Where planetary solids survive sublimation around young and hot white dwarfs

All observed planetary systems orbiting single white dwarfs have lived through the hot stellar transition from an asymptotic giant branch star. In this post-nebular transition period, the initial conditions for planetary system evolution throughout white dwarf cooling are established. The hottest ($\gtrsim$ 20,000 K) and youngest ($\lesssim$ 20 Myr-old) white dwarf planetary system host stars differ significantly from their canonical older and colder counterparts by failing to support solid body accumulation in the immediate vicinity (a few $R_{\odot}$) of the white dwarf. Here, we analyse the likely locations of both solid-body survival and the sublimated gaseous content during this pivotal epoch, and the consequences. We find that (i) reservoirs of iron-rich, rocky and water-rich asteroids of radius $R$ that later observably enrich, or pollute, the white dwarf need to remain parked for the first tens of Myr of white dwarf cooling beyond critical distances of (16 au)$\times(1 {\rm km}/R)^{1/2}$ (for iron), (30 au)$\times(1 {\rm km}/R)^{1/2}$ (for rock) and (130 au)$\times(1 {\rm km}/R)^{1/2}$ (for snow), (ii) sublimation acts much more quickly than radiatively-driven orbital drifts from Poynting-Robertson drag or the Yarkovsky effect, and (iii) although large asteroids ($R \approx$ 10-1000 km) that are kicked on highly eccentric orbits around newly born white dwarfs could survive sublimation, they may fragment into debris which will sublime before the white dwarf cools. These results support, but do not necessitate, dynamical origin scenarios of polluted white dwarfs that feature delayed gravitational instability subsequent to the host star's asymptotic giant branch phase at Kuiper Belt-like distances, and beyond.