  Numerical simulations, based on the core-nucleated accretion model, are
presented for the formation of Jupiter at 5.2 AU in 3 primordial disks with
three different assumed values of the surface density of solid particles. The
grain opacities in the envelope of the protoplanet are computed using a
detailed model that includes settling and coagulation of grains and that
incorporates a recalculation of the grain size distribution at each point in
time and space. We generally find lower opacities than the 2% of interstellar
values used in previous calculations [Hubickyj, O., Bodenheimer, P., Lissauer,
J. J., 2005. Icarus 179, 415--431; Lissauer, J. J., Hubickyj, O., D'Angelo, G.,
Bodenheimer, P., 2009. Icarus 199, 338-350]. These lower opacities result in
more rapid heat loss from and more rapid contraction of the protoplanetary
envelope. For a given surface density of solids, the new calculations result in
a substantial speedup in formation time as compared with those previous
calculations. Formation times are calculated to be 1.0, 1.9, and 4.0 Myr, and
solid core masses are found to be 16.8, 8.9, and 4.7 Earth masses, for solid
surface densities, sigma, of 10, 6, and 4 grams per squared centimeter,
respectively. For sigma=10 and sigma=6 g/cm^2, respectively, these formation
times are reduced by more than 50% and more than 80% compared with those in a
previously published calculation with the old approximation to the opacity.
