Appendix B: Sputtering time scales for the shocked CSM

Here we derive sputtering rates specific to the physical conditions and abundances encountered in the shocked HII region around SN 1987A. At the high temperatures involved, sputtering is independent of grain charge and nearly independent of the plasma temperature. Sputtering reduces the radius of all grains of a given composition in a time $\Delta t$ by the same amount $\Delta a(\Delta t)$. To derive the life times of the grains due to sputtering we used the formula (Eq. (27)) given by Draine & Salpeter (1979a) for non rotating grains moving with a relative velocity $v_{\rm gr}$ with respect to the gas with a temperature $T_{{\rm i}}$. Sputtering yields were adopted from Tielens et al. (1994), and we considered sputtering due to H, He, C, N and O, adopting plasma abundances as given in Sect. 2.1. The initial relative velocities of grains overtaken by the blast wave ( $v_{\rm gr}=\frac{3}{4}v_{\rm S}$) are so high that at first the sputtering is almost non thermal. Due to the drag forces the sputtering becomes thermal after some time, which increases the sputtering yield slightly (10%-30%). Here we simply take the average of the sputtering yield of the two limits $v_{\rm gr}=0$ and $v_{\rm gr}=3v_{\rm s}/4$. The resulting life times of the considered grains are:

$$\tau = \frac{a[0.01~\mu{{\rm m}}]}{n_{\rm H}[{\rm cm^{-3}}]}\... ...times 10^3 & \quad \mbox{iron} \end{array}} \quad {\rm years}$$ (B.1)

in model I and

$$\tau = \frac{a[0.01~\mu{{\rm m}}]}{n_{{\rm H}}[{\rm cm^{-3}}]... ...times 10^3 & \quad \mbox{iron} \end{array}} \quad {\rm years}$$ (B.2)

in model II.