PINTA Pipeline: Indian Pulsar Timing Array

• PINTA is an integrated, high-precision data analysis pipeline that converts dual-band radio observations into timing products for gravitational wave detection and pulsar studies.
• The system utilizes advanced techniques including dual RFI mitigation, accurate calibration, frequency-resolved modeling, and iterative DM and ToA estimation to address frequency-dependent systematic errors.
• It incorporates rigorous noise modeling and ephemeris construction to enable robust cross-correlation analyses, supporting global PTA collaborations.

The pipeline for the Indian Pulsar Timing Array (PINTA) is an integrated, high-precision observational and data-analysis system that transforms raw, dual-band radio data from the upgraded Giant Metrewave Radio Telescope (uGMRT) into timing products suitable for detecting nanohertz gravitational waves, conducting pulsar astrophysics, and performing precision tests of fundamental physics. PINTA implements a comprehensive workflow that combines advanced radio-frequency interference (RFI) mitigation, accurate calibration, frequency-resolved profile modeling, iterative dispersion measure (DM) and time-of-arrival (ToA) estimation, and rigorous time-series noise analysis, culminating in robust gravitational wave signal searches. The following sections outline the key facets of the PINTA pipeline, with emphasis on technical procedures and their scientific motivations.

1. Observational Strategy and Dual-Band Data Acquisition

PINTA leverages the unique capabilities of the uGMRT, utilizing simultaneous, dual-band observations (commonly spanning 300–500 MHz and 1260–1460 MHz) to maximize sensitivity to chromatic propagation effects and to mitigate frequency-dependent systematic errors (Tarafdar et al., 2022, Joshi et al., 2022, Rana et al., 20 Jun 2025). The array can be configured into sub-arrays, enabling concurrent multi-band monitoring of multiple millisecond pulsars (MSPs). This is essential for characterizing frequency-dependent delays due to the interstellar medium (ISM) and solar wind, as well as for resolving frequency-evolving pulse profiles.

Raw data are acquired in a minimally formatted binary format, accompanied by external metadata specifying Central Local Oscillator frequency, bandwidth, sideband designation, number of frequency channels, sampling time, number of phase bins, and other instrumental parameters (Susobhanan et al., 2020). This dual-band, high time- and frequency-resolution acquisition forms the foundation of PINTA’s subsequent analysis chain.

2. RFI Mitigation, Calibration, and Standardization

PINTA employs an automated reduction pipeline that includes aggressive, dual-branch RFI mitigation schemes. Two independent algorithms, gptool (median/MAD and mean-to-RMS filtering, with local median replacement) and RFIClean (Fourier-domain excision plus robust thresholding), are run in parallel, each producing separate RFI-cleaned data products. This redundancy allows post hoc selection of the optimal RFI strategy for each dataset (Susobhanan et al., 2020). The raw data are converted to a standard filterbank or PSRFITS format for further processing.

Calibration steps include time-stamping with GPS-disciplined rubidium clocks for absolute accuracy, bandpass equalization to suppress instrumental frequency response, and injection of a noise diode for polarimetric and absolute flux calibration, as in the Parkes PTA legacy (Kerr et al., 2020). Bandpass-equalized, noise-reduced templates are generated using wavelet smoothing (undecimated wavelet transform), ensuring high-fidelity pulse shape recovery and minimizing the influence of instrumental artifacts (Rana et al., 20 Jun 2025).

3. Frequency Sub-band Optimization and Template Alignment

To address insufficient S/N and frequency-dependent profile evolution, PINTA implements an empirical optimization of sub-band selection. Given $N$ sub-bands across bandwidth $\Delta\nu$, the S/N per sub-band is scaled as

$$\text{S/N}_{\text{sub-band}} \propto \frac{\text{Integrated S/N}}{\sqrt{N}}$$

(Equation 1, Editor’s term for clarity—see (Rana et al., 20 Jun 2025)).

For each pulsar, this optimization entails scrunching candidate sub-bands until the median ToA precision is balanced between bands, and rejecting sub-band sets where profile differences do not follow a Gaussian distribution—thus filtering out RFI or unmodeled evolution (Rana et al., 20 Jun 2025). Formally,

$$|f(p_i) - f(\bar{p})| \leq \epsilon\cdot[\text{median}(|f(p_i) - f(\tilde{p})|)]\times1.4826$$

(Equation 2, where $f(\cdot)$ is the root-mean-square function, and $\epsilon$ is a user-defined threshold).

Templates from both bands undergo iterative DM alignment so that the reference DM corresponds consistently across all frequency channels, circumventing the need for additional frequency-dependent (FD) timing model parameters (Rana et al., 20 Jun 2025).

