave signal.

If this is right

  • The gravitational wave background spectrum appears quieter at fixed index and steeper when the index is allowed to vary.
  • The effective search volume for continuous gravitational wave sources increases by a factor of 3.2.
  • Evidence for a scalar-transverse gravitational wave polarization mode decreases.
  • Posterior distributions for both supermassive black hole binary and cosmological source models shift only marginally.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Improved separation of noise from signal could help future larger datasets distinguish astrophysical from cosmological origins of the background.
  • The same noise-modeling strategy may be worth testing on independent pulsar timing arrays to check consistency of the correlation signature.
  • If the models hold, earlier analyses may have underestimated the strength of the nanohertz gravitational wave signal mainly because of residual chromatic noise.

Load-bearing premise

The customized chromatic noise models correctly capture all relevant noise processes without removing or biasing any gravitational wave signal component.

What would settle it

An independent analysis of the same timing residuals that applies different noise models and recovers a Bayes factor near the earlier lower value would indicate that the reported increase depends on the specific noise modeling choice.

Figures

Figures reproduced from arXiv: 2606.28554 by Aaron D. Johnson, Abhimanyu Susobhanan, Adam Brazier, Aiden Gundersen, Akash Anumarlapudi, Alessandra Amosso, Alexander McEwen, Alexander Saffer, Anala K. Sreekumar, Andrea Mitridate, Anjana Ashok, Anne M. Archibald, Ann Schmiedekamp, Ashley Martsen, Bence Becsy, Benetge B. P. Perera, Bjorn Larsen, Bradley W. Meyers, Brent J. Shapiro-Albert, Caitlin A. Witt, Carl Schmiedekamp, Cayenne Matt, Cherry Ng, Chiara M. F. Mingarelli, Chung-Pei Ma, C. J. Harris, Daniel J. Oliver, Daniel R. Stinebring, David J. Nice, David L. Kaplan, David Wright, Deborah C. Good, Doa Hashemi Asl, Duncan R. Lorimer, Dustin R. Madison, Elizabeth C. Ferrara, Emiko C. Gardiner, Emmanuel Fonseca, Fronefield Crawford, Gabriel E. Freedman, Gabriella Agazie, Graham M. Doskoch, Haley M. Wahl, Heling Deng, Henri A. Radovan, H. Thankful Cromartie, Ingrid H. Stairs, Jacob E. Turner, Jacob Taylor, James M. Cordes, James W. McKee, J. Andrew Casey-Clyde, Jeffrey S. Hazboun, Jeremy G. Baier, Jessie C. Runnoe, Jing Luo, Joey S. Key, Joris P. W. Verbiest, Joseph D. Romano, Joseph Glaser, Joseph K. Swiggum, Joseph Simon, Kai Schmitz, Kalista Wayt, Kathryn Crowter, Kayhan Gultekin, Ken D. Olum, Kevin P. Wilson, Kevin Stovall, Kyle A. Gersbach, Lankeswar Dey, Laura Blecha, Levi Schult, Luke Zoltan Kelley, Maria Charisi, Matthew Kerr, Matthew T. Miles, Maura A. McLaughlin, Megan E. DeCesar, Megan L. Jones, Mercedes S. Thompson, Michael T. Lam, Michele Vallisneri, Natalia Lewandowska, Natasha McMann, Nate Garver-Daniels, Neil J. Cornish, Nihan S. Pol, Nikita Agarwal, Nima Laal, Olivia Young, Patrick M. Meyers, Paul B. Demorest, Paul R. Brook, Paul S. Ray, Paul T. Baker, Peter A. Gentile, Polina Petrov, Rand Burnette, Robin Case, Robin Strahler, Ross J. Jennings, Rutger van Haasteren, Ryan S. Lynch, Sarah Burke-Spolaor, Sarah J. Vigeland, Scott M. Ransom, Shami Chatterjee, Shania Nichols, Shashwat C. Sardesai, Sophia V. Sosa Fiscella, Stella K. Ocker, Stephen R. Taylor, Timothy Dolch, Timothy T. Pennucci, Tingting Liu, T. Joseph W. Lazio, Tyler Cohen, William Fiore, William G. Lamb, Xavier Siemens, Yu-Ting Chang, Zaven Arzoumanian.

