Gas Giant Protoplanet Formation: Disk Instability Models with Thermodynamics and Radiative Transfer

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Abstract
Doppler spectroscopy of nearby stars has shown that extrasolar gas giant planets often have masses considerably in excess of that of Jupiter, while observations of young stars imply that the gaseous portions of protoplanetary disks have lifetimes typically of no more than a few million years. Both discoveries raise questions about the universality of the mechanism long favored for Jupiter formation: core accretion. Forming Jupiter by core accretion requires a gas surface density at 5 AU of about 103 g cm-2. Combined with midplane temperatures cold enough to form comets (<50 K), this leads to a marginally gravitationally unstable gas disk. High spatial resolution, three-dimensional hydrodynamical models of "locally isothermal" disks have shown that gas giant protoplanets may form in such a marginally unstable disk, with masses comparable to the more massive extrasolar planets, and well within expected disk lifetimes. However, locally isothermal models err on the side of encouraging protoplanetary clumps to form, whereas models by other workers using less permissive thermodynamical assumptions have suggested that clump formation is prohibited. We present three-dimensional models with an approximate treatment of heating and cooling, including radiative transfer in the diffusion approximation, that show that disk instability can still proceed in much the same manner as in locally isothermal models because the timescale for significant nebular cooling is comparable to that for the instability to grow, i.e., an orbital period. The models suggest that disk instability remains as a likely means for the widespread formation of gas giant planets. Core accretion apparently requires exceptionally long-lived disks to form Jupiters and so would predict that gas giant planets are relatively rare. If the disk instability mechanism can occur, however, extrasolar gas giant planets should be relatively abundant.