Formation of planetary debris discs around white dwarfs – II. Shrinking extremely eccentric collisionless rings

The formation channel of the tens of compact debris discs which orbit white dwarfs (WDs) at a distance of 1 R⊙ remains unknown. Asteroids that survive the giant branch stellar phases beyond a few au are assumed to be dynamically thrust towards the WD and tidally disrupted within its Roche radius, generating extremely eccentric (e > 0.98) rings. Here, we establish that WD radiation compresses and circularizes the orbits of supermicron to cm-sized ring constituents to entirely within the WD's Roche radius. We derive a closed algebraic formula which well-approximates the shrinking time as a function of WD cooling age, the physical properties of the star and the physical and orbital properties of the ring particles. The shrinking time-scale increases with both particle size and cooling age, yielding age-dependent WD debris disc size distributions.