Can the second time-derivative of the orbital frequency of binary pulsars be used for testing general relativity?

TL;DR

This paper investigates whether the second derivative of the orbital frequency in binary pulsars can serve as a test for general relativity, by estimating relativistic contributions and comparing them to observed data.

Contribution

The authors develop a formalism to estimate the relativistic contribution to the second derivative of orbital frequency in pulsars, and evaluate its significance using real and synthetic data.

Findings

Relativistic contribution is negligible compared to observed values.

Formalism allows estimation of relativistic effects on orbital frequency derivatives.

Second derivative of orbital frequency is not a practical test for general relativity.

Abstract

With precision pulsar timing, measured values of a large set of pulsar parameters are obtainable. For some of those parameters, such as the time-derivatives of spin or orbital periods (in the case of binary pulsars), the measured values are not the intrinsic values of the parameters as they contain contributions from the dynamical effects. In the case of orbital period derivatives, the intrinsic values are essentially the general relativistic results. Pulsar timing solution also provides measurement of higher time-derivatives of orbital frequency for some pulsars. We specifically focus on the second time-derivative of the orbital frequency to explore its application in testing general relativity. In this work, we have provided a formalism to estimate the general relativistic contribution to the second derivative of the orbital frequency. We have calculated the dynamical effect contributions as well as the general relativistic contributions to the second time-derivative of the orbital period for real as well as synthetic pulsars. We find that the general relativistic contribution to the second time-derivative of the orbital period is negligibly small compared to the observed values of the real pulsars.