Unstable low-mass planetary systems as drivers of white dwarf pollution

At least 25 per cent of white dwarfs show atmospheric pollution by metals, sometimes accompanied by detectable circumstellar dust/gas discs or (in the case of WD 1145+017) transiting disintegrating asteroids. Delivery of planetesimals to the white dwarf by orbiting planets is a leading candidate to explain these phenomena. Here, we study systems of planets and planetesimals undergoing planet-planet scattering triggered by the star's post-main-sequence mass loss, and test whether this can maintain high rates of delivery over the several Gyr that they are observed. We find that low-mass planets (Earth to Neptune mass) are efficient deliverers of material and can maintain the delivery for Gyr. Unstable low-mass planetary systems reproduce the observed delayed onset of significant accretion, as well as the slow decay in accretion rates at late times. Higher-mass planets are less efficient, and the delivery only lasts a relatively brief time before the planetesimal populations are cleared. The orbital inclinations of bodies as they cross the white dwarf's Roche limit are roughly isotropic, implying that significant collisional interactions of asteroids, debris streams and discs can be expected. If planet-planet scattering is indeed responsible for the pollution of white dwarfs, many such objects, and their main-sequence progenitors, can be expected to host (currently undetectable) super-Earth planets on orbits of several au and beyond.