On the relation between hot jupiters and the Roche limit

Many of the known extrasolar planets are hot Jupiters, giant planets with orbital periods of just a few days. We use the observed distribution of hot Jupiters to constrain the location of its inner edge in the mass- period diagram. If we assume a slope corresponding to the classical Roche limit, then we find that the edge corresponds to a separation close to twice the Roche limit, as expected if the planets started on highly eccentric orbits that were later circularized. In contrast, any migration scenario would predict an inner edge right at the Roche limit, which applies to planets approaching on nearly circular orbits. However, the current sample of hot Jupiters is not sufficient to provide a precise constraint simultaneously on both the location and the slope of the inner edge.