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Register a new userLambda Perturbations of Keplerian Orbits
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Yurii V. Dumin
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To estimate influence of the dark energy on the Keplerian orbits, we solve the general relativistic equations of motion of a test particle in the field of a point-like mass embedded in the cosmological background formed by the Lambda-term with realistic cosmological Robertson-Walker asymptotics at infinity. It is found that under certain relations between three crucial parameters of the problem--the initial radius of the orbit, Schwarzschild and de Sitter radii--the specific secular perturbation caused by the Lambda-term becomes significant, i.e. can reach the rate of the standard Hubble flow. This fact is interesting both by itself and may have important consequences for the long-term dynamics of planets and stellar binary systems.
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We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star as a potential scenario to dynamically put to the test certain post-Keplerian effects of both Newtonian and post-Newtonian nature. We numerically produce time series of the perturbations $Deltaleft(deltatauright)$ of the R{o}mer-like, orbital component of the pulsars time delay $deltatau$ induced over 10 years by the pN gravitoelectric mass monopole, quadrupole, gravitomagnetic spin dipole and octupole accelerations along with the Newtonian quadrupolar one. We do not deal with the various propagation time delays due to the travelling electromagnetic waves. It turns out that, for a Be-type star with $M = 15 textrm{M}_odot$, $R_textrm{e} = 5.96 textrm{R}_odot$, $ u = 0.203$, $S = 3.41times 10^{45} textrm{J} textrm{s}$, $J_2 = 1.92times 10^{-3}$ orbited by a pulsar with an orbital period $P_textrm{b}simeq 40-70 textrm{d}$, the classical oblateness-driven effects are at the $lesssim 4-150 textrm{s}$ level, while the pN shifts are of the order of $lesssim 1.5-20 textrm{s} left(GMc^{-2}right)$, $lesssim 10-40 textrm{ms} left(GMR^2_textrm{e} J_2 c^{-2}right)$, $lesssim 0.5 - 6 textrm{ms} left(GSc^{-2}right)$, $lesssim 5 - 20 mutextrm{s} left(GSR^2_textrm{e} varepsilon^2 c^{-2}right)$, depending on their orbital configuration. The root-mean-square (rms) timing residuals $sigma_{tau}$ of almost all the existing non-recycled, non-millisecond pulsars orbiting massive, fast rotating main sequence stars are $lesssimtextrm{ms}$. Thus, such kind of binaries have the potential to become interesting laboratories to measure, or, at least, constrain, some Newtonian and post-Newtonian key features of the distorted gravitational fields of the fast rotating stars hosted by them [Abridged].
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