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

We use a semianalytic 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 to 3M(circle dot). Stars more massive than 3 M-circle dot 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-circle dot stars and 10% for 1.5 M-circle dot stars. This result is largely insensitive to our assumed model parameters. Finally, the movement of the snow line as stars greater than or similar to 2.5 M-circle dot move to the main sequence may allow the ocean planets suggested by Le'ger et al. to form without migration.