Saturn and Jupiter is the same; the size of the horseshoe regions of the two planets (and hence the magnitude of the corotation torque felt by each planet) is proportional to $M_p^\gamma$ for some $\gamma < 1$; thus, the effect on the migration rate $\dot a_p$ of the planet is proportional to $M_p^{(\gamma-1)}$, namely it is larger for a lighter planet. So, if the corotation torque dominated the evolution of the planets, Saturn would be extracted from the resonance and would migrate away from Jupiter. As long as this does not happen (as in Fig. \[MS-Hr\]), the corotation torque cannot be the dominant force driving the planets’ migration.

For a further [**indication**]{} that the corotation torque [**is weaker**]{} than the torque felt by Jupiter from the inner disk (Lindblad torque), we have done another simulation, still with $H/r=3$% and $\nu=10^{-5.5}$, but with an initial gas density reduced by a factor of 2. The Lindblad torque scales with the gas density. Conversely, the corotation torque [**does not scale simply with the gas density because a component of it depends on the the radial speed of the planet relative to the gas, which in turn also depends on the gas density**]{} (Masset 