Abstract
The giant planet occurrence rate rises with orbital period out to at least
$\sim$300 days. Large-scale planetary migration through the disk has long been
suspected to be the physical origin of this feature, as the timescale of
standard Type I migration in a standard solar nebula is longer farther from the
star. These calculations also find that typical Jupiter-bearing cores shuttle
towards the disk inner edge on timescales orders of magnitude shorter than the
gas disk lifetime. The presence of gas giants at myriad distances requires
mechanisms to slow large-scale migration. We revisit the migration paradigm by
deriving model occurrence rate profiles from migration of cores, mass growth by
gas accretion, and planetary gap opening. We show explicitly that the former
two processes occur in tandem. Radial transport of planets can slow down
significantly once deep gaps are carved out by their interaction with disk gas.
Disks are more easily perturbed closer to the star, so accounting for gap
opening flattens the final orbital period distribution. To recover the observed
rise in occurrence rate, gas giants need to be more massive farther out, which
is naturally achieved if their envelopes are dust-free. The range of mass
gradients we find to reconcile the observed occurrence rate of Jupiters is too
abrupt to account for the mass-period distribution of low-eccentricity giant
planets, challenging disk migration as the dominant origin channel of hot and
warm Jupiters. Future efforts in characterizing the unbiased mass distribution
will place stronger constraints on predictions from migration theory.
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