A multi-messenger mass determination method for LISA Neutron-Star White-Dwarf Binaries

Determining the mass of the neutron stars (NSs) accurately improves our understanding of the NS interior and complicated binary evolution. However, the masses of the systems are degenerate with orbital inclination angle when using solely gravitational waves (GWs) or electromagnetic measurements, especially for face-on binaries. Taking advantages of both GWs and optical observations for LISA neutron-star white-dwarf (NS-WD) binaries, we propose a mass determination method utilising multi-messenger observational information. By combining the binary mass function obtained from optical observations and a GW mass function, that we introduce, derived from GW observations, we demonstrate how we can set improved constraints on the NS mass and break the degeneracy in the mass and viewing inclination determination. We further comment on the universal relation of the error bar of the GW mass function versus GW signal-to-noise ratio (SNR), and propose a simple method for the estimate of capability of GW observations on mass determination with {LISA}. We show that for ultra-compact NS-WD binaries within our Galaxy, the mass of the NS can be constrained to within an accuracy of +- 0.2 \solarmass with the proposed method.