Destruction of the interstellar dust by a supernova

Destruction of the interstellar dust proceeds primary behind supernova shocks. The previous estimates of the mass of the interstellar dust destroyed in the SN remnant do not take into account the physical properties of the ambient medium. Here we consider how some parameters, i.e. gas density and metallicity, can influence the destruction of the interstellar dust. We show that there are two regimes of the interstellar dust grains destruction in SN remnants: rapid and almost complete in compact low-mass SN remnants expanding in dense medium, and gradual and weak destruction in massive remnants evolving in the low-dense environment. When time for thermal sputtering is close to the dynamical one, i.e. to the SN remnant age, the mass of the interstellar dust destroyed in the SN remnant reaches its maximum value. We find that change of the ambient gas density results in the reduction of the dust mass logarithmically. We argue that dust cooling suppresses the interstellar dust destruction up to a factor of 1.6 by mass. This factor decreases for higher density of the ambient medium. We found that the dust mass depends linearly on gas metallicity as ${\rm log}~M_d \sim {\rm [Z/H]}$ or, in other words, on the dust-to-gas ratio as $M_d \sim \zeta_d$. In turn, the destruction efficiency is higher in low-metallicity environments due to relatively longer adiabatic phase. We point out that the mass of the interstellar dust destroyed per one SN in a high density environment of the high star formation regions like in local ultraluminous infrared and high-redshift massive galaxies is about several times smaller than that in the Milky Way diffuse medium.