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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., Comment: 13 pages, 12 figures, 3 tables, accepted for Publication of the Astronomical Society of Australia

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., Comment: 10 pages, 8 figures, Accepted for publication in MNRAS

Close hyperbolic encounters of black holes (BHs) generate certain Burst With Memory (BWM) events in the frequency windows of the operational, planned, and proposed gravitational wave (GW) observatories. We present detailed explorations of the detectable parameter space of such events that are relevant for the LIGO-Virgo-KAGRA and the International Pulsar Timing Array (IPTA) consortia. The underlying temporally evolving GW polarization states are adapted from Cho et al. [Phys. Rev. D 98, 024039 (2018)] and therefore incorporate general relativistic effects up to the third post-Newtonian order. Further, we provide a prescription to ensure the validity of our waveform family while describing close encounters. Preliminary investigations reveal that optimally placed BWM events should be visible to megaparsec distances for the existing ground-based observatories. In contrast, maturing IPTA datasets should be able to provide constraints on the occurrences of such hyperbolic encounters of supermassive BHs to gigaparsec distances., Comment: 19 pages, 11 figures, accepted for publication in Phys. Rev. D

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., Comment: Published in MNRAS

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., Comment: Accepted for publication in PRD, 30 pages, 17 figures, 4 tables

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., Comment: Accepted for publication in Journal of Astronomy and Astrophysics for Special Issue on Indian Participation in the SKA (Editors : Abhirup Datta, Nirupam Roy, Preeti Kharb and Tirthankar Roy Choudhury)

We study the bound orbit conditions for equatorial and eccentric orbits around a Kerr black hole both in the parameter space ($E$, $L$, $a$) representing the energy, angular momentum of the test particle, and spin of the black hole, and also ($e$, $\mu$, $a$) space representing the eccentricity, inverse-latus rectum of the orbit, and spin. We apply these conditions and implement the relativistic precession (RP) model to M82X-1, which is an Intermediate-mass black hole (IMBH) system, where two high-frequency Quasi-Periodic Oscillations (HFQPOs) and a low-frequency QPO were simultaneously observed. Assuming that the QPO frequencies can also be generated by equatorial and eccentric trajectories, we calculate the probability distributions to infer $e$, $a$, and periastron distance, $r_p$, of the orbit giving rise to simultaneous QPOs. We find that an eccentric orbit solution is possible in the region between innermost stable circular orbit (ISCO) and the marginally bound circular orbit (MBCO) for $e=0.2768^{+0.0657}_{-0.0451}$, $a=0.2897 \pm 0.0087$, and $r_p=4.6164^{+0.0694}_{-0.1259}$., Comment: 7 pages, 2 figures, Conference: Proceedings of the MG15 Meeting on General Relativity

We derive the conditions for a non-equatorial eccentric bound orbit to exist around a Kerr black hole in two-parameter spaces: the energy, angular momentum of the test particle, spin of the black hole, and Carter's constant space ($E$, $L$, $a$, $Q$), and eccentricity, inverse-latus rectum space ($e$, $\mu$, $a$, $Q$). These conditions distribute various kinds of bound orbits in different regions of the ($E$, $L$) and ($e$, $\mu$) planes, depending on which pair of roots of the effective potential forms a bound orbit. We provide a prescription to select these parameters for bound orbits, which are useful inputs to study bound trajectory evolution in various astrophysical applications like simulations of gravitational wave emission from extreme-mass ratio inspirals, relativistic precession around black holes, and the study of gyroscope precession as a test of general relativity., Comment: 7 pages, 2 figures, Conference: Proceedings of the MG15 Meeting on General Relativity

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., Comment: 23 pages, 21 figures, 3 tables. Published in PASA

PSR J1713+0747 is one of the most precisely timed pulsars in the international pulsar timing array experiment. This pulsar showed an abrupt profile shape change between April 16, 2021 (MJD 59320) and April 17, 2021 (MJD 59321). In this paper, we report the results from multi-frequency observations of this pulsar carried out with the upgraded Giant Metrewave Radio Telescope (uGMRT) before and after the event. We demonstrate the profile change seen in Band 5 (1260 MHz - 1460 MHz) and Band 3 (300 MHz - 500 MHz). The timing analysis of this pulsar shows a disturbance accompanying this profile change followed by a recovery with a timescale of $\sim 159$ days. Our data suggest that a model with chromatic index as a free parameter is preferred over models with combinations of achromaticity with DM bump or scattering bump. We determine the frequency dependence to be $\sim\nu^{+1.34}$., Comment: Accepted for publication in MNRAS-Letters

