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We utilise the phenomenologically parameterized piecewise polytropic equations of state to study various neutron star properties. We investigate the compliance of these equations of state with several astronomical observations. We also demonstrate that the theoretical estimates of the fractional moment of inertia cannot explain all the pulsar glitches observed. We model the crust as a solid spheroidal shell to calculate the fractional moment of inertia of fast-spinning neutron stars. We also show that the braking index obtained in a simple magnetic dipole radiation model with a varying moment of inertia deviates significantly from the observed data. Future developments in both theory and observations may allow us to use the fractional moment of inertia and braking index as observational constraints for neutron star equation of state.

The spin-down law of pulsars is generally perturbed by two types of timing irregularities: glitches and timing noise. Glitches are sudden changes in the rotational frequency of pulsars, while timing noise is a discernible stochastic wandering in the phase, period, or spin-down rate of a pulsar. We present the timing results of a sample of glitching pulsars observed using the Ooty Radio Telescope (ORT) and the upgraded Giant Metrewave Radio Telescope (uGMRT). Our findings include timing noise analysis for 17 pulsars, with seven being reported for the first time. We detected five glitches in four pulsars and a glitch-like event in PSR J1825-0935. The frequency evolution of glitch in pulsars, J0742-2822 and J1740-3015, is presented for the first time. Additionally, we report timing noise results for three glitching pulsars. The timing noise was analyzed separately in the pre-glitch region and post-glitch regions. We observed an increase in the red noise parameters in the post-glitch regions, where exponential recovery was considered in the noise analysis. Timing noise can introduce ambiguities in the correct evaluation of glitch observations. Hence, it is important to consider timing noise in glitch analysis. We propose an innovative glitch verification approach designed to discern between a glitch and strong timing noise. The novel glitch analysis technique is also demonstrated using the observed data.

There are two types of timing irregularities seen in pulsars: glitches and timing noise. Both of these phenomena can help us probe the interior of such exotic objects. This article presents a brief overview of the observational and theoretical aspects of pulsar timing irregularities and the main results from the investigations of these phenomena in India. The relevance of such Indian programs for monitoring of young pulsars with the Square Kilometer Array (SKA) is presented, highlighting possible contributions of the Indian neutron star community to the upcoming SKA endeavour.

Glitches are the observational manifestations of superfluidity inside neutron stars. The aim of this paper is to describe an automated glitch detection pipeline, which can alert the observers on possible real-time detection of rotational glitches in pulsars. Post alert, the pulsars can be monitored at a higher cadence to measure the post-glitch recovery phase. Two algorithms namely, Median Absolute Deviation (MAD) and polynomial regression have been explored to detect glitches in real time. The pipeline has been optimized with the help of simulated timing residuals for both the algorithms. Based on the simulations, we conclude that the polynomial regression algorithm is significantly more effective for real time glitch detection. The pipeline has been tested on a few published glitches. This pipeline is presently implemented at the Ooty Radio Telescope. In the era of upcoming large telescopes like SKA, several hundreds of pulsars will be observed regularly and such a tool will be useful for both real-time detection as well as optimal utilization of observation time for such glitching pulsars.

In an accompanying publication, the MeerKAT Pulsar Timing Array (MPTA) collaboration reports tentative evidence for the presence of a stochastic gravitational-wave background, following observations of similar signals from the European and Indian Pulsar Timing Arrays, NANOGrav, the Parkes Pulsar Timing Array and the Chinese Pulsar Timing Array. If such a gravitational-wave background signal originates from a population of inspiraling supermassive black-hole binaries, the signal may be anisotropically distributed on the sky. In this Letter we evaluate the anisotropy of the MPTA signal using a spherical harmonic decomposition. We discuss complications arising from the covariance between pulsar pairs and regularisation of the Fisher matrix. Applying our method to the 4.5 yr dataset, we obtain two forms of sky maps for the three most sensitive MPTA frequency bins between 7 -21 nHz. Our \"clean maps'' estimate the distribution of gravitational-wave strain power with minimal assumptions. Our radiometer maps answer the question: is there a statistically significant point source? We find a noteworthy hotspot in the 7 nHz clean map with a \\(p\\)-factor of \\(p=0.015\\) (not including trial factors). Future observations are required to determine if this hotspot is of astrophysical origin.

Pulsar Timing Arrays search for nanohertz-frequency gravitational waves by regularly observing ensembles of millisecond pulsars over many years to look for correlated timing residuals. Recently the first evidence for a stochastic gravitational wave background has been presented by the major Arrays, with varying levels of significance (\\(\\sim\\)2-4\\(\\sigma\\)). In this paper we present the results of background searches with the MeerKAT Pulsar Timing Array. Although of limited duration (4.5 yr), the \\(\\sim\\) 250,000 arrival times with a median error of just \\(3 \\mu\\)s on 83 pulsars make it very sensitive to spatial correlations. Detection of a gravitational wave background requires careful modelling of noise processes to ensure that any correlations represent a fit to the underlying background and not other misspecified processes. Under different assumptions about noise processes we can produce either what appear to be compelling Hellings-Downs correlations of high significance (3-3.4\\(\\sigma\\)) with a spectrum close to that which is predicted, or surprisingly, under slightly different assumptions, ones that are insignificant. This appears to be related to the fact that many of the highest precision MeerKAT Pulsar Timing Array pulsars are in close proximity and dominate the detection statistics. The sky-averaged characteristic strain amplitude of the correlated signal in our most significant model is \\(h_{c, {\\rm yr}} = 7.5^{+0.8}_{-0.9} \\times 10^{-15}\\) measured at a spectral index of \\(\\alpha=-0.26\\), decreasing to \\(h_{c, {\\rm yr}} = 4.8^{+0.8}_{-0.9} \\times 10^{-15}\\) when assessed at the predicted \\(\\alpha=-2/3\\). These data will be valuable as the International Pulsar Timing Array project explores the significance of gravitational wave detections and their dependence on the assumed noise models.

