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

摘要

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 $$mathbf S $$ S , dimensionless mass quadrupole moment $$J_2$$ J 2 , equatorial and polar radii $$R_ext {e},~R_ext {p}$$ R e , R p , flattening $$u doteq (R_ext {e}-R_ext {p})/R_ext {e}$$ ν ? ( R e - R p ) / R e , and ellipticity $$arepsilon doteq sqrt{1-R_ext {p}^2/R_ext {e}^2}$$ ε ? 1 - R p 2 / R 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 $$Delta left( delta au ight) $$ Δ δ τ of the R?mer-like, orbital component of the pulsar’s time delay $$delta au $$ δ τ induced over 10 years by the pN gravitoelectric mass monopole $$left( ext {Schwarzschild}, GMc^{-2}ight) $$ Schwarzschild , G M c - 2 , quadrupole $$left( GMR^2_ext {e}J_2 c^{-2}ight) $$ G M R e 2 J 2 c - 2 , gravitomagnetic spin dipole $$left( ext {Lense}{-}ext {Thirring},~GSc^{-2}ight) $$ Lense - Thirring , G S c - 2 and octupole $$left( GSR^2_ext {e}arepsilon ^2 c^{-2}ight) $$ G S R e 2 ε 2 c - 2 accelerations along with the Newtonian quadrupolar $$left( GMR^2_ext {e}J_2ight) $$ G M R e 2 J 2 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 $$M = 15~ext {M}_odot ,~R_ext {e} = 5.96~ext {R}_odot ,~u = 0.203,~S = 3.41imes $$ M = 15 M ⊙ , R e = 5.96 R ⊙ , ν = 0.203 , S = 3.41 × $$10^{45}~ext {J}~ext {s},,J_2 = 1.92imes 10^{-3}$$ 10 45 J s , J 2 = 1.92 × 10 - 3 orbited by a pulsar with an orbital period $$P_mathrm{b}simeq $$ P b ? 40–70 days, the classical oblateness-driven effects are at the $$lesssim 4-150~ext {s}$$ ? 4 - 150 s level, while the pN shifts are of the order of $$ lesssim 1.5-20~ext {s}~left( GMc^{-2}ight) ,~ lesssim 10-40~ext {ms}~left( GMR^2_ext {e} J_2 c^{-2}ight) ,$$ ? 1.5 - 20 s G M c - 2 , ? 10 - 40 ms G M R e 2 J 2 c - 2 , $$~ lesssim 0.5-6~ext {ms}~left( GSc^{-2}ight) ,~ lesssim 5-20~upmu ext {s}~left( GSR^2_ext {e}arepsilon ^2 c^{-2}ight) $$ ? 0.5 - 6 ms G S c - 2 , ? 5 - 20 μ s G S R e 2 ε 2 c - 2 , depending on their orbital configuration. The root-mean-square (rms) timing residuals $$upsigma _{au }$$ σ τ of almost all the existing non-recycled, non-millisecond pulsars orbiting massive, fast rotating main sequence stars are $$lesssim ext {ms}$$ ? ms . Thus, such kind of binaries have the potential to become interesting laboratories to measure, or, at least, constrain, some Newtonian and post-Newtonian ( $$GMc^{-2},,GMJ_2c^{-2}$$ G M c - 2 , G M J 2 c - 2 , and, perhaps, $$GSc^{-2}$$ G S c - 2 as well) key features of the distorted gravitational fields of the fast rotating stars hosted by them.