A growing number of debris disks have been detected around metal-polluted white dwarfs. They are thought to originate from tidally disrupted planetary bodies and are responsible for metal accretion onto host WDs. To explain (1) the observationally inferred accretion rate higher than that induced by Poynting-Robertson (PR) drag, and (2) refractory-rich photosphere composition indicating the accretion of terrestrial rocky materials, previous studies (Rafikov 2011; Metzger et al. 2012) proposed runaway accretion of silicate particles due to gas drag by the increasing silicate vapor produced by the sublimation of the particles. However, the effect of re-condensation of the silicate vapor remained an unsolved issue.
In this study, 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 disk. We find that silicate vapor density in the region overlapping the solid particles can exist only up to the saturating vapor pressure and that no runaway accretion occurs if the re-condensation is taken into account. This always limits the accretion rate from mono-compositional silicate disks to the PR-drag flux in the equilibrium state. Alternatively, by performing additional simulations that couple the volatile gas (e.g. water vapor), we demonstrate that it enhances the silicate accretion to rates larger than PR-drag flux through gas drag. The refractory-rich accretion is simultaneously reproduced when the initial volatile fraction of the disk is less than ~10 wt% because of the suppression of volatile accretion due to the efficient back-reaction of solid to gas. The C-type asteroid analogs like Ceres would be a plausible origin of such disks with a small but non-negligible fraction of volatile.