We present a unified model for X-ray quasi-periodic oscillations (QPOs) seen in Narrow-line Seyfert 1 (NLSy1) galaxies, $\gamma$-ray and optical band QPOs that are seen in Blazars. The origin of these QPOs is attributed to the plasma motion in corona or jets of these AGN. In the case of X-ray QPOs, we applied the general relativistic precession model for the two simultaneous QPOs seen in NLSy1 1H 0707-945 and deduce orbital parameters, such the radius of the emission region, and spin parameter $a$ for a circular orbit; we obtained the Carter's constant $Q$, $a$, and the radius in the case of a spherical orbit solution. In other cases where only one X-ray QPO is seen, we localized the orbital parameters for NLSy1 galaxies REJ 1034+396, 2XMM J123103.2+110648, MS 2254.9-3712, Mrk 766, and MCG-06-30-15. By applying the lighthouse model, we found that a kinematic origin of the jet based $\gamma$-ray and optical QPOs, in a relativistic MHD framework, is possible. Based on the inbuilt Hamiltonian formulation with a power-law distribution in the orbital energy of the plasma consisting of only circular or spherical trajectories, we show that the resulting Fourier power spectral density (PSD) has a break corresponding to the energy at ISCO. Further, we derive connection formulae between the slopes in the PSD and that of the energy distribution. Overall, given the preliminary but promising results of these relativistic orbit models to match the observed QPO frequencies and PSD at diverse scales in the inner corona and the jet, it motivates us to build detailed models, including a transfer function for the energy spectrum in the corona and relativistic MHD jet models for plasma flow and its polarization properties., Comment: 28 pages, 11 figures [24 sub-figures], 6 Tables, final edited version, Accepted in Galaxies; special issue on "X-ray flux and spectral variability of Blazars"

We expand the relativistic precession model to include nonequatorial and eccentric trajectories and apply it to quasi-periodic oscillations (QPOs) in black hole X-ray binaries (BHXRBs) and associate their frequencies with the fundamental frequencies of the general case of nonequatorial (with Carter's constant, $Q\neq 0$) and eccentric ($e\neq 0$) particle trajectories, around a Kerr black hole. We study cases with either two or three simultaneous QPOs and extract the parameters \{$e$, $r_p$, $a$, $Q$\}, where $r_p$ is the periastron distance of the orbit, and $a$ is the spin of the black hole. We find that the orbits with $\left[Q=0-4\right]$ should have $e\lesssim 0.5$ and $r_p \sim 2-20$ for the observed range of QPO frequencies, where $a \in [0,1]$, and that the spherical trajectories \{$e=0$, $Q \neq0$\} with $Q=2-4$ should have $r_s \sim 3-20$. We find nonequatorial eccentric solutions for both M82 X-1 and GROJ 1655-40. We see that these trajectories, when taken together, span a torus region and give rise to a strong QPO signal. For two simultaneous QPO cases, we found equatorial eccentric orbit solutions for XTEJ 1550-564, 4U 1630-47, and GRS 1915+105, and spherical orbit solutions for BHXRBs M82 X-1 and XTEJ 1550-564. We also show that the eccentric orbit solution fits the Psaltis-Belloni-Klis correlation observed in BHXRB GROJ 1655-40. Our analysis of the fluid flow in the relativistic disk edge suggests that instabilities cause QPOs to originate in the torus region. We also present some useful formulae for trajectories and frequencies of spherical and equatorial eccentric orbits., Comment: 60 pages, 12 tables, 30 figures with 97 sub-figures, 5 appendices; Accepted in ApJ, final edited version

We derive alternate and new closed-form analytic solutions for the non-equatorial eccentric bound trajectories, $\{ \phi \left( r, \theta \right)$, $\ t \left( r, \theta \right),\ r \left( \theta \right) \}$, around a Kerr black hole by using the transformation $1/r=\mu \left(1+ e \cos \chi \right)$. The application of the solutions is straightforward and numerically fast. We obtain and implement translation relations between energy and angular momentum of the particle, ($E$, $L$), and eccentricity and inverse-latus rectum, ($e$, $\mu$), for a given spin, $a$, and Carter's constant, $Q$, to write the trajectory completely in the ($e$, $\mu$, $a$, $Q$) parameter space. The bound orbit conditions are obtained and implemented to select the allowed combination of parameters ($e$, $\mu$, $a$, $Q$). We also derive specialized formulae for spherical and separatrix orbits. A study of the non-equatorial analog of the previously studied equatorial separatrix orbits is carried out where a homoclinic orbit asymptotes to an energetically bound spherical orbit. Such orbits simultaneously represent an eccentric orbit and an unstable spherical orbit, both of which share the same $E$ and $L$ values. We present exact expressions for $e$ and $\mu$ as functions of the radius of the corresponding unstable spherical orbit, $r_s$, $a$, and $Q$, and their trajectories, for ($Q\neq0$) separatrix orbits; they are shown to reduce to the equatorial case. These formulae have applications to study the gravitational waveforms from EMRIs besides relativistic precession and phase space explorations. We obtain closed-form expressions of the fundamental frequencies of non-equatorial eccentric trajectories that are equivalent to the previously obtained quadrature forms and also numerically match with the equivalent formulae previously derived. We sketch several orbits and discuss their astrophysical applications., Comment: Typos corrected in this version; reference to the final published article given below; 49 pages, 12 figures, 36 sub-figures; includes 7 appendices referred to in the journal article