The opacity of grains in protoplanetary atmospheres

We have computed the size distribution of silicate grains in the outer radiative region of the envelope of a protoplanet evolving according to the scenario of Pollack et al. (1996). Our computation includes grain growth due to Brownian motion and overtake of smaller grains by larger ones. We also include the input of new grains due to the breakup of planetesimals in the atmosphere. We follow the procedure of Podolak (2003), but have speeded it up significantly. This allows us to test the sensitivity of the code to various parameters. We have also made a more careful estimate of the resulting grain opacity. We find that the grain opacity is of the order of $10^{-2}\ \mathrm{cm^2 g^{-1}}$ throughout most of the outer radiative zone as Hubickyj et al. (2005) assumed for their low opacity case, but near the outer edge of the envelope, the opacity can increase to $\sim{1} \mathrm{cm^2 g^{-1}}$. We discuss the effect of this on the evolution of the models.