Probing structural and orbital properties of binary pulsars [HBNI Th206]

Abstract

The timing analysis of radio pulsars gives many interesting results and is expected to contribute further in many areas of fundamental physics in the future. In this connection, it is important to understand the external factors affecting the values of the parameters estimated in the timing analysis. Among all these timing parameters, the measured values of the time-derivatives of the frequencies (both the spin and the orbital) are affected by the velocity, the acceleration, the jerk, etc. of the pulsar. These effects are known as ‘dynamical contributions’. In this thesis, we explore these dynamical effects in the first as well as the second time-derivatives of the frequency (both the spin and the orbital). The previous studies on estimation of the dynamical terms contributing to the first and the second derivatives of the frequency (or the period) resorted to approximate methods which fail to provide accurate values of these parameters for all the pulsars spread across the Galaxy. We point out the limitations of existing methods to calculate the dynamical effects in the first and the second derivatives of the frequency and argue the need for improved methods to extract these effects. We present improved methods to do so and emphasize the fact that these methods should be used for pulsars located away from the solar system, especially when precise values of the first and the second derivatives of the frequency are needed. We provide analytical expressions for all the dynamical terms contributing to the first and the second derivatives of the frequency without resorting to any numerical fitting. These analytical expressions are derived in terms of the Galactic coordinates, the proper motion, the distance, the radial velocity, and the observed values of the frequency and its derivatives, with the assumption that the gravitational potential of the Galaxy is the only cause of the acceleration and the jerk of the pulsar. We introduce a package, ‘GalDynPsr’, that evaluates these different dynamical effects in the first derivative of the period (both the spin and the orbital), following the traditional as well as improved methods based on a well-known model of the Galactic potential. We also demonstrate the differences between the results returned by the improved methods from those obtained using the traditional ones. We then introduce another python package ‘GalDynPsrFreq’ that estimates the dynamical terms in the measured values of the first and the second time derivatives of the frequency (both the spin and the orbital). We demonstrate the usage of 'GalDynPsrFreq' in the study of the effect of the dynamics on the measured values of the second derivative of the frequency for real as well as simulated pulsars. We establish the fact that all dynamical terms affecting the measured values of the second derivative of the frequency are equally important. With the help of simulated pulsars, we demonstrate that the effects of the dynamics would be much larger for pulsars near the Galactic centre than those for the pulsars in the Galactic field. We also show how dynamics can affect values of the braking index and the second derivative of the orbital frequency.