Explaining the variability of WD 1145+017 with simulations of asteroid tidal disruption

Post-main-sequence planetary science has been galvanised by the striking variability, depth and shape of the photometric transit curves due to objects orbiting white dwarf WD 1145+017, a star which also hosts a dusty debris disc and circumstellar gas, and displays strong metal atmospheric pollution. However, the physical properties of the likely asteroid which is discharging disintegrating fragments remain largely unconstrained from the observations. This process has not yet been modelled numerically. Here, we use the N-body code PKDGRAV to compute dissipation properties for asteroids of different spins, densities, masses, and eccentricities. We simulate both homogeneous and differentiated asteroids, for up to two years, and find that the disruption timescale is strongly dependent on density and eccentricity, but weakly dependent on mass and spin. We find that primarily rocky differentiated bodies with moderate (~3-4 g/cm^3) bulk densities on near-circular (e <~ 0.1) orbits can remain intact while occasionally shedding mass from their mantles. These results suggest that the asteroid orbiting WD 1145+017 is differentiated, resides just outside of the Roche radius for bulk density but just inside the Roche radius for mantle density, and is more akin physically to an asteroid like Vesta instead of one like Itokawa.