Parametric derivation of the observable relativistic periastron advance for binary pulsars

TL;DR

This paper derives a parametric formula for the relativistic periastron advance in binary pulsars, applicable to specific precession cases, and confirms its consistency with previous 2PN results for the double pulsar PSR J0737--3039.

Contribution

It introduces a new parametric derivation of the relativistic periastron advance for certain binary pulsar configurations, extending previous methods.

Findings

Derived a parametric expression for the periastron advance parameter $k$.

Confirmed agreement with existing 2PN formulas for PSR J0737--3039.

Applicable to binaries with specific spin configurations.

Abstract

We compute the dimensionless relativistic periastron advance parameter $k$, which is measurable from the timing of relativistic binary pulsars. We employ for the computation the recently derived Keplerian-type parametric solution to the post-Newtonian (PN) accurate conservative dynamics of spinning compact binaries moving in eccentric orbits. The parametric solution and hence the parameter $k$ are applicable for the cases of \emph{simple precession}, namely, case (i), the binary consists of equal mass compact objects, having two arbitrary spins, and case (ii), the binary consists of compact objects of arbitrary mass, where only one of them is spinning with an arbitrary spin. Our expression, for the cases considered, is in agreement with a more general formula for the 2PN accurate $k$, relevant for the relativistic double pulsar PSR J0737--3039, derived by Damour and Sch\"afer many years ago, using a different procedure.