Thermal and non-thermal dust sputtering in hydrodynamical simulations of the multiphase interstellar medium

We study the destruction of interstellar dust via sputtering in supernova (SN) shocks using three-dimensional hydrodynamical simulations. With a novel numerical framework, we follow both sputtering and dust dynamics governed by direct collisions, plasma drag, and betatron acceleration. Grain-grain collisions are not included and the grain-size distribution is assumed to be fixed. The amount of dust destroyed per SN is quantified for a broad range of ambient densities and fitting formulae are provided. Integrated over the grain-size distribution, non-thermal (inertial) sputtering dominates over thermal sputtering for typical ambient densities. We present the first simulations that explicitly follow dust sputtering within a turbulent multiphase interstellar medium. We find that the dust destruction time-scales τ are 0.35 Gyr for silicate dust and 0.44 Gyr for carbon dust in solar neighbourhood conditions. The SN environment has an important impact on τ. SNe that occur in pre-existing bubbles destroy less dust as the destruction is limited by the amount of dust in the shocked gas. This makes τ about 2.5 times longer than the estimate based on results from a single SN explosion. We investigate the evolution of the dust-to-gas mass ratio (DGR), and find that a spatial inhomogeneity of ∼14 per cent develops for scales below 10 pc. It locally correlates positively with gas density but negatively with gas temperature even in the exterior of the bubbles due to incomplete gas mixing. This leads to an ∼30 per cent lower DGR in the volume filling warm gas compared to that in the dense clouds.