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 $k^{\mathrm{PK}}$. Along with other PK parameters, it is used in testing general relativity once it is translated into the periastron precession ${\dot{\omega }}^{\mathrm{PK}}$. It was recently remarked that the periastron $\omega$ 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 ${\dot{\omega }}^{\mathrm{LT},\mathrm{A}}\simeq -0.00060^{\circ }{\mathrm{yr}}^{-1}$ from the experimentally determined periastron rate ${\dot{\omega }}_{\mathrm{obs}}$ provided that the other post--Newtonian (PN) contributions to ${\dot{\omega }}_{\exp }$ can be accurately modeled. Among them, the 2PN one seems to be of the same order of magnitude of ${\dot{\omega }}^{\mathrm{LT},\mathrm{A}}$. An analytical expression of the total 2PN periastron precession ${\dot{\omega }}^{2PN}$ in terms of the osculating Keplerian orbital elements, valid not only for binary pulsars, is provided elucidating the subtleties implied in correctly calculating it from $k^{1PN}+k^{2PN}$ and correcting some past errors by the present author. The formula for ${\dot{\omega }}^{2PN}$ is demonstrated to be equivalent to that obtainable from $k^{1PN}+k^{2PN}$ by Damour and Schäfer expressed in the Damour-Deruelle (DD) parameterization. ${\dot{\omega }}^{2PN}$ actually depends on the initial orbital phase, hidden in the DD picture, so that $-0.00080^{\circ }{\mathrm{yr}}^{-1}\le {\dot{\omega }}^{2PN}\le -0.00045^{\circ }{\mathrm{yr}}^{-1}$. A recently released prediction of ${\dot{\omega }}^{2PN}$ for \psrab\, is discussed.

LaTex2e, 16 pages, 2 figures, no tables

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