Gas surface densities according to different works. The red curve shows the result of the hydro-dynamical simulation by Morbidelli & Crida (2007), with Jupiter and Saturn in 2:3 resonance. This is the profile that we assumed in this paper, possibly scaled by a factor f_d. The blue line is from Weidenschilling (1977) and is proportional to 1/r. The green line is from Hayashi (1981) and is proportional to 1/r^3/2. The magenta curve reports the amount of gas required in the Pollack et al. (1996) model of giant planet accretion.