A road-map to white dwarf pollution: tidal disruption, eccentric grind-down, and dust accretion

A significant fraction of white dwarfs show metal lines indicative of pollution with planetary material but the accretion process remains poorly understood. The main aim of this paper is to produce a road-map illustrating several potential routes for white dwarf pollution and to link these paths to observational outcomes. Our proposed main road begins with the tidal disruption of a scattered asteroid and the formation of a highly eccentric tidal disc with a wide range of fragment sizes. Accretion of these fragments by Poynting-Robertson (PR) drag alone is too slow to explain the observed rates. Instead, in the second stage, several processes including differential apsidal precession cause high-velocity collisions between the eccentric fragments. Large asteroids produce more fragments when they disrupt, causing rapid grind-down and generating short and intense bursts of dust production, whereas smaller asteroids grind down over longer periods of time. In the final stage, the collisionally produced dust circularizes and accretes on to the white dwarf via drag forces. We show that optically thin dust accretion by PR drag produces large infrared (IR) excesses when the accretion rate exceeds 10(7) g s(-1). We hypothesize that around white dwarfs accreting at a high rate, but with no detected IR excess, dust circularization requires enhanced drag - for instance due to the presence of gas near the disc's pericentre.