One-dimensional calculations of a large impact on Uranus

The large obliquity (98°) of the planet Uranus suggests that it may have suffered an oblique impact by a large body during its formation. Considerations of angular momentum and possible impact parameters show that a 1- to 2 M ⊗ impactor body would be sufficient to account for the total angular momentum of the Uranus system, if it arrived at escape velocity. We present one-dimensional spherically symmetric hydrodynamic calculations of the effect of such an impact on the gaseous envelope of the planet. The effect of the impact on the solid/liquid “core” of the planet is treated very simply as a rapid addition of mass and energy to the core. We characterize an impact by a partition of energy such that a fraction is deposited directly into the envelope and the rest heats the core. The initial state for the calculations is taken from the models of Bodenheimer and Pollack(1986). The most important parameter determing the fate of the gaseous envelope is the amount of energy deposited directly into it. If the amount is comparable to or greater than one-half of the gravitational potential energy of the envelope, the gas can be completely removed by the impact. Since the impactor mass is generally comparabel to or greater than the mass of Uranus' present H 2/He envelope, that energy need not be a large fraction of the total impact energy. We find a sharp transition between the cases of nearly complete retention and dispersal, corresponding to energy deposition fractions below or above a critical value. Within a reasonable range of parameters, it is possible to explain the angular momentum of the Uranus system as well as the retention of a gaseous envelope of ∼ 1 M ⊗.