Toward an exact approach to pulsar timing

The pulsar timing technique, which compares the observed arrival times of electromagnetic radiation from a pulsar with the predicted arrival times derived from a theoretical model of the pulsar system, is used in pulsar astronomy to infer a multitude of physical information and to constrain possible corrections to general relativity (GR). The propagation delay is usually computed using formulas based on a post-Newtonian approach, for both the light trajectory and the orbital motion. However, evidence has recently emerged that this approximation may no longer be sufficient when the companion object is a supermassive black hole; deviations from a full GR computation of the propagation delay can reach a few seconds. In this paper, we analyze the case of binary pulsars with a stellar or intermediate black hole companion, whose discovery and timing are key goals of SKA. With a numerical algorithm, we have found that in this case, the full GR value depends only on the semimajor axis of the relative orbit and on the mass of the black hole companion. If the mass of the latter is sufficiently large ($100{M}_{\ensuremath{\bigodot}}$), the maximum difference between the two approaches is significant ($\ensuremath{\sim}{10}^{\ensuremath{-}7}\text{ }\text{ }\mathrm{s}$) even for large binaries ($\ensuremath{\sim}{10}^{16}\text{ }\text{ }\mathrm{cm}$), and increases up to $\ensuremath{\sim}{10}^{\ensuremath{-}4}\text{ }\text{ }\mathrm{s}$ when the mass is ${10}^{5}{M}_{\ensuremath{\bigodot}}$. We also consider relativistic corrections to the orbital motion, and discover that they can strongly affect the value of the propagation delay. We conclude that in the future, post-Newtonian formulas should be replaced with a more accurate approach in these systems, especially in view of future discoveries made by new large telescopes such as SKA.