Figure 1
Figure 1. Figure 1: Changes in the GWB spectrum. We compare the inference of the HD-correlated GWB model under the different noise models of CNM (blue) and DMX (orange) for different parameterizations of the PSD. The violins compare the full posteriors of a free spectral parameterization while the blue and orange curves compare the MAP power-law spectra modeled through 14 Fourier modes. The green curve is the MAP inference of… view at source ↗
Figure 2
Figure 2. Figure 2: Changes in the power law GWB inference. Parameter posteriors for a 14 frequency power-law HD model are shown for DMX in orange and CNM in blue. CNM re￾covers a steeper spectral index, closer to the theoretical value of γ = 13/3 for GW-driven SMBHB mergers (dashed, black line). GWB posteriors under the CNM are nearly identical whether varying the chromatic parameters (dark blue, dot￾dashed) or holding them … view at source ↗
Figure 4
Figure 4. Figure 4: Changes to the fixed-γ GWB inference. Es￾timates of the GWB characteristic strain spectral amplitude A at a reference frequency of 1/yr, assuming a 14f power law spectrum with fixed γ = 13/3 from 2 to 28 nHz, with (top panel) no interpulsar correlations (CURN), and (bottom panel) Hellings-Downs (HD) correlations. We estimate a sys￾tematically lower strain amplitude of AHD = 2.1 +0.6 −0.5 ×10−15 using the C… view at source ↗
Figure 5
Figure 5. Figure 5: HD significance at different frequencies. [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Changes in detection statistics for the GWB. [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Alternative polarization search. Poste￾riors for the spectral parameters of a TT-polarized (HD￾correlated) GWB and an ST-polarized GWB. Baseline re￾sults using the DMX chromatic model (orange) are repro￾duced from Agazie et al. (2024). Using our CNMs (blue) substantially improves the evidence/constraints for the HD￾correlated mode, and reduces support for a large ST mode. dataset using the single-component… view at source ↗
Figure 9
Figure 9. Figure 9: Low-frequency candidate sky localization. [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: All-Sky CW significance The top panel re￾produces a portion of [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 11
Figure 11. Figure 11: Upper limits on the chirp mass for 3C 66B [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Improved GW sensitivity with CNM. The top panel compares DMX (dashed, orange) and CNM (solid, blue) via their GWB sensitivity curves. A power-law GWB is plotted for the MAP values of the background with both DMX and CNM. The middle panel compares the all-sky CW sensitivity by shading a region of sensitivity at each frequency which spans the minimum and maximum sensi￾tivity across the sky at that frequency… view at source ↗
Figure 13
Figure 13. Figure 13: Significant red noise populations. The top panel reproduces [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Astrophysical population inference. Marginalized posteriors for the astrophysical parameters fitted against the DMX (orange) and the CNM (blue) HD-only free spectra. Histograms show our raw results and we show smoothed KDEs to aid in interpretation. Priors are shown as black dashed lines and were the same for both fits. The MBH–Mbulge normalization µ and intrinsic scatter εµ, as well as the GSMF normaliza… view at source ↗
Figure 15
Figure 15. Figure 15: Astrophysical spectral fits. Free-spectral representation of the GWB spectrum with astrophysical fits to the spectra. The violins represent the KDE reconstruc￾tions of the DMX (orange) CNM (blue) HD-only free spec￾trum. The correspondingly colored shaded regions are the 68% confidence regions for the best-fit astrophysical spectra to the data for the two noise models. With the free-spectrum representation… view at source ↗
Figure 16
Figure 16. Figure 16: Inflation and Cosmological Phase Transition. [PITH_FULL_IMAGE:figures/full_fig_p021_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Cosmic Strings. Parameter inference for a third exotic interpretations of the NG15 signal: GWs from stable cosmic strings. As in [PITH_FULL_IMAGE:figures/full_fig_p022_17.png] view at source ↗
read the original abstract

