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Disk fragmentation resulting from the gravitational instability has beenproposed as an efficient mechanism for forming giant planets. We use the planetFomalhaut b, the triple-planetary system HR 8799, and the potential protoplanetassociated with HL Tau to test the viability of this mechanism. We choose theabove systems since they harbor planets with masses and orbital characteristicsfavored by the fragmentation mechanism. We do not claim that these planets musthave formed as the result of fragmentation, rather the reverse: if planets canform from disk fragmentation, then these systems are consistent with what weshould expect to see. We use the orbital characteristics of these recentlydiscovered planets, along with a new technique to more accurately determine thedisk cooling times, to place both lower and upper limits on the disk surfacedensity--and thus mass--required to form these objects by disk fragmentation.Our cooling times are over an order of magnitude shorter than those of Rafikov(2005),which makes disk fragmentation more feasible for these objects. We findthat the required mass interior to the planet's orbital radius is ~0.1 Msun forFomalhaut b, the protoplanet orbiting HL Tau, and the outermost planet of HR8799. The two inner planets of HR 8799 probably could not have formed in situby disk fragmentation.

Did Fomalhaut, HR 8799, and HL Tauri Form Planets via the Gravitational Instability? Placing Limits on the Required Disk Masses