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

Abstract

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.

Might the 2PN Perihelion Precession of Mercury Become Measurable in the Next Future?

“…The total 2PN net 2 precession of the argument of pericenter ω of a binary system made of two static, spherically symmetric bodies A and B, written in terms of the usual osculating Keplerian orbital elements, is [22] eq. (18)…”

“…It should be recalled that Equation (1) does not come only from the direct 3 effect of the 2PN acceleration A 2PN entering the equation of motion (see, e.g., [22] eq. ( 38), p. 8).…”

“…The 2PN precession of the pericentre of a two-body system, recently worked out 1 [22] in a perturbative way with the Gauss Equations [23] and the standard osculating Ke-plerian orbital elements [24], was investigated in [25] for the double pulsar PSR J0737-3039A/B [26,27] since it is viewed as a major source of systematic error in the expected future determination of the spin-orbit Lense-Thirring periastron precession [20] since it should fall within the envisaged sensitivity level.…”

“…The paper is organized as follows. In Section 2, we review the calculational strategy put forth in [22] to obtain the total 2PN precession of the pericenter of a two-body system. The results are applied in Section 3 to Mercury and compared to the latest figures for the uncertainty in determining its perihelion rate.…”

Current and Future Tests of General Relativity

“…The "grand picture", beautiful as it may appear from a distance, should not be trusted unless all details have been checked independently. Calculations based on post-Newtonian approximation schemes are central but delicate and need to be cross-checked independently [8][9][10]. How much goes into this, and how much can be drawn from it, can be nicely exemplified by the pericenter precession that more than 100 years ago led to the first stunning success of GR.…”