  Nearly $15-20%$ of solar type stars contain one or more gas giant planet.
According to the core-accretion scenario, the acquisition of their gaseous
envelope must be preceded by the formation of super-critical cores with masses
ten times or larger than that of the Earth. It is natural to link the formation
probability of gas giant planets with the supply of gas and solid in their
natal disks. However, a much richer population of super Earths suggests that 1)
there is no shortage of planetary building-block material, 2) gas giants'
growth barrier is probably associated with whether they can merge into
super-critical cores, and 3) super Earths are probably failed cores which did
not attain sufficient mass to initiate efficient accretion of gas before it is
severely depleted. Here we construct a model based on the hypothesis that
protoplanetary embryos migrated extensively before they were assembled into
bona fide planets. We construct a Hermite-Embryo code based on a unified
viscous-irradiation disk model and a prescription for the embryo-disk tidal
interaction. This code is used to simulate 1) the convergent migration of
embryos, and 2) their close encounters and coagulation. Around the progenitors
of solar-type stars, the progenitor super-critical-mass cores of gas giant
planets primarily form in protostellar disks with relatively high ($\gtrsim
10^{-7} M_\odot$ yr$^{-1}$) mass accretion rates whereas systems of super
Earths (failed cores) are more likely to emerge out of natal disks with modest
mass accretion rates, due to the mean motion resonance barrier and retention
efficiency.
