Measuring Mass Transfer Rates in Coalescing Neutron Star--White Dwarf Binaries with Deci-Hz Gravitational-wave Detectors

Abstract: Coalescing neutron star--white dwarf (NS-WD) binaries are among the primary targets for upcoming space-borne gravitational wave (GW) detectors such as LISA, TaiJi, TianQin, etc. During close interaction, these binaries undergo mass transfer, emitting simultaneous X-rays and GWs. This offers a unique opportunity to measure mass transfer rates and study compact binary evolution. To analyze mass transfer rates, we employ the TaylorF2 frequency domain waveform model within the stationary phase approximation (SPA). Through this approach, we derive the GW phase induced during the mass transfer phase and perform Markov Chain Monte Carlo (MCMC) simulations to estimate the minimal detectable mass transfer rate given specific signal-to-noise ratios (SNRs). Our results suggest that for a NS-WD binary with a $0.5 \rm M_\odot$ white dwarf companion, we could measure mass transfer rates down to $10^{-7}\rm M_\odot , {\rm yr}^{-1}$ at SNR=20 and $10^{-9}\rm M_\odot , {\rm yr}^{-1}$ at SNR=1000. This measurement holds significance for studying compact binary evolution involving mass transfer and has potential applications in forecasting tidal disruption events.