Classical and general relativistic post-Keplerian effects in binary pulsars hosting fast rotating main sequence stars

Description

We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star of mass M, spin angular momentum $\mathbf S $ , dimensionless mass quadrupole moment $J_2$ , equatorial and polar radii $R_\text {e},~R_\text {p}$ , flattening $\nu \doteq (R_\text {e}-R_\text {p})/R_\text {e}$ , and ellipticity $\varepsilon \doteq \sqrt{1-R_\text {p}^2/R_\text {e}^2}$ 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 $\Delta \left( \delta \tau \right) $ of the Rømer-like, orbital component of the pulsar's time delay $\delta \tau $ induced over 10 years by the pN gravitoelectric mass monopole $\left( \text {Schwarzschild}, GMc^{-2}\right) $ , quadrupole $\left( GMR^2_\text {e}J_2 c^{-2}\right) $ , gravitomagnetic spin dipole $\left( \text {Lense}{-}\text {Thirring},~GSc^{-2}\right) $ and octupole $\left( GSR^2_\text {e}\varepsilon ^2 c^{-2}\right) $ accelerations along with the Newtonian quadrupolar $\left( GMR^2_\text {e}J_2\right) $ 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~\text {M}_\odot ,~R_\text {e} = 5.96~\text {R}_\odot ,~\nu = 0.203,~S = 3.41\times $ $10^{45}~\text {J}~\text {s},\,J_2 = 1.92\times 10^{-3}$ orbited by a pulsar with an orbital period $P_\mathrm{b}\simeq $ 40–70 days, the classical oblateness-driven effects are at the $\lesssim 4-150~\text {s}$ level, while the pN shifts are of the order of $ \lesssim 1.5-20~\text {s}~\left( GMc^{-2}\right) ,~ \lesssim 10-40~\text {ms}~\left( GMR^2_\text {e} J_2 c^{-2}\right) ,$ $~ \lesssim 0.5-6~\text {ms}~\left( GSc^{-2}\right) ,~ \lesssim 5-20~\upmu \text {s}~\left( GSR^2_\text {e}\varepsilon ^2 c^{-2}\right) $ , depending on their orbital configuration. The root-mean-square (rms) timing residuals $\upsigma _{\tau }$ of almost all the existing non-recycled, non-millisecond pulsars orbiting massive, fast rotating main sequence stars are $\lesssim \text {ms}$ . Thus, such kind of binaries have the potential to become interesting laboratories to measure, or, at least, constrain, some Newtonian and post-Newtonian ( $GMc^{-2},\,GMJ_2c^{-2}$ , and, perhaps, $GSc^{-2}$ as well) key features of the distorted gravitational fields of the fast rotating stars hosted by them.

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