  The origin of a recently discovered close-in Neptune-mass planet around GJ436
poses a challenge to the current theories of planet formation. Based on the
sequential accretion hypothesis and the standard theory of gap formation and
orbital migration, we show that around M dwarf stars, close-in Neptune-mass
ice-giant planets may be relatively common, while close-in Jupiter-mass
gas-giant planets are relatively rare. The mass distribution of close-in
planets generally has two peaks at about Neptune mass and Jupiter mass. The
lower-mass peak takes the maximum frequency for M dwarfs. Around more massive
solar-type stars (G dwarfs), the higher-mass peak is much more pronounced.
These are because planets tend to undergo type II migration after fully
accreting gas around G dwarfs while they tend to migrate faster than gas
accretion around M stars. Close-in Neptune-mass planets may also exist around G
dwarfs, though they tend to be mostly composed of silicates and iron cores and
their frequency is expected to be much smaller than that of Neptune-mass
planets around M dwarfs and that of gas giants around G dwarfs. We also show
that the conditions for planets' migration due to their tidal interaction with
the disk and the stellar-mass dependence in the disk-mass distribution can be
calibrated by the mass distribution of short-period planets around host stars
with various masses.
