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Dust sputtering by Reverse Shocks in Supernova Remnants

We consider sputtering of dust grains, believed to be formed in cooling supernovae ejecta, under the influence of reverse shocks. In the regime of self-similar evolution of reverse shocks, we can follow the evolution of ejecta density and temperature analytically as a function of time in different parts of the ejecta, and calculate the sputtering rate of graphite and silicate grains embedded in the ejecta as they encounter the reverse shock. Through analytic (1D) calculations, we find that a fraction of dust mass ($ 1\hbox{--}20$% for silicates and %$\le 5$% for graphites) can be sputtered by reverse shocks, the fraction varying with the grain size distribution and the steepness of the density profile of the ejecta mass. It is expected that many more grains will get sputtered in the region between the forward and reverse shocks, so that our analytical results provide a lower limit to the destroyed fraction of dust mass.