The Indian Pulsar Timing Array Data Release 2: II. Customised Single-Pulsar Noise Analysis and Noise Budget

TL;DR

This work delivers a customised single-pulsar noise analysis for 27 MSPs in the InPTA-DR2 data set, combining deterministic timing with stochastic noise modeled as stationary Gaussian processes across ARN, DMN, FCN, and SCN, plus a deterministic solar-wind component. Employing Bayesian inference with ENTERPRISE and Dynesty, the authors perform model selection and optimal Fourier-harmonics determination, followed by thorough parameter estimation and Gaussianity checks of post-noise residuals. They find a mix of fully Gaussian, nearly Gaussian, and non-Gaussian residuals across pulsars, with several objects showing strong red-noise signatures and a subset affected by solar-wind biases, underscoring the importance of accurate noise modeling for robust GW background inference. The results largely align with the InPTA-DR1 noise budget, while highlighting the need for more advanced approaches to solar-wind and chromatic noise to prevent spurious detections and to sharpen constraints on the nHz gravitational-wave background.

Abstract

We present the results of customised single-pulsar noise analysis of 27 millisecond pulsars from the second data release of the Indian Pulsar Timing Array (InPTA-DR2). We model various stochastic noise sources present in the dataset using stationary Gaussian processes and estimate the noise budget of the InPTA-DR2 using Bayesian inference, involving model selection, Fourier harmonics selection, and parameter estimation for each pulsar. We check the efficacy of our noise characterisation by performing the Anderson-Darling test for Gaussianity on the noise-subtracted residuals. We find that all 11 pulsars with time baseline $\lesssim2.5\,\text{yr}$ show Gaussian residuals and do not have evidence for any red noise process in the optimal model, except for PSR J1944$+$0907, which shows presence of DM noise. PSRs J0437$-$4715, J1909$-$3744 and J1939$+$2134 show preference for the most complicated noise model, having achromatic and chromatic red noise processes. Only 4 out of 15 pulsars with time baseline $\gtrsim2.5\,\text{yr}$ show significant non-Gaussianity in noise-subtracted residuals. We suspect that this may require more advanced methods to model noise processes properly. A comparative study of six pulsars with data removed near solar conjunctions showed deviations from the parameter estimates obtained with the original dataset, indicating potential bias in red noise processes due to unmodeled solar-wind effects. The results presented in this work remain broadly consistent with the InPTA-DR1 noise budget, with better constraints obtained on noise processes for several pulsars and support for achromatic red noise in PSR J1012$+$5307 due to the extended time baseline.

Figures (45)

• Figure 1: Results of the optimal Fourier harmonics selection procedure with the dropout power-law model for PSR J1643$-$1224 for the ARN, DMN and FCN red noise processes. The median parameter estimates are listed at the top for each red noise process.
• Figure 1: Complete noise parameter posteriors obtained after the parameter estimation procedure for PSR J1909$-$3744.
• Figure 1: Distribution of the normalised pre-noise and post-noise residuals for PSR J0030$+$0451.
• Figure 1: Parameter posterior comparison and tension estimate for the DMN process using the full and SW-cut datasets for PSR J1022$+$1001.
• Figure 2: Consolidated plot of the ARN amplitude and spectral index posterior distributions for the InPTA DR2 pulsars having ARN in the optimum noise model (see Table \ref{['tab:noise-models']}).