Producing planetary debris exterior to white dwarf Roche radii through sublimative rotational fission

Abstract: The majority of white dwarfs that host periodic transiting planetary debris do so at distances that exceed the rubble-pile Roche limit, in disagreement with canonical formation models that focus on the tidal disruption of minor planets. Here, we quantify the conditions by which rotational fission due to sublimative outgassing ("SYORP" break-up) can occur outside of the Roche sphere in the distance range of 1-5 Roche radii. We use the Many Materials Orbital Sublimation (MaMOS) model to quantify the outgassing properties of three representative types of planetary materials: cores (iron), mantles (forsterite olivine) and comets (water ice), and characterise the resulting spin-up rate analytically by adopting SYORP coefficients in the range of $10^{-5}-10^{-3}$. We then compare this rate to that generated by the radiative YORP effect with YORP coefficients of $10^{-3}-10^{-2}$, and focus on planetesimals with radii of 0.1, 1.0, and 10 km. We find that for white dwarf cooling ages of up to $\sim$ 1 Gyr, sublimative fission of planetesimals and fragments $\lesssim$ 0.1 km in size due to water ice outgassing occur on observable timescales (within 10 yr), regardless if the spin-up is monotonic or stochastic. Further, these timescales are orders of magnitude shorter than the corresponding YORP fission timescales. For drier planetesimals, both iron and forsterite outgassing can be effective at 10-100 Myr cooling ages. Our results do not substantially differ for strengthless rubble piles versus objects with 1 kPa of internal strength. These findings add to growing evidence that gravitationally scattered comets and asteroids do not need to adopt pericentres within a white dwarf's Roche radius to eventually enrich, or pollute, the star with metals.