Post-Newtonian Roche-Lobe-Overflow Prescription for Compact Binary Mass Transfer and the Corresponding Gravitational Waveforms

Mass transfer in binary systems is central to many astrophysical phenomena, including the evolution of compact interacting binaries. Starting from the first post-Newtonian hydrodynamic equations in the corotating frame, we derive the first post-Newtonian Roche potential and construct the corresponding post-Newtonian form of the Roche lobe overflow mass transfer prescription. We then include the time dependence of the component masses in the binary dynamics and compute the associated corrections to the equations of motion, gravitational-wave energy and angular-momentum fluxes, and far-zone polarization waveforms. Finally, we apply the model to representative ultracompact binary systems. We find that mass transfer can play an important role in the dynamical evolution of compact binaries. For gravitational-wave observations, its main effect appears as a secular phase drift accumulated over long observation times.