Determining the nature of white dwarfs from low-frequency gravitational waves

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