We report updated nHz gravitational wave (GW) significance, characterization, and interpretations using the customized chromatic-noise models (CNMs) developed in Larsen, Baier et al. (2026). for the NANOGrav 15-year data set. We find increased evidence for the Hellings-Downs (HD) correlation signature of the stochastic gravitational wave background (GWB), with a Bayes factor of $1571\pm14$ for HD-correlations over a common uncorrelated red-noise process using a power-law model with $14$ Fourier modes. We find this $\sim8\times$ increase in Bayes factor from Agazie et al. (2023a) is a result of improved noise mitigation. Assuming an analytic null distribution for the frequentist interpulsar correlation statistic, this corresponds to a slightly more significant measurement from $3.16\sigma$ to $3.32\sigma$ against the no-correlation scenario. Spectral inference with CNMs brings the power-law GWB amplitude down to $A_{\rm GWB} = 2.1^{+0.6}_{-0.5}\times10^{-15}$ at fixed $\gamma_{\rm GWB} = 13/3$. In a varied-$\gamma$ analysis, the spectral index increases to $\gamma_{\rm GWB}=3.5^{+0.7}_{-0.6}$. We report updates on an all-sky continuous gravitational wave (CW) search as well as select targeted searches and calculate a $3.2\times$ larger detection volume for the NANOGrav detector. With CNMs, we find reduced evidence for a non-Einsteinian, scalar-transverse mode of gravity. Finally, we reinterpret the GWB first with the assumption of an astrophysical background sourced by SMBHBs and then assuming the more exotic origins of cosmic inflation, a first-order cosmological phase transition, and stable cosmic strings. Under both the SMBHB hypothesis and the cosmological hypotheses, we see only marginal shifts in model parameter posteriors which are consistent with the slightly quieter and steeper power-law GWB spectrum.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports an updated analysis of the NANOGrav 15-year pulsar timing array data set using customized chromatic noise models (CNMs) from a companion paper. It claims an approximately 8-fold increase in the Bayes factor (to 1571±14) favoring the Hellings-Downs correlation over a common uncorrelated red-noise process (power-law model with 14 Fourier modes), a modest rise in frequentist significance from 3.16σ to 3.32σ, a lower GWB amplitude (A_GWB = 2.1^{+0.6}_{-0.5}×10^{-15} at γ_GWB=13/3), a steeper spectral index when γ is free (3.5^{+0.7}_{-0.6}), a 3.2× larger CW detection volume, reduced evidence for scalar-transverse modes, and only marginal shifts in SMBHB and cosmological model posteriors.

Significance. If the CNMs demonstrably preserve the common-process signal, the work would provide a concrete demonstration that refined per-pulsar noise modeling can substantially strengthen evidence for the HD signature and tighten GWB parameter constraints. The numerical updates and dual astrophysical/cosmological reinterpretations would be useful benchmarks for the PTA community. The modest frequentist significance gain and the dependence on an unvalidated separation between chromatic and achromatic terms limit the immediate strength of the conclusions.

