Post-Newtonian orbital evolution and gravitational wave forms of inspiralling compact binaries with mass transfer and spin corrections

In this article, we focus on the effects of mass transfer between binary stars and stellar spin on the post-Newtonian (PN) orbital evolution and gravitational waveforms of compact binary systems. We employ the 2.5PN approximation and the mass quadrupole formula to compute the orbital evolution and gravitational waveforms. After an exhaustive discussion of the astrophysical processes relevant to the scenarios of interest, we summarize a one-dimensional mass transfer model that uniformly treats common envelope evolution and tidal disruption, and derive an approximate expression for the dependence of the mass transfer rate of the material flow through the first Lagrange point L1 on the orbital angular velocity. Furthermore, based on the perturbed Keplerian approach, we present a two-dimensional model for the orbital evolution of compact binary systems that simultaneously accounts for mass transfer and stellar spin corrections. Through numerical simulations, we investigate binary systems with significant relativistic effects, namely NS-NS (neutron star-neutron star), NS-BH (neutron star-black hole), and BH-BH (black hole-black hole) systems, and demonstrate the influence of mass transfer and spin corrections on the orbital evolution and polarization waveforms of gravitational waves of these compact binaries systems.