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Pulsars are believed to be one of the most important celestial objects in the universe. The emission mechanism of pulsars is still a big paradox for physicists, as no completely acceptable theory can reach a suitable consensus with observation. Some complicated coherent plasma processes and acceleration-based mechanisms in the pulsar magnetosphere generate a powerful radio beam. There have been dedicated theories such as the geometrical and relativistic phase shift (RPS) methods. The relativistic phase shift method is owing to the combined effects of aberration-retardation (A/R) and polar cap current effect (PCC), etc., and by implementing this method, we make quantitative inspections to deduce the emission altitude of the pulsar’s radio emission components. Here, we have shown the estimation of the emission height of pulsar PSR B2111+46 for both core and conal components at 925 MHz, 1.25 GHz, 1.65 GHz, and 4.85 GHz. Moreover, we have estimated the foot point, normalized with the last open field line constant, corresponding to pulse edges at multiple bands. Current analysis of the paper shows that at least for PSR B2111+46, the full polar cap is not sensitive to radio emission for most of the cases in the given stretch of radio frequency.

The radio-emitting neutron star population encompasses objects with spin periods ranging from milliseconds to tens of seconds. As they age and spin more slowly, their radio emission is expected to cease. We present the discovery of an ultra-long-period radio-emitting neutron star, PSR J0901-4046, with spin properties distinct from the known spin- and magnetic-decay-powered neutron stars. With a spin period of 75.88 s, a characteristic age of 5.3 Myr and a narrow pulse duty cycle, it is uncertain how its radio emission is generated and challenges our current understanding of how these systems evolve. The radio emission has unique spectro-temporal properties, such as quasi-periodicity and partial nulling, that provide important clues to the emission mechanism. Detecting similar sources is observationally challenging, which implies a larger undetected population. Our discovery establishes the existence of ultra-long-period neutron stars, suggesting a possible connection to the evolution of highly magnetized neutron stars, ultra-long-period magnetars and fast radio bursts. Using the MeerKAT radio telescope, the authors have discovered a neutron star with an ultra-long spin period of 76 s. Though it resides in the neutron star graveyard, it emits radio waves and challenges our understanding of neutron star evolution.

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.

The radio-emitting neutron star population encompasses objects with spin periods ranging from milliseconds to tens of seconds. As they age and spin more slowly, their radio emission is expected to cease. We present the discovery of an ultra-long period radio-emitting neutron star, PSR J0901-4046, with spin properties distinct from the known spin and magnetic-decay powered neutron stars. With a spin-period of 75.88 s, a characteristic age of 5.3 Myr, and a narrow pulse duty-cycle, it is uncertain how radio emission is generated and challenges our current understanding of how these systems evolve. The radio emission has unique spectro-temporal properties such as quasi-periodicity and partial nulling that provide important clues to the emission mechanism. Detecting similar sources is observationally challenging, which implies a larger undetected population. Our discovery establishes the existence of ultra-long period neutron stars, suggesting a possible connection to the evolution of highly magnetized neutron stars, ultra-long period magnetars, and fast radio bursts.

We present the long-term spectro-temporal evolution of the average radio emission properties of the magnetar XTE J1810-197 (PSR J1809-1943) following its most recent outburst in late 2018. We report the results from two and a half years of monitoring campaign with the upgraded Giant Metrewave Radio Telescope carried out over the frequency range of 300 - 1450 MHz. Our observations show intriguing time variability in the average profile width, flux density, spectral index and the broadband spectral shape. While the average profile width appears to gradually decrease at later epochs, the flux density shows multiple episodes of radio re-brightening over the course of our monitoring. Our systematic monitoring observations reveal that the radio spectrum has steepened over time, resulting in evolution from a magnetar-like to a more pulsar-like spectrum. A more detailed analysis reveals that the radio spectrum has a turnover, and this turnover shifts towards lower frequencies with time. We present the details of our analysis leading to these results, and discuss our findings in the context of magnetar radio emission mechanisms as well as potential manifestations of the intervening medium. We also briefly discuss whether an evolving spectral turnover could be an ubiquitous property of radio magnetars.

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.

XTE J1810-197 (PSR J1809-1943) was the first ever magnetar which was found to emit transient radio emission. It has recently undergone another radio and high-energy outburst. This is only the second radio outburst that has been observed from this source. We observed J1810-197 soon after its recent radio outburst at low radio frequencies using the Giant Metrewave Radio Telescope. We present the 650 MHz flux density evolution of the source in the early phases of the outburst, and its radio spectrum down to frequencies as low as 300 MHz. The magnetar also exhibits radio emission in the form of strong, narrow bursts. We show that the bursts have a characteristic intrinsic width of the order of 0.5-0.7 ms, and discuss their properties in the context of giant pulses and giant micropulses from other pulsars. We also show that the bursts exhibit spectral structures which cannot be explained by interstellar propagation effects. These structures might indicate a phenomenological link with the repeating fast radio bursts which also show interesting, more detailed frequency structures. While the spectral structures are particularly noticeable in the early phases of the outburst, these seem to be less prominent as well as less frequent in the later phases, suggesting an evolution of the underlying cause of these spectral structures.

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.