On the equations of states of white dwarfs from low-frequency gravitational waves

An extreme-mass-ratio system composed by a white dwarf (WD) and a massive black hole can be observed by the low-frequency gravitational wave detectors like LISA. When the mass of black hole is around $10^4 \sim 10^5 M_\odot$, the WD will be disrupted by the tidal interaction at the final inspiralling stage. The event position and time of the tidal disruption of the WD can be accurately determined by the gravitational wave (GW) signals. Such position and time depend on the mass of black hole and especially on the density of WD. We present that by using LISA-like GW detectors, the mass-radius relation and then the equations of states of WDs can be constrained strictly (accuracy better than $0.1\%$). We also point out that LISA can accurately predict the disruption time of WD, and forecast the electromagnetic followup of this tidal disruption event.