major comments (2)
  1. [Abstract and Results] Abstract and main results: The central claim that the ~8× Bayes-factor increase results from improved noise mitigation requires explicit verification that the additional per-pulsar chromatic degrees of freedom do not absorb power from the spatially correlated common red-noise process. No injection-recovery tests, posterior comparisons of the common-process parameters with/without CNMs, or other separation diagnostics are described; the formal distinction between chromatic and achromatic spectra does not by itself guarantee that the joint posterior remains unbiased.
  2. [Results] Results on frequentist significance: The reported rise from 3.16σ to 3.32σ assumes an analytic null distribution for the interpulsar correlation statistic, but the manuscript does not state whether this null distribution has been recomputed or adjusted to account for the extra free parameters introduced by the CNMs.
minor comments (2)
  1. [Abstract] The citation 'Larsen, Baier et al. (2026)' should include a preprint identifier or note on publication status, as the CNMs are central to all quantitative claims.
  2. [Abstract] The quoted uncertainties on the Bayes factor (1571±14) and on A_GWB, γ_GWB are given to high precision; the text should briefly indicate the sampling method or convergence diagnostics used to obtain them.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and for identifying areas where the manuscript can be strengthened. We address each major comment below. Where appropriate, we will revise the manuscript to provide additional clarification and supporting material.

read point-by-point responses

  1. Referee: [Abstract and Results] Abstract and main results: The central claim that the ~8× Bayes-factor increase results from improved noise mitigation requires explicit verification that the additional per-pulsar chromatic degrees of freedom do not absorb power from the spatially correlated common red-noise process. No injection-recovery tests, posterior comparisons of the common-process parameters with/without CNMs, or other separation diagnostics are described; the formal distinction between chromatic and achromatic spectra does not by itself guarantee that the joint posterior remains unbiased.

    Authors: We agree that additional diagnostics would strengthen the presentation. The companion paper validates the CNMs through extensive per-pulsar tests, and the separation relies on the distinct frequency scaling of chromatic versus achromatic processes. In the revised manuscript we will add direct posterior comparisons of the common-process amplitude and spectral index with and without CNMs to demonstrate that the spatially correlated signal is preserved rather than absorbed. We will also expand the discussion of why the frequency-dependent separation provides robustness. Full injection-recovery tests specific to the GWB analysis are not included here but are referenced to ongoing work; the observed Bayes-factor increase is consistent with reduced per-pulsar noise variance allowing clearer recovery of the correlated component. revision: partial

  2. Referee: [Results] Results on frequentist significance: The reported rise from 3.16σ to 3.32σ assumes an analytic null distribution for the interpulsar correlation statistic, but the manuscript does not state whether this null distribution has been recomputed or adjusted to account for the extra free parameters introduced by the CNMs.

    Authors: The analytic null distribution is the same as that used in Agazie et al. (2023a) because the CNMs are pulsar-specific noise models that do not alter the structure of the correlation statistic or the null hypothesis of no spatial correlations. The extra degrees of freedom are absorbed into individual pulsar likelihoods and do not change the distribution of the statistic under the null. We will revise the text to explicitly state this assumption and provide the justification that recomputation is unnecessary. revision: yes

Circularity Check

0 steps flagged

Standard Bayesian GW analyses with companion-supplied noise models show no algebraic reduction to inputs

full rationale

The paper performs standard likelihood comparisons (Bayes factors for HD correlations vs. common uncorrelated red noise, spectral inference on power-law GWB parameters) after substituting the CNMs developed in the cited companion paper. These outputs are computed quantities from the data and the fixed noise-model parameterization; they are not equivalent by construction to the CNM parameters themselves, nor do any equations define the target GWB evidence in terms of the noise-model fit. The self-citation supplies the per-pulsar chromatic terms but does not carry the load of proving the HD signature; the correlation statistic and model comparison remain independent of that construction. No self-definitional steps, fitted inputs relabeled as predictions, or imported uniqueness theorems appear in the reported chain.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The analysis depends on the accuracy of the CNMs from the companion paper and on standard PTA assumptions; only the abstract is available so the full parameter count cannot be audited.

free parameters (2)
  • A_GWB = 2.1 x 10^{-15}
    Amplitude of the power-law GWB spectrum fitted at fixed gamma=13/3
  • gamma_GWB = 3.5
    Spectral index of the GWB when allowed to vary
axioms (1)
  • domain assumption Hellings-Downs correlations are the expected signature for an isotropic stochastic gravitational wave background in general relativity
    Used as the target model for the Bayes factor comparison

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Reference graph

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