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

Abstract

Abstract 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 $$J_2$$ J2 , equatorial and polar radii $$R_\text {e},~R_\text {p}$$ Re,Rp , flattening $$\nu \doteq (R_\text {e}-R_\text {p})/R_\text {e}$$ ν≐(Re-Rp)/Re , and ellipticity $$\varepsilon \doteq \sqrt{1-R_\text {p}^2/R_\text {e}^2}$$ ε≐1-Rp2/Re2 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 $$\Delta \left( \delta \tau \right) $$ Δδτ of the Rømer-like, orbital component of the pulsar’s time delay $$\delta \tau $$ δτ induced over 10 years by the pN gravitoelectric mass monopole $$\left( \text {Schwarzschild}, GMc^{-2}\right) $$ Schwarzschild,GMc-2 , quadrupole $$\left( GMR^2_\text {e}J_2 c^{-2}\right) $$ GMRe2J2c-2 , gravitomagnetic spin dipole $$\left( \text {Lense}{-}\text {Thirring},~GSc^{-2}\right) $$ Lense-Thirring,GSc-2 and octupole $$\left( GSR^2_\text {e}\varepsilon ^2 c^{-2}\right) $$ GSRe2ε2c-2 accelerations along with the Newtonian quadrupolar $$\left( GMR^2_\text {e}J_2\right) $$ GMRe2J2 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 $$M = 15~\text {M}_\odot ,~R_\text {e} = 5.96~\text {R}_\odot ,~\nu = 0.203,~S = 3.41\times $$ M=15M⊙,Re=5.96R⊙,ν=0.203,S=3.41× $$10^{45}~\text {J}~\text {s},\,J_2 = 1.92\times 10^{-3}$$ 1045Js,J2=1.92×10-3 orbited by a pulsar with an orbital period $$P_\mathrm{b}\simeq $$ Pb≃ 40–70 days, the classical oblateness-driven effects are at the $$\lesssim 4-150~\text {s}$$ ≲4-150s level, while the pN shifts are of the order of $$ \lesssim 1.5-20~\text {s}~\left( GMc^{-2}\right) ,~ \lesssim 10-40~\text {ms}~\left( GMR^2_\text {e} J_2 c^{-2}\right) ,$$ ≲1.5-20sGMc-2,≲10-40msGMRe2J2c-2, $$~ \lesssim 0.5-6~\text {ms}~\left( GSc^{-2}\right) ,~ \lesssim 5-20~\upmu \text {s}~\left( GSR^2_\text {e}\varepsilon ^2 c^{-2}\right) $$ ≲0.5-6msGSc-2,≲5-20μsGSRe2ε2c-2 , depending on their orbital configuration. The root-mean-square (rms) timing residuals $$\upsigma _{\tau }$$ στ of almost all the existing non-recycled, non-millisecond pulsars orbiting massive, fast rotating main sequence stars are $$\lesssim \text {ms}$$ ≲ms . Thus, such kind of binaries have the potential to become interesting laboratories to measure, or, at least, constrain, some Newtonian and post-Newtonian ($$GMc^{-2},\,GMJ_2c^{-2}$$ GMc-2,GMJ2c-2 , and, perhaps, $$GSc^{-2}$$ GSc-2 as well) key features of the distorted gravitational fields of the fast rotating stars hosted by them.