Further investigations of random models of Uranus and Neptune

We present a series of computer models for Uranus and Neptune where the interior density distribution is randomly chosen. The only constraints placed on the distribution are that the density does not decrease with decreasing radius, and that the density distribution fits the observed mass and gravitational moments of these planets. Previous models of these planets all had a density discontinuity at about 70% of the total radius. We use our models to explore the space of density distributions that fit the observed gravitational moments, and set limits on the position and size of this discontinuity. We find that models are possible with no discontinuity in the mantle. In addition a density discontinuity as large as 3 g cm^-3 is possible for Uranus if the discontinuity is inward of about 0.75 Uranus radii. Closer to the surface the discontinuity must be smaller. For Neptune, the larger uncertainties in the measured moments result in coarser limits on the size of the density jump. Other means of limiting the range of acceptable models are discussed.