The sand reckoner
Four out of five astrophysicists surveyed recommend the core-accretion theory to those interested in planet formation theories.
Oklo regulars know that I lean toward core-accretion over gravitational instability as an explanation of the dominant mode of planet formation. I think that core-accretion does a superb job of explaining the planet-metallicity connection, and I don’t think that the initial conditions that underlie hydrodynamical calculations that show disk fragmentation are physically realistic.
The key aspect of core-accretion is that it is a threshold phenomenon. If a planetary core reaches a Neptune-like mass of ~10-20 Earth masses while there is still gas in the protoplanetary disk, then it will rapidly accrete that gas, and (in most cases) increase its mass by a factor of ten or more. On the other hand, if a core reaches a Neptune mass after the gas is gone, then the growth will cut off, and the core will end its days as a modest ice giant.
The amount of time that it takes for a core to reach the phase of rapid gas accretion depends sensitively on the amount of solid material that is available in the disk in the form of planetesimals. A disk with a high surface density of solids is capable of rapidly assembling a core, thereby forming a Jovian-mass gas giant quite quickly. Recent simulations suggest that an average protostellar disk surrounding a star of solar metallicity will lie right at the threshold of being able to manufacture a Jovian planet. This result gives a satisfying mesh with the observations. As stellar metallicity exceeds solar, the fraction of stars with detectable Jovian-mass planets increases very rapidly. Disks that form their Jovian planets early-on are better able to migrate them into the terrestrial region where they can easily be detected. Stars of solar mass and metallicity will tend to have giant planets that remained, like Jupiter, more or less where they formed. Stars with subsolar metallicity will rarely be accompanied by Jupiter-mass planets.
In addition to explaining the planet-metallicity connection, core-accretion provides a number of other testable predictions. Our simulations suggest that a growing planet orbiting a star with 40 percent of the Sun’s mass will require more than 10 million years to “go Jovian.” After 10 million years, however, the gas in most protostellar disks is long gone. The core-accretion theory predicts, therefore, that low-mass red dwarf stars should very often be accompanied by Neptune-mass planets but should almost never have Jupiter-mass companions.
The surface density of solids in a protostellar disk is correlated with metallicity, and some heavy elements are more important than others. Oxygen, for example, in the form of water ice, is of fundamental importance for building cores. At given mass and overall metallicity, therefore, a disk that is naturally rich in oxygen should be better able to form Jupiter-mass planets. Silicon-rich disks too, should have an enhanced capacity for building gas giants.