Towards a Deterministic Model of Planetary Formation I: a Desert in the Mass and Semi Major Axis Distributions of Extra Solar Planets

In an attempt to develop a deterministic theory for planet formation, we examine the accretion of cores of giant planets from planetesimals, gas accretion onto the cores, and their orbital migration. We adopt a working model for nascent protostellar disks with a wide variety of surface density distributions in order to explore the range of diversity among extra solar planetary systems. We evaluate the cores’ mass-growth rate Ṁc through runaway planetesimal accretion and oligarchic growth. The accretion rate of cores is estimated with a two-body approximation. In the inner regions of disks, the cores’ eccentricity is effectively damped by the ambient disk gas and their early growth is stalled by “isolation”. In the outer regions, the cores’ growth rate is much slower. If some cores can acquire more mass than a critical value of several Earth masses during the persistence of the disk gas, they would be able to rapidly accrete gas and evolve into gas giant planets. The gas accretion process is initially regulated by the Kelvin-Helmholtz contraction of the planets’ gas envelope. Based on the assumption that the exponential decay of the disk-gas mass occurs on the time scales ∼ 106−107 years and that the disk mass distribution is comparable to those inferred from the observations of circumstellar disks of T Tauri stars, we carry out simulations to predict the distributions of masses and semi major axes of extra solar planets. In disks as massive as the minimum-mass disk for the Solar system, gas giants can form only slightly outside the “ice boundary” at a few AU. But, cores can rapidly grow above the critical mass interior to the ice boundary in protostellar disks with 5 times more heavy elements than those of the minimum-mass disk. Thereafter, these massive cores accrete gas prior to its depletion and evolve into gas giants. Unimpeded dynamical accretion of gas is a runaway process