4. Iterative DM and ToA Estimation

PINTA precisely measures DM and ToA by cross-correlating sub-banded, RFI-cleaned profiles with the noise-reduced template archives. An iterative method is applied: first, the initial archive is dedispersed using the “template epoch” DM, and then, using TEMPO2 (or wideband timing packages such as PulsePortraiture), frequency-resolved ToAs are extracted and aligned (Nobleson et al., 2021, Tarafdar et al., 2022, Rana et al., 20 Jun 2025).

This process is iterated until the DM is self-consistent for both bands at the template epoch. The result is a set of sub-banded ToAs and DM time-series with typical epoch-averaged DM uncertainties down to $10^{-4}$–$10^{-6}$ pc cm$^{-3}$, and sub-microsecond ToA precision (Nobleson et al., 2021, Rana et al., 20 Jun 2025).

5. Noise Modeling and Temporal Stability

PINTA incorporates detailed noise modeling inherited from state-of-the-art international PTA methodologies (Manchester et al., 2012, Antoniadis et al., 2023). The pipeline decomposes the post-fit residuals into:

• Achromatic red noise (RN), attributed to intrinsic spin or GWB,
• Time-variable DM (DMv), following $\nu^{-2}$ scaling,
• Chromatic noise scaling as $\nu^{-4}$ (CN$_4$), associated with scattering,
• Stochastic or deterministic solar wind contributions.

A Gaussian process (GP) framework models these components, with covariance structures:

$$S^\lambda(f) = \frac{A_\lambda^2}{12\pi^2}\left(\frac{f}{f_{\text{yr}}}\right)^{-\gamma_\lambda}f_{\text{yr}}^{-3}$$

and

$$F^\lambda_\mu(t)\propto \left(\frac{\nu}{\nu_{\rm ref}}\right)^{-\chi_\lambda}$$

with frequency scaling indices $\chi_\lambda = 0,2,4$ for RN, DMv, and CN$_4$, respectively (Iraci et al., 6 Oct 2025). Bayesian evidence is used to select optimal noise models, and frequency-dependent noise is separated robustly by leveraging the dual-band dataset.

Solar wind delays are modeled as both deterministic functions of ecliptic latitude and stochastic processes. Unmodeled residuals, particularly during solar conjunctions, are absorbed into DMv, highlighting the need for careful solar wind parameterization (Iraci et al., 6 Oct 2025).

6. Ephemeris Construction and Gravitational Wave Signal Extraction

Final sub-band ToAs and DM time-series are combined in the timing model, allowing simultaneous solution of spin, astrometric, binary, and propagation parameters. In this refined timing solution, DM variations are accounted for on an epoch-by-epoch basis; all data products retain full provenance.

The cleaned residuals are used in cross-correlation analyses (Hellings–Downs search) for a common red noise signature consistent with a stochastic GWB. The pipeline supports “optimal statistic” frequentist estimators as well as Bayesian inference using current PTA standard tools (Antoniadis et al., 2023). Dual-band coverage and high DM precision directly reduce red noise leakage, enhancing sensitivity to quadrupolar spatial correlations intrinsic to gravitational wave backgrounds.

7. Integration within Global PTA Efforts and Future Prospects

PINTA’s pipeline is designed for seamless integration into joint international datasets (IPTA DR3 onwards), with industry-standard data formats, provenance-aware reduction, and calibration compatible with the consortium’s requirements (Manchester, 2013, Antoniadis et al., 2023, Rana et al., 20 Jun 2025). Methodological advances such as frequency sub-band optimization, automated RFI flagging, and robust noise modeling transfer directly to combined analyses and can be scaled as the uGMRT expands or merges into the Square Kilometre Array framework (Joshi et al., 2022).

The approach adopted in PINTA—high time and frequency resolution, simultaneous dual-band observation, and explicit environmental noise modeling—establishes a procedural template for next-generation pulsar timing and gravitational wave detection, as well as ancillary science in timekeeping, solar system dynamics, and ISM structure.

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In summary, the PINTA pipeline is a fully integrated, automated system designed for the Indian Pulsar Timing Array, utilizing dual-band uGMRT observations, sophisticated RFI mitigation, sub-band profile optimization, iterative DM/ToA estimation, and frequency-dependent noise modeling to maximize timing precision and sensitivity to low-frequency gravitational waves. Its architecture and methodology closely follow and extend international PTA best practices, positioning PINTA to play a major role in the joint detection and characterization of nanohertz gravitational wave signals.