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.
Highlights
Hu et al [1] performed a detailed analysis of the perspectives of measuring, or effectively constraining, the moment of inertia (MOI) IA of the pulsar PSR J0737
Lense–Thirring periastron precession ω LT, A [4] induced by its spin angular momentum
Among the competing dynamical effects acting as potential sources of systematic uncertainty, Hu et al [1] included the periastron precession ω 2PN to the second postNewtonian (2PN) order which, along with the much larger1 1PN precession
Summary
Hu et al [1] performed a detailed analysis of the perspectives of measuring, or effectively constraining, the moment of inertia (MOI) IA of the pulsar PSR J0737–. An accurate prediction of the 2PN periastron precession, or of the experimental quantity related to it, which is determined in real data analyses, is of the utmost importance since, according to Equation (3), it may cancel Equation (4) to a large extent To this aim, it is important to stress that, seemingly unnoticed so far in the literature, a certain amount of uncertainty should be deemed as still lingering on that matter because, perhaps, of how ωis routinely expressed in most of the papers devoted to binary pulsars. It is important to stress that, seemingly unnoticed so far in the literature, a certain amount of uncertainty should be deemed as still lingering on that matter because, perhaps, of how ωis routinely expressed in most of the papers devoted to binary pulsars As it will be shown here, the way usually adopted in the literature to write the total 2PN periastron precession hides its dependence on the initial conditions which, is buried in the parameterization used.
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