Gravitational wave signatures and detectability of the mass transfer effect in compact binaries

The mass transfer process is prevalent during the inspiral phase of compact binary systems. Our study focuses on systems comprising low-mass white dwarfs, particularly in neutron star-white dwarf binaries and double white dwarf binaries, where a stable mass transfer process occurs at low frequencies. By analyzing the evolution of gravitational wave frequencies in the presence of mass transfer within quasi-circular orbits, we derive an analytical expression for the time-dependent frequency across different frequency bands and the waveforms emitted by compact binaries. Considering gravitational waves emitted by compact binaries in the $1\thicksim10$ mHz band, based on the Fisher analysis, we find that the mass transfer rate can be measured as accurately as $10^{-7} M_\odot/\text{year}$ by space-based gravitational-wave detectors with a signal-to-noise ratio of the order of $10^3$. Including the mass transfer effect in the waveforms provides a new possibility to measure the individual masses of double white dwarf binaries. The relative error of measured white dwarf masses can be down to the order of $0.01$.