On the 2PN Periastron Precession of the Double Pulsar PSR J0737–3039A/B

One of the post-Keplerian (PK) parameters determined in timing analyses of several binary pulsars is the fractional periastron advance per orbit kPK. Along with other PK parameters, it is used in testing general relativity once it is translated into the periastron precession ω˙PK. It was recently remarked that the periastron ω of PSR J0737–3039A/B may be used to measure/constrain the moment of inertia of A through the extraction of the general relativistic Lense–Thirring precession ω˙LT,A≃−0.00060∘yr−1 from the experimentally determined periastron rate ω˙obs provided that the other post-Newtonian (PN) contributions to ω˙exp can be accurately modeled. Among them, the 2PN seems to be of the same order of magnitude of ω˙LT,A. An analytical expression of the total 2PN periastron precession ω˙2PN in terms of the osculating Keplerian orbital elements, valid not only for binary pulsars, is provided, thereby elucidating the subtleties implied in correctly calculating it from k1PN+k2PN and correcting some past errors by the present author. The formula for ω˙2PN is demonstrated to be equivalent to that obtainable from k1PN+k2PN by Damour and Schäfer expressed in the Damour–Deruelle (DD) parameterization. ω˙2PN actually depends on the initial orbital phase, hidden in the DD picture, so that −0.00080∘yr−1≤ω˙2PN≤−0.00045∘yr−1. A recently released prediction of ω˙2PN for PSR J0737–3039A/B is discussed