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The bright blazar OJ 287 is the best-known candidate for hosting a nanohertz gravitational wave (GW) emitting supermassive binary black hole (SMBBH) in the present observable universe. The binary black hole (BBH) central engine model, proposed by Lehto and Valtonen in 1996, was influenced by the two distinct periodicities inferred from the optical light curve of OJ 287. The current improved model employs an accurate general relativistic description to track the trajectory of the secondary black hole (BH) which is crucial to predict the inherent impact flares of OJ 287. The successful observations of three predicted impact flares open up the possibility of using this BBH system to test general relativity in a hitherto unexplored strong field regime. Additionally, we briefly describe an ongoing effort to interpret observations of OJ 287 in a Bayesian framework.

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 Vela, an efficient, modular, easy-to-use Bayesian pulsar timing and noise analysis package written in Julia. Vela provides an independent, efficient, and parallelized implementation of the full non-linear pulsar timing and noise model along with a Python binding named pyvela. One-time operations such as data file input, clock corrections, and solar system ephemeris computations are performed by pyvela with the help of the PINT pulsar timing package. Its reliability is ensured via careful design utilizing Julia's type system, strict version control, and an exhaustive test suite. This paper describes the design and usage of Vela focusing on the narrowband paradigm.

Pulsar Timing Array (PTA) experiments are expected to be sensitive to gravitational waves (GWs) emitted by individual supermassive black hole binaries (SMBHBs) inspiralling along eccentric orbits. We compare the computational cost of different methods of computing the PTA signals induced by relativistic eccentric SMBHBs, namely approximate analytic expressions, Fourier series expansion, post-circular expansion, and numerical integration. We show that the fastest method for evaluating PTA signals is by using the approximate analytic expressions, which provides up to ~50 times improvement in computational speed over the alternative methods. We investigate the accuracy of the approximate analytic expressions by employing a mismatch metric valid for PTA signals. We show that this method is accurate within the region of the binary parameter space that is of interest to PTA experiments. We introduce a spline-based method to further accelerate the PTA signal evaluations for narrowband PTA datasets. The efficient methods for computing the eccentric SMBHB-induced PTA signals were implemented in the GWecc.jl package and can be readily accessed from the popular ENTERPRISE package to search for such signals in PTA datasets. Further, we simplify the eccentric SMBHB PTA signal expression for the case of a single-pulsar search and demonstrate our computationally efficient methods by performing a single-pulsar search in the 12.5-year NANOGrav narrowband dataset of PSR J1909-3744 using the simplified expression. These results will be crucial for searching for eccentric SMBHBs in large PTA datasets.

Vela is a package for performing Bayesian pulsar timing & noise analysis written in Julia and Python. In the wideband paradigm of pulsar timing, simultaneous time of arrival and dispersion measure measurements are derived from a radio observation using frequency-resolved integrated pulse profiles and templates without splitting the observation into multiple frequency sub-bands. We describe the implementation of the wideband timing paradigm in Vela, and demonstrate its usage using the NANOGrav 12.5-year wideband data of PSR J1923+2515. Vela is the first software package to provide this functionality.

We present Vela.jl, an efficient, modular, easy-to-use Bayesian pulsar timing and noise analysis package written in Julia. Vela.jl provides an independent, efficient, and parallelized implementation of the full non-linear pulsar timing and noise model along with a Python binding named pyvela. One-time operations such as data file input, clock corrections, and solar system ephemeris computations are performed by pyvela with the help of the PINT pulsar timing package. Its reliability is ensured via careful design utilizing Julia's type system, strict version control, and an exhaustive test suite. This paper describes the design and usage of Vela.jl focusing on the narrowband paradigm.

The ionized interstellar medium disperses pulsar radio signals, resulting in a stochastic time-variable delay known as the dispersion measure (DM) noise. In the wideband paradigm of pulsar timing, we measure a DM together with a time of arrival from a pulsar observation to handle frequency-dependent profile evolution, interstellar scintillation, and radio frequency interference more robustly, and to reduce data volumes. In this paper, we derive a method to incorporate arbitrary models of DM variation, including Gaussian process models, in pulsar timing and noise analysis and pulsar timing array analysis. This generalizes the existing method for handling DM noise in wideband datasets.

Burst with memory events are potential transient gravitational wave sources for the maturing pulsar timing array (PTA) efforts. We provide a computationally efficient prescription to model pulsar timing residuals induced by supermassive black hole pairs in general relativistic hyperbolic trajectories employing a Keplerian-type parametric solution. Injection studies have been pursued on the resulting bursts with linear GW memory (LGWM) events with simulated datasets to test the performance of our pipeline, followed by its application to the publicly available NANOGrav 12.5-year (NG12.5) dataset. Given the absence of any evidence of LGWM events within the real NG12.5 dataset, we impose \\(95\\%\\) upper limits on the PTA signal amplitude as a function of the sky location of the source and certain characteristic frequency (\\(n\\)) of the signal. The upper limits are computed using a signal model that takes into account the presence of intrinsic timing noise specific to each pulsar, as well as a common, spatially uncorrelated red noise, alongside the LGWM signal. Our investigations reveal that the \\(95\\%\\) upper limits on LGWM amplitude, marginalized over all other parameters, is 3.48 \\(\\pm 0.51 \\ \\mu\\)s for \\(n>3.16\\) nHz. This effort should be relevant for constraining both burst and memory events in the upcoming International Pulsar Timing Array data releases.

Individual supermassive black hole binaries in non-circular orbits are possible nanohertz gravitational wave sources for the rapidly maturing Pulsar Timing Array experiments. We develop an accurate and efficient approach to compute Pulsar Timing Array signals due to gravitational waves from inspiraling supermassive black hole binaries in relativistic eccentric orbits. Our approach employs a Keplerian-type parametric solution to model third post-Newtonian accurate precessing eccentric orbits while a novel semi-analytic prescription is provided to model the effects of quadrupolar order gravitational wave emission. These inputs lead to a semi-analytic prescription to model such signals, induced by non-spinning black hole binaries inspiralling along arbitrary eccentricity orbits. Additionally, we provide a fully analytic prescription to model Pulsar Timing Array signals from black hole binaries inspiraling along moderately eccentric orbits, influenced by Boetzelet al.[Phys. Rev. D 96,044011(2017)]. These approaches are being incorporated into Enterprise and TEMPO2 for searching the presence of such binaries in Pulsar Timing Array datasets.

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.