The Signature of the Ice Line and Modest Type I Migration in the Observed Exoplanet Mass-Semimajor Axis Distribution

Abstract

Existing exoplanet radial velocity surveys are complete in the planetary mass-semimajor axis (Mp-a) plane over the range 0.1 AU < a < 2.0 AU where Mp >~ 100 M_Earth. We marginalize over mass in this complete domain of parameter space and demonstrate that the observed semimajor axis distribution is inconsistent with models of planet formation that use the full Type I migration rate derived from a linear theory and that do not include the effect of the ice line on the disk surface density profile. However, the efficiency of Type I migration can be suppressed by both nonlinear feedback and the barriers introduced by local maxima in the disk pressure distribution, and we confirm that the synthesized Mp-a distribution is compatible with the observed data if we account for both retention of protoplanetary embryos near the ice line and an order-of-magnitude reduction in the efficiency of Type I migration. The validity of these assumption can be checked because they also predict a population of short-period rocky planets with a range of masses comparable to that of the Earth as well as a "desert" in the Mp-a distribution centered around Mp ~ 30-50 M_Earth and a < 1 AU. We show that the expected "desert" in the Mp-a plane will be discernible by a radial velocity survey with 1 m/s precision and n ~ 700 radial velocity observations of program stars.