The NANOGrav 12.5-year Data Set: Chromatic Noise Characterization & Mitigation with Time-Domain Kernels

TL;DR

The paper develops time-domain Gaussian-process kernels to model chromatic noise in pulsar timing data, offering a computationally efficient alternative to traditional Fourier-domain approaches. By applying a Bayesian model-selection framework to the NG12.5-year data, it shows pulsars prefer a variety of kernels (including Ridge, SE, RQ, and quasi-periodic forms), with multi-dimensional kernels (QP_RF) capturing frequency-dependent dispersion effects. Deterministic components (annual variations, transients) and an enhanced solar wind model are integrated, revealing how chromatic modeling reshapes white/red-noise inferences and affects the common red-noise spectral characterization relevant to the gravitational-wave background. The results underscore the need for tailored, pulsar-specific noise models in future PTA analyses (NG15/IPTA DR3) to robustly detect or constrain gravitational waves while mitigating ISM/IPM systematics.

Abstract

Pulsar timing arrays (PTAs) have recently entered the detection era, quickly moving beyond the goal of simply improving sensitivity at the lowest frequencies for the sake of observing the stochastic gravitational wave background (GWB), and focusing on its accurate spectral characterization. While all PTA collaborations around the world use Fourier-domain Gaussian processes to model the GWB and intrinsic long time-correlated (red) noise, techniques to model the time-correlated radio frequency-dependent (chromatic) processes have varied from collaboration to collaboration. Here we test a new class of models for PTA data, Gaussian processes based on time-domain kernels that model the statistics of the chromatic processes starting from the covariance matrix. As we will show, these models can be effectively equivalent to Fourier-domain models in mitigating chromatic noise. This work presents a method for Bayesian model selection across the various choices of kernel as well as deterministic chromatic models for non-stationary chromatic events and the solar wind. As PTAs turn towards high frequency (>1/yr) sensitivity, the size of the basis used to model these processes will need to increase, and these time-domain models present some computational efficiencies compared to Fourier-domain models.

Figures (13)

• Figure 1: Time-domain basis size compared to Fourier-domain basis size. The blue line indicates the scaling of the Fourier basis size vs $dt$, given the high-frequency cutoff $f_{\mathrm{max}} = 2/dt$ and $N_f = f_{\mathrm{max}}T$, while the black lines show how the time-domain basis size scales vs $dt$ for different pulsars from the $12.5$-year data set.
• Figure 2: Flowchart illustrating the full model customization framework. For each pulsar, we begin by selecting the DM kernel, Initially set to the SE kernel for all pulsars. We then check if the pulsar additionally favors a QP kernel, and then check the radio frequency dependence. Next we select the Chrom kernel: If the pulsar favors an SE kernel, we test for QP, otherwise no Chrom kernel is applied. After kernel selection we check for deterministic signals. If one is found we repeat the kernel selection process. Once no further deterministic signals are detected, we bin the SW and fix the values to the median across all pulsars. Final parameter estimation is then performed using these fixed SW densities.
• Figure 3: Red noise spectral index ($\gamma_{\rm RN}$) posterior changes between NANOGrav's standard noise model and the "customized" model found in this work. The points represent the median posterior values while the crosses cover the 16$^{\rm th}$ to 84$^{\rm th}$ percentile regions. The blue markers indicate pulsars where red noise was found to be present in both cases. The green markers indicate pulsars (PSR J1600$-$3053 and PSR J2043+1711) where red noise was found to be significant under the standard noise model, but insignificant under custom noise models, while the red marker indicates a pulsar (PSR J1455$-$3330) where the insignificant red noise recovered with the standard noise model was found to be significant when utilizing a custom noise model. In general, shallow spectral indices indicate that unmodeled chromatic noise may be leaking into the red noise model, while steeper spectral indices are more in line with the expectations for red noise, either from individual pulsar mechanisms, such as spin noise, or from a common GWB. There are eight pulsars where there is no significant red noise found when using either model; as such, they are not shown in this plot.
• Figure 4: White noise changes between NANOGrav's standard noise model and the customized noise model found in this work. We only plot parameters which are significant in both the standard noise and custom noise. All plots show the difference in median posterior value relative to the $1\sigma$ uncertainty from the standard noise posteriors. Negative values show where the new models from this work reduce the white noise values, while positive values show an increase. The different colors and markers correspond to the various receiver and backend combinations present in the data. Differences in EFAC are shown on the left, EQUAD in the center, and ECORR on the right. The changes to EFAC and EQUAD are relatively minor, however, PSR B1937+21 displays a significant reduction in both EFAC and EQUAD from the standard model to chromatic model. The ECORR changes are much more dramatic across the board, with no clear trends visible in this plot, however, we will discuss the significance of these changes and some potential causes in §\ref{['sec:chrom_models_ecorr']}.
• Figure 5: Pulsar/backend combinations that showed changes in ECORR significance with custom noise modeling, corresponding to the bolded entries in Table \ref{['tab:ecorr_params']}.