On the 2PN Periastron Precession of the Double Pulsar PSR J0737–3039A/B - Lorenzo Iorio (MDPI AG, 2021)
One of the post-Keplerian (PK) parameters determined in timing analyses of several binary pulsars is the fractional periastron advance per orbit <semantics>kPK</semantics>. Along with other PK parameters, it is used in testing general relativity once it is translated into the periastron precession <semantics><mover accent="true">ω˙</mover>PK</semantics>. It was recently remarked that the periastron <semantics>ω</semantics> 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 <semantics><mover accent="true">ω˙</mover>LT,<mspace width="0.166667em"></mspace>A≃−0.00060∘<mspace width="0.166667em"></mspace>yr−1</semantics> from the experimentally determined periastron rate <semantics><mover accent="true">ω˙</mover>obs</semantics> provided that the other post-Newtonian (PN) contributions to <semantics><mover accent="true">ω˙</mover>exp</semantics> can be accurately modeled. Among them, the 2PN seems to be of the same order of magnitude of <semantics><mover accent="true">ω˙</mover>LT,<mspace width="0.166667em"></mspace>A</semantics>. An analytical expression of the total 2PN periastron precession <semantics><mover accent="true">ω˙</mover>2PN</semantics> 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 <semantics>k1PN+k2PN</semantics> and correcting some past errors by the present author. The formula for <semantics><mover accent="true">ω˙</mover>2PN</semantics> is demonstrated to be equivalent to that obtainable from <semantics>k1PN+k2PN</semantics> by Damour and Schäfer expressed in the Damour–Deruelle (DD) parameterization. <semantics><mover accent="true">ω˙</mover>2PN</semantics> actually depends on the initial orbital phase, hidden in the DD picture, so that <semantics>−0.00080∘<mspace width="0.166667em"></mspace>yr−1≤<mover accent="true">ω˙</mover>2PN≤−0.00045∘<mspace width="0.166667em"></mspace><mspace width="0.166667em"></mspace>yr−1</semantics>. A recently released prediction of <semantics><mover accent="true">ω˙</mover>2PN</semantics> for PSR J0737–3039A/B is discussed.