Quantifying Orbital Migration from Exoplanet Statistics and Host Metallicities

We investigate how the statistical distribution of extrasolar planets may becombined with knowledge of the host stars' metallicity to yield constraints onthe migration histories of gas giant planets. At any radius, planets thatbarely manage to form around the lowest metallicity stars accrete theirenvelopes just as the gas disk is being dissipated, so the lower envelope ofplanets in a plot of metallicity vs semi-major axis defines a sample ofnon-migratory planets that will have suffered less than average migrationsubsequent to gap opening. Under the assumption that metallicity largelycontrols the initial surface density of planetesimals, we use simplified coreaccretion models to calculate how the minimum metallicity needed for planetformation varies as a function of semi-major axis. Models that do not includecore migration prior to gap opening (Type I migration) predict that thecritical metallicity is largely flat between the snow line and a semimajor axisof about 6 AU, with a weak dependence on the initial surface density profile ofplanetesimals. When slow Type I migration is included, the critical metallicityis found to increase steadily from 1-10 AU. Large planet samples, that includeplanets at modestly greater orbital radii than present surveys, therefore havethe potential to quantify the extent of migration in both Type I and Type IIregimes.Comment: ApJ, in pres