Fallback rates in partial tidal disruptions of white dwarfs by intermediate mass black holes

Fallback rate of debris after a partial tidal disruption event of a star with an intermediate mass black hole (IMBH) might provide important signatures of such black holes, compared to supermassive ones. Here using smoothed particle hydrodynamics methods, we provide a comprehensive numerical analysis of this phenomenon. We perform numerical simulations of single partial tidal disruptions of solar mass white dwarfs in parabolic orbits, with a non-spinning $10^3M_{\odot}$ IMBH for various values of the impact parameter, and determine the core mass fractions and fallback rates of debris into the IMBH. For supermassive black holes, in a full disruption processes, it is known that the late time fallback rate follows a power law $t^{-5/3}$, whereas for partial disruptions, such a rate has been recently conjectured to saturate to a steeper power law $t^{-9/4}$, independent of the mass of the remnant core. We show here that for IMBHs, partial disruptions significantly alter this conclusion. That is, the fallback rate at late times do not asymptote to a $t^{-9/4}$ power law, and this rate is also a strong function of the core mass. We derive a robust formula for the late time fallback rate as a function of the core mass fraction, that is independent of the white dwarf mass, as we verify numerically by varying the mass of the white dwarf.