Planet formation around stars of various masses: The snow line and the frequency of giant planets

We use a semi-analytic circumstellar disk model that considers movement of the snow line through evolution of accretion and the central star to investigate how gas giant frequency changes with stellar mass. The snow line distance changes weakly with stellar mass; thus giant planets form over a wide range of spectral types. The probability that a given star has at least one gas giant increases linearly with stellar mass from 0.4 M_sun to 3 M_sun. Stars more massive than 3 M_sun evolve quickly to the main-sequence, which pushes the snow line to 10-15 AU before protoplanets form and limits the range of disk masses that form giant planet cores. If the frequency of gas giants around solar-mass stars is 6%, we predict occurrence rates of 1% for 0.4 M_sun stars and 10% for 1.5 M_sun stars. This result is largely insensitive to our assumed model parameters. Finally, the movement of the snow line as stars >2.5 M_sun move to the main-sequence may allow the ocean planets suggested by Leger et. al. to form without migration.