Dynamical effects in the observed rate of change of the orbital and the spin periods of radio pulsars: Improvement in the method of estimation and its implications

The observed values of the rate of change of the orbital and the spin periods of pulsars are affected by different dynamical effects, for example, the line-of-sight acceleration and the proper motion of the pulsar relative to the sun. We explore these dynamical effects thoroughly and point out the drawbacks of popular methods. We introduce a package, `GalDynPsr', that evaluates different dynamical effects following traditional as well as improved methods based on the model of the Galactic potential provided in a publicly available package called `galpy'. We argue that the improved methods introduced in this paper should be used for pulsars located 1 kpc or farther away from the solar system, especially when precise values of the rate of change of the periods are required, e.g., while placing limits on alternative theories of gravity, calculating the spin-down limit of the continuous gravitational waves emitted from a rotationally deformed neutron star, understanding pulsar `death-line', etc. GalDynPsr is available online and open for contributions.