Post-Newtonian dynamics of compact binaries with mass transfer

Taking into account the mass transfer effect, we derive the equations of motion of a compact binary system at the second-half post-Newtonian order. Applying such equations of motion to quasi-circular orbits, we obtain the time derivative of the orbital frequency, which is consistent with the angular momentum balance equation. Numerical estimates of the phase of gravitational waves are provided for typical mass transfer rates. Our result can be used to improve the waveforms of gravitational waves emitted by compact binaries with mass transfer.