Indian Pulsar Timing Array (InPTA)

• Indian Pulsar Timing Array (InPTA) is a collaborative pulsar timing experiment using dual-band uGMRT observations to detect nanohertz-frequency gravitational waves.
• It employs advanced noise modeling, simultaneous timing and dispersion measure measurements, and optimized sub-band strategies to achieve sub-microsecond precision.
• InPTA enhances global PTA efforts by contributing critical dual-band data to the IPTA, improving gravitational wave detection sensitivity and astrophysical constraints.

The Indian Pulsar Timing Array (InPTA) is a collaborative astrophysical experiment that employs high-precision timing of millisecond pulsars (MSPs), primarily utilizing the upgraded Giant Metrewave Radio Telescope (uGMRT), to search for nanohertz-frequency gravitational waves, test fundamental physics, and probe the astrophysics of neutron stars and the interstellar medium. InPTA is a principal member of the International Pulsar Timing Array (IPTA), contributing low-frequency, dual-band timing data and advanced analysis methodologies. Its scientific program spans the detection of the stochastic gravitational wave background (GWB), noise characterization for precision timing, and ancillary studies of astrophysical, cosmological, and dark matter phenomena.

1. Scientific Motivation and Context

Pulsar timing arrays (PTAs) operate by coherently monitoring the pulse times of arrival (ToAs) from a carefully selected ensemble of MSPs distributed over the sky, each acting as a high-stability cosmic clock. The presence of gravitational waves (GWs) is inferred from correlated residuals in these ToAs across the array, exhibiting the characteristic quadrupolar pattern predicted by the Hellings–Downs correlation function: $$\zeta(\theta) = \frac{3}{2}\,x\ln x - \frac{x}{4} + \frac{1}{2}, \quad x = \frac{1-\cos\theta}{2}$$ where $\theta$ is the angular separation between pulsar pairs. PTA experiments are most sensitive to low-frequency (nHz) GWs originating from an astrophysical stochastic background, principally due to supermassive black hole binaries (SMBHBs) in distant galaxies, or cosmological sources such as cosmic strings and relics from inflation (Manchester, 2010, Joshi, 2013, Antoniadis et al., 2023).

The InPTA, by leveraging uGMRT’s dual-band capabilities (simultaneous 300–500 MHz and 1260–1460 MHz coverage), provides crucial broad-band, low-frequency pulsar data within this international multi-array framework.

2. Observational Strategies and Dataset Architecture

InPTA's core observational mode utilizes the uGMRT’s multi-sub-array configuration, enabling simultaneous dual-frequency monitoring of MSPs. This unique approach facilitates epoch-wise, high-precision measurement of both ToAs and dispersion measures (DM), the latter quantifying the integrated column of free electrons along the pulsar line of sight and dominating frequency-dependent propagation delays (Tarafdar et al., 2022, Rana et al., 20 Jun 2025).

The second data release (DR2) encompasses seven years of observations for 27 IPTA MSPs, producing sub-banded ToAs, high-fidelity ephemerides, and DM time series. A key technical innovation is the empirical optimization of sub-band splitting to balance S/N per sub-band and minimize profile evolution artifacts. This dual-band, contemporaneous acquisition ensures robust mitigation of chromatic propagation effects without temporal ambiguities due to non-simultaneity (Rana et al., 20 Jun 2025).

The data reduction is handled by the “pinta” pipeline, which implements advanced radio frequency interference (RFI) mitigation (via both median-based and Fourier-domain tools), folding, dedispersion, and template-matching steps. Calibration of instrumental offsets across uGMRT backend modes leverages cross-matched giant pulse observations and detailed engineering alignment, ensuring sub-microsecond timing fidelity (Susobhanan et al., 2020).

3. Timing Analysis, Dispersion Measure Estimation, and Noise Characterization

InPTA’s analysis employs both narrowband and wideband timing techniques:

• Narrowband: The observing bandwidth is split into multiple frequency channels; frequency-resolved templates are cross-correlated to extract ToAs and DM variations, employing iterative alignment (DMCalc) and robust outlier rejection (Huber regression) (Tarafdar et al., 2022, Joshi et al., 2022).
• Wideband: Pulse profile evolution across frequency is modeled using principal component analysis (PCA) and spline interpolation, providing simultaneous ToA and DM estimates from the full portrait (PulsePortraiture package). The multi-band extension combines non-contiguous bands using the Combined Portrait and Combined Chi-squared methods to further enhance timing and DM precision (Nobleson et al., 2021, Paladi et al., 2023).

The resulting dataset achieves DM uncertainties as low as $10^{-6}$ pc cm$^{-3}$, and post-fit timing residuals in the $\sim$30 ns to sub-$\mu$s range for key PTA pulsars (Nobleson et al., 2021, Rana et al., 20 Jun 2025). These precision levels are competitive with or superior to those achieved at higher frequencies in other PTA experiments.

Noise modeling in InPTA analysis incorporates white noise (EFAC/EQUAD), achromatic red noise (power-law spectrum), DM variations (chromatic power-law, $\propto\nu^{-2}$), and scattering variations (potentially non-Kolmogorov, $\propto\nu^{-x}$ with $x$ fitted per pulsar) (Srivastava et al., 2023, Antoniadis et al., 2023). Bayesian model selection determines the optimal combination of noise terms for each MSP and quantifies the corresponding spectral parameters. The low-frequency coverage allows the effective decoupling of chromatic and achromatic noise, improving the robustness of GW searches (Antoniadis et al., 2023).

