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

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

Problem Statement
Pulsar Timing Arrays (PTAs) rely on the rotational stability of millisecond pulsars to detect nanohertz gravitational waves (GWs). However, PTA datasets are heavily contaminated by noise sources, including intrinsic spin noise, interstellar medium (ISM) variations causing dispersion measure (DM) fluctuations, solar wind effects, and timing model errors. Mis-modeling these chromatic (frequency-dependent) noise sources can bias the inference of a common-spectrum process, potentially inflating or suppressing the Hellings-Downs (HD) correlation signature of the stochastic gravitational wave background (GWB). Previous analyses of the NANOGrav 15-year (NG15) dataset utilized standard noise models (e.g., DMX for DM variations), but recent work suggests that customized chromatic-noise models (CNMs) may better mitigate these systematics. This paper investigates how replacing standard noise models with CNMs impacts GWB significance, spectral characterization, and searches for continuous waves (CWs) and alternative gravity polarizations.

Methodology
The authors reanalyzed the NG15 dataset using the CNMs developed in Larsen, Baier et al. (2026). Key methodological components include:

• Noise Modeling: The standard "DMX" model for dispersion measure was replaced with a Gaussian Process (DMGP) model. Additionally, the CNM framework tests for and applies customized chromatic signals (e.g., free chromatic variations, stochastic solar wind, transient events) for each of the 67 pulsars based on Bayesian evidence.
• Likelihood Implementation: To handle the computational cost of per-pulsar chromatic models, the authors implemented a "Cached-Chromatic Likelihood." This technique extends the two-step marginalization process to an $N+2$-step process, allowing chromatic noise parameters (fixed to their maximum a posteriori values from single-pulsar analyses) to be marginalized out before the main GW analysis. This reduced likelihood evaluation times by factors of $\sim2$ (for common uncorrelated red noise) to $\sim4$ (for HD correlations) compared to traditional implementations.
• Analysis Scope: The study reproduced key GW analyses from Agazie et al. (2023a, 2023d, 2024) and Agarwal et al. (2025), including:
  • GWB spectral characterization (power-law, broken power-law, and free spectrum).
  • HD correlation significance (Bayes factors and Optimal Statistic).
  • Searches for scalar-transverse (ST) polarization modes.
  • All-sky and targeted continuous wave searches.
  • Astrophysical and cosmological interpretations of the GWB.

Key Contributions and Results

1. Enhanced HD Correlation Significance:

   • The Bayes factor for HD correlations over a common uncorrelated red noise (CURN) process increased by approximately $8\times$, from $\sim185$ (in Agazie et al. 2023a) to $1571 \pm 14$ using the CNMs with 14 Fourier modes.
   • Frequentist analysis using the Optimal Statistic showed an improvement in signal-to-noise ratio (S/N) from $5.0$ to $5.3$.
   • The Bayesian $p$-value decreased from $7.9 \times 10^{-4}$ ($3.16\sigma$) to $4.5 \times 10^{-4}$ ($3.32\sigma$).
   • The authors attribute this increase to improved noise mitigation, particularly in the 10–30 nHz frequency range, rather than the addition of new data.

2. Spectral Characterization:

   • The inferred GWB amplitude decreased to $A_{\text{GWB}} = 2.1^{+0.6}_{-0.5} \times 10^{-15}$ (at fixed $\gamma = 13/3$), a $\sim12\%$ reduction from previous estimates.
   • The spectral index increased to $\gamma_{\text{GWB}} = 3.5^{+0.7}_{-0.6}$ in varied-$\gamma$ analyses, moving closer to the theoretical expectation of $13/3$ for supermassive black hole binaries (SMBHBs).
   • A previously reported significant excursion in the power spectrum at 16 nHz (in Agazie et al. 2025a) was found to be a noise-model-dependent artifact linked to PSR J1713+0747 and is no longer significant under CNMs.

3. Alternative Polarizations and Continuous Waves:

   • Evidence for a non-Einsteinian scalar-transverse (ST) mode was reduced. The Bayes factor favoring HD over ST increased from $\sim2.3$ to $\sim158$, and the 95% upper limit on the ST amplitude decreased by $\sim26\%$.
   • In all-sky CW searches, the significance of a low-frequency candidate ($\sim4.2$ nHz) remained statistically insignificant when modeled against an HD-correlated background ($B_{\text{HD+CW}}^{\text{HD}} = 1.69 \pm 0.06$).
   • Targeted CW searches for specific AGN candidates (SDSS J0729+4008 and SDSS J1536+0441) showed reduced significance, with the Bayes factors dropping to levels consistent with the general population of candidates.
   • The detection volume for the NANOGrav array increased by a factor of $3.2$ for CW searches due to reduced white noise floors at mid-to-high frequencies.

4. Red-Noise Budget and Detector Sensitivity:

   • The number of pulsars exhibiting significant intrinsic red noise (IRN) alongside the common process dropped from 12 (in Agazie et al. 2023b) to 6. This suggests that previous IRN detections were likely mismodeled chromatic noise.
   • Sensitivity curves indicate that CNMs provide substantial gains in sensitivity at mid-to-high frequencies, shifting the most sensitive frequency band from $\sim5$ nHz (DMX) to $\sim6.5$ nHz.

5. Astrophysical and Cosmological Interpretations:

   • Astrophysical (SMBHB): The updated spectral characterization is consistent with an SMBHB origin. Fits to phenomenological population models showed only marginal shifts, with a slight preference for lower galaxy characteristic masses and inner hardening slopes.
   • Cosmological: Reinterpretations involving cosmic inflation, first-order phase transitions, and stable cosmic strings showed only slight quantitative shifts in parameter posteriors. For cosmic strings, the best-fit tension $G\mu$ decreased by $\sim35\%$, implying a lower energy scale for the string-producing phase transition.

Significance and Claims
The paper claims that the primary impact of CNMs is the improved mitigation of chromatic noise, which leads to a more robust and statistically significant detection of the HD correlation signature. The authors state that the GWB spectral characterization is now "less tension" with galaxy population models and that the amplitude is slightly quieter and steeper.

Crucially, the authors emphasize that while the statistical evidence for the GWB has strengthened, the overall astrophysical and cosmological interpretations remain largely unchanged because they are currently "prior dominated." The paper concludes that detailed modeling of chromatic effects is imperative for future datasets to optimize detector sensitivity and ensure accurate characterization of the nanohertz GW background, but it does not claim to have resolved all tensions between the GWB signal and theoretical models. The work serves as a validation of the CNM framework for future NANOGrav analyses.