Modelling the evolution of silicate/volatile accretion discs around white dwarfs

A growing number of debris discs have been detected around metal-polluted white dwarfs. They are thought to be originated from tidally disrupted exoplanetary bodies and responsible for metal accretion on to host WDs. To explain (1) the observationally inferred accretion rate higher than that induced by Poynting–Robertson drag, M , and (2) refractory-rich photosphere composition indicating the accretion of terrestrial rocky materials, previous studies proposed runaway accretion of silicate particles due to gas drag by the increasing silicate vapour produced by the sublimation of the particles. Because re-condensation of the vapour diffused beyond the sublimation line was neglected, we revisit this problem by one-dimensional advection/diffusion simulation that consistently incorporates silicate sublimation/condensation and back-reaction to particle drift due to gas drag in the solid-rich disc. We find that the silicate vapour density in the region overlapping the solid particles follows the saturating vapour pressure and that no runaway accretion occurs if the re-condensation is included. This always limits the accretion rate from mono-compositional silicate discs to M in the equilibrium state. Alternatively, by performing additional simulations that couple the volatile gas (e.g. water vapour), we demonstrate that the volatile gas enhances the silicate accretion to > M through gas drag. The refractory-rich accretion is simultaneously reproduced when the initial volatile fraction of disc is ≲ 10 wt per cent because of the suppression of volatile accretion due to the efficient back-reaction of solid to gas. The discs originating from C-type asteroid analogues might be a possible clue to the high-M puzzle.