4. Contributions to Gravitational Wave Detection and PTA Science

InPTA plays a pivotal role in advancing GW detection in multiple ways:

• Integration with Global Arrays: By contributing high-precision, dual-band low-frequency data for a common set of IPTA pulsars, InPTA augments both the pulsar sample and sky coverage, increasing the statistical significance of the observed Hellings–Downs correlations and overall PTA sensitivity (Postnov et al., 31 Jan 2025, Antoniadis et al., 2023).
• Impact on Noise Modeling: The inclusion of InPTA data in IPTA/EPTA analyses enables improved noise characterization, particularly disambiguating DM and scattering processes from the achromatic red signal attributed to GWBs (Antoniadis et al., 2023, Antoniadis et al., 2023).
• Evidence for a Stochastic GW Background: The EPTA+InPTA combined dataset shows strong Bayesian evidence (Bayes factors up to 60) for a common red-spectrum process with quadrupolar (HD-like) spatial correlations and amplitude $A \sim (2.5\pm0.7)\times 10^{-15}$ at $1\,\mathrm{yr}^{-1}$, consistent with a stochastic GWB due to SMBHBs (Antoniadis et al., 2023, Postnov et al., 31 Jan 2025). The InPTA data enhance noise modeling and marginally increase the GWB detection significance in recent IPTA analyses.

Table: Select Features of InPTA Data Releases

Release	Pulsars	Bands	Span	DM Precision	GW Sensitivity
DR1	14	300–500, 1260–1460 MHz	3.5 years	$\sim10^{-5}$ pc cm$^{-3}$	Integrated in IPTA analyses
DR2	27	300–500, 1260–1460 MHz	7 years	$10^{-6}$ pc cm$^{-3}$	Augments IPTA DR3

Improvements in DM estimations directly reduce chromatic timing noise, which constitutes a major limiting factor for GWB searches at low frequencies.

5. Methodological Advances and Technical Innovations

Key advances pioneered or refined by InPTA include:

• Multi-band, Simultaneous Observing: Simultaneous dual-band (and prospectively, multi-band) timing permits direct contemporaneous measurement of frequency-dependent ISM effects, mitigating DM and scattering-induced systematics (Joshi et al., 2022, Paladi et al., 2023).
• Robust Template Generation: Signal processing pipelines create noise-free, frequency-resolved pulse profile templates, enabling high-fidelity cross-correlation for ToA extraction even in the regime of strong profile evolution (Susobhanan et al., 2020, Rana et al., 20 Jun 2025).
• Optimized Sub-band Partitioning: Algorithmic selection of sub-band size balances S/N and intra-band profile variation, enhancing both timing and dispersion precision (Rana et al., 20 Jun 2025).
• Dynamic RFI Excising and Calibration: The “pinta” pipeline combines statistical and Fourier-based RFI identification; automated relative timing calibration between backend modes is validated through both engineering and astrophysical datasets (Susobhanan et al., 2020).

6. Impact on Fundamental Physics, Cosmology, and Synergies

Beyond GW detection, InPTA data feature in constraints on exotic physics and astrophysical processes:

• Astrophysical Origin: Current GWB amplitude and spectral shape from InPTA+EPTA analyses are compatible with an astrophysical SMBHB background, placing constraints on black hole-galaxy scaling relations and merger timescales (Antoniadis et al., 2023).
• Early Universe and Dark Matter Constraints: Participation in IPTA provides joint limits on cosmic string tension, inflationary spectral tilt, and ultralight dark matter (ULDM) abundance, using both timing and polarimetric data (Postnov et al., 31 Jan 2025, Vagnozzi, 2023).
• Testing Fundamental Physical Theories: The high-precision ToAs and DMs measured by InPTA allow for detailed studies of neutron star interiors (via monitoring of glitches and timing noise), limits on non-GR polarization modes, and constraints on scalar field couplings (Singha et al., 2022, Postnov et al., 31 Jan 2025).

InPTA’s methodological framework and analysis pipelines are directly relevant for next-generation PTA facilities such as the Square Kilometre Array (SKA), where similar dual/multi-band, multi-sub-array architectures will be adopted (Joshi et al., 2022).

7. Future Prospects and Ongoing Integration

The InPTA dataset is being integrated into IPTA DR3, where its dual-band, multi-year timing solution is expected to play a decisive role in improved detection and spectral characterization of the nanohertz GW background. Further technical advances are planned in broadband polarization calibration, real-time RFI rejection, extended subarray modes, and joint pulsar-Earth term GW burst searches. The InPTA approach is being adopted as a template for upcoming PTA science with the SKA and allied mega-facilities, ensuring continued international leadership in the low-frequency GW regime (Rana et al., 20 Jun 2025, Joshi et al., 2022).

The innovations established by InPTA—particularly simultaneous multi-band timing, empirical noise modeling, and the integration of low-frequency data into global PTA analyses—are establishing new standards in PTA methodology, directly enhancing sensitivity to gravitational waves, informing astrophysical and cosmological inference, and strengthening the IPTA’s ability to interpret future GW detections.