A pulsar's pulse profile gets broadened at low frequencies due to dispersion along the line of sight or due to multi-path propagation. The dynamic nature of the interstellar medium makes both of these effects time-dependent and introduces slowly varying time delays in the measured times-of-arrival similar to those introduced by passing gravitational waves. In this article, we present an improved method to correct for such delays by obtaining unbiased dispersion measure (DM) measurements by using low-frequency estimates of the scattering parameters. We evaluate this method by comparing the obtained DM estimates with those, where scatter-broadening is ignored using simulated data. A bias is seen in the estimated DMs for simulated data with pulse-broadening with a larger variability for a data set with a variable frequency scaling index, \\(\\alpha\\), as compared to that assuming a Kolmogorov turbulence. Application of the proposed method removes this bias robustly for data with band averaged signal-to-noise ratio larger than 100. We report the measurements of the scatter-broadening time and \\(\\alpha\\) from analysis of PSR J1643\\(-\\)1224, observed with upgraded Giant Metrewave Radio Telescope as part of the Indian Pulsar Timing Array experiment. These scattering parameters were found to vary with epoch and \\(\\alpha\\) was different from that expected for Kolmogorov turbulence. Finally, we present the DM time-series after application of this technique to PSR J1643\\(-\\)1224.

High-precision pulsar timing observations are limited in their accuracy by the jitter noise that appears in the arrival time of pulses. Therefore, it is important to systematically characterise the amplitude of the jitter noise and its variation with frequency. In this paper, we provide jitter measurements from low-frequency wideband observations of PSR J0437\\(-\\)4715 using data obtained as part of the Indian Pulsar Timing Array experiment. We were able to detect jitter in both the 300 - 500 MHz and 1260 - 1460 MHz observations of the upgraded Giant Metrewave Radio Telescope (uGMRT). The former is the first jitter measurement for this pulsar below 700 MHz, and the latter is in good agreement with results from previous studies. In addition, at 300 - 500 MHz, we investigated the frequency dependence of the jitter by calculating the jitter for each sub-banded arrival time of pulses. We found that the jitter amplitude increases with frequency. This trend is opposite as compared to previous studies, indicating that there is a turnover at intermediate frequencies. It will be possible to investigate this in more detail with uGMRT observations at 550 - 750 MHz and future high sensitive wideband observations from next generation telescopes, such as the Square Kilometre Array. We also explored the effect of jitter on the high precision dispersion measure (DM) measurements derived from short duration observations. We find that even though the DM precision will be better at lower frequencies due to the smaller amplitude of jitter noise, it will limit the DM precision for high signal-to-noise observations, which are of short durations. This limitation can be overcome by integrating for a long enough duration optimised for a given pulsar.

The wideband timing technique enables the high-precision simultaneous estimation of pulsar Times of Arrival (ToAs) and Dispersion Measures (DMs) while effectively modeling frequency-dependent profile evolution. We present two novel independent methods that extend the standard wideband technique to handle simultaneous multi-band pulsar data incorporating profile evolution over a larger frequency span to estimate DMs and ToAs with enhanced precision. We implement the wideband likelihood using the libstempo python interface to perform wideband timing in the tempo2 framework. We present the application of these techniques to the dataset of fourteen millisecond pulsars observed simultaneously in Band 3 (300 - 500 MHz) and Band 5 (1260 - 1460 MHz) of the upgraded Giant Metrewave Radio Telescope (uGMRT) with a large band gap of 760 MHz as a part of the Indian Pulsar Timing Array (InPTA) campaign. We achieve increased ToA and DM precision and sub-microsecond root mean square post-fit timing residuals by combining simultaneous multi-band pulsar observations done in non-contiguous bands for the first time using our novel techniques.

The Indian Pulsar Timing Array (InPTA) collaboration has recently made its first official data release (DR1) for a sample of 14 pulsars using 3.5 years of uGMRT observations. We present the results of single-pulsar noise analysis for each of these 14 pulsars using the InPTA DR1. For this purpose, we consider white noise, achromatic red noise, dispersion measure (DM) variations, and scattering variations in our analysis. We apply Bayesian model selection to obtain the preferred noise models among these for each pulsar. For PSR J1600\\(-\\)3053, we find no evidence of DM and scattering variations, while for PSR J1909\\(-\\)3744, we find no significant scattering variations. Properties vary dramatically among pulsars. For example, we find a strong chromatic noise with chromatic index \\(\\sim\\) 2.9 for PSR J1939+2134, indicating the possibility of a scattering index that doesn't agree with that expected for a Kolmogorov scattering medium consistent with similar results for millisecond pulsars in past studies. Despite the relatively short time baseline, the noise models broadly agree with the other PTAs and provide, at the same time, well-constrained DM and scattering variations.