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Radio pulsars show remarkable clock-like stability, which make them useful astronomy tools in experiments to test equation of state of neutron stars and detecting gravitational waves using pulsar timing techniques. A brief review of relevant astrophysical experiments is provided in this paper highlighting the current state-of-the-art of these experiments. A program to monitor frequently glitching pulsars with Indian radio telescopes using high cadence observations is presented, with illustrations of glitches detected in this program, including the largest ever glitch in PSR B0531+21. An Indian initiative to discover sub-\\[\\mu \\]Hz gravitational waves, called Indian Pulsar Timing Array (InPTA), is also described briefly, where time-of-arrival uncertainties and post-fit residuals of the order of \\[\\mu \\]s are already achievable, comparable to other international pulsar timing array experiments. While timing the glitches and their recoveries are likely to provide constraints on the structure of neutron stars, InPTA will provide upper limits on sub-\\[\\mu \\]Hz gravitational waves apart from auxiliary pulsar science. Future directions for these experiments are outlined.

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.

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.

We consider a neutrino-free hot neutron star that contains antikaon condensates in its core and is at finite entropy per baryon. We find the equation of state for a range of entropies and antikaon optical potentials and generate the mass profile of static as well as rotating stars. Rotation induces many changes in the stellar equilibrium, and hence its structural properties evolve. In this work, we report the effect of rotation on the mass and shape of a hot neutron star for different equations of state and thermodynamic conditions. Temperature profile of hot, static neutron star is also explored. We also make a crude estimate of the amplitude of gravitational waves emitted by an axisymmetric rotating NS with high magnetic field.

We present the pulse arrival times and high-precision dispersion measure estimates for 14 millisecond pulsars observed simultaneously in the 300-500 MHz and 1260-1460 MHz frequency bands using the upgraded Giant Metrewave Radio Telescope (uGMRT). The data spans over a baseline of 3.5 years (2018-2021), and is the first official data release made available by the Indian Pulsar Timing Array collaboration. This data release presents a unique opportunity for investigating the interstellar medium effects at low radio frequencies and their impact on the timing precision of pulsar timing array experiments. In addition to the dispersion measure time series and pulse arrival times obtained using both narrowband and wideband timing techniques, we also present the dispersion measure structure function analysis for selected pulsars. Our ongoing investigations regarding the frequency dependence of dispersion measures have been discussed. Based on the preliminary analysis for five millisecond pulsars, we do not find any conclusive evidence of chromaticity in dispersion measures. Data from regular simultaneous two-frequency observations are presented for the first time in this work. This distinctive feature leads us to the highest precision dispersion measure estimates obtained so far for a subset of our sample. Simultaneous multi-band uGMRT observations in Band 3 and Band 5 are crucial for high-precision dispersion measure estimation and for the prospect of expanding the overall frequency coverage upon the combination of data from the various Pulsar Timing Array consortia in the near future. Parts of the data presented in this work are expected to be incorporated into the upcoming third data release of the International Pulsar Timing Array.

High-precision measurements of the pulsar dispersion measure (DM) are possible using telescopes with low-frequency wideband receivers. We present an initial study of the application of the wideband timing technique, which can simultaneously measure the pulsar times of arrival (ToAs) and DMs, for a set of five pulsars observed with the upgraded Giant Metrewave Radio Telescope (uGMRT) as part of the Indian Pulsar Timing Array (InPTA) campaign. We have used the observations with the 300-500 MHz band of the uGMRT for this purpose. We obtain high precision in DM measurements with precisions of the order 10^{-6}cm^{-3}pc. The ToAs obtained have sub-{\\mu}s precision and the root-mean-square of the post-fit ToA residuals are in the sub-{\\mu}s range. We find that the uncertainties in the DMs and ToAs obtained with this wideband technique, applied to low-frequency data, are consistent with the results obtained with traditional pulsar timing techniques and comparable to high-frequency results from other PTAs. This work opens up an interesting possibility of using low-frequency wideband observations for precision pulsar timing and gravitational wave detection with similar precision as high-frequency observations used conventionally.

Decades long monitoring of millisecond pulsars, which exhibit highly stable rotational periods, in pulsar timing array experiments is on the threshold of discovering nanohertz stochastic gravitational wave background. This paper describes the Indian Pulsar timing array (InPTA) experiment, which employs the upgraded Giant Metrewave Radio Telescope (uGMRT) for timing an ensemble of millisecond pulsars for this purpose. We highlight InPTA's observation strategies and analysis methods, which are relevant for a future PTA experiment with the more sensitive Square Kilometer Array (SKA) telescope. We show that the unique multi-sub-array multi-band wide-bandwidth frequency coverage of the InPTA provides Dispersion Measure estimates with unprecedented precision for PTA pulsars, e.g., ~ 2 x 10{-5} pc-cm{-3} for PSR J1909-3744. Configuring the SKA-low and SKA-mid as two and four sub-arrays respectively, it is shown that comparable precision is achievable, using observation strategies similar to those pursued by the InPTA, for a larger sample of 62 pulsars requiring about 26 and 7 hours per epoch for the SKA-mid and the SKA-low telescopes respectively. We also review the ongoing efforts to develop PTA-relevant general relativistic constructs that will be required to search for nanohertz gravitational waves from isolated super-massive black hole binary systems like blazar OJ 287. These efforts should be relevant to pursue persistent multi-messenger gravitational wave astronomy during the forthcoming era of the SKA telescope, the Thirty Meter Telescope, and the next-generation Event Horizon Telescope.

Pulsar radio emission undergoes dispersion due to the presence of free electrons in the interstellar medium (ISM). The dispersive delay in the arrival time of pulsar signal changes over time due to the varying ISM electron column density along the line of sight. Correcting for this delay accurately is crucial for the detection of nanohertz gravitational waves using Pulsar Timing Arrays. In this work, we present in-band and inter-band DM estimates of four pulsars observed with uGMRT over the timescale of a year using two different template alignment methods. The DMs obtained using both these methods show only subtle differences for PSR 1713+0747 and J1909\\(-\\)3744. A considerable offset is seen in the DM of PSR J1939+2134 and J2145\\(-\\)0750 between the two methods. This could be due to the presence of scattering in the former and profile evolution in the latter. We find that both methods are useful but could have a systematic offset between the DMs obtained. Irrespective of the template alignment methods followed, the precision on the DMs obtained is about \\(10^{-3}\\) pc cm\\(^{-3}\\) using only BAND3 and \\(10^{-4}\\) pc cm\\(^{-3}\\) after combining data from BAND3 and BAND5 of the uGMRT. In a particular result, we have detected a DM excess of about \\(5\\times10^{-3}\\) pc cm\\(^{-3}\\) on 24 February 2019 for PSR J2145\\(-\\)0750. This excess appears to be due to the interaction region created by fast solar wind from a coronal hole and a coronal mass ejection (CME) observed from the Sun on that epoch. A detailed analysis of this interesting event is presented.