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

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