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Formation of Giant Planets by Disk Instability on Wide Orbits Around Protostars with Varied Masses

Doppler surveys have shown that more massive stars have significantly higher frequencies of giant planets inside $\sim$ 3 AU than lower mass stars, consistent with giant planet formation by core accretion. Direct imaging searches have begun to discover significant numbers of giant planet candidates around stars with masses of $\sim$ 1 $M_\odot$ to $\sim$ 2 $M_\odot$ at orbital distances of $\sim$ 20 AU to $\sim$ 120 AU. Given the inability of core accretion to form giant planets at such large distances, gravitational instabilities of the gas disk leading to clump formation have been suggested as the more likely formation mechanism. Here we present five new models of the evolution of disks with inner radii of 20 AU and outer radii of 60 AU, for central protostars with masses of 0.1, 0.5, 1.0, 1.5, and 2.0 $M_\odot$, in order to assess the likelihood of planet formation on wide orbits around stars with varied masses. The disk masses range from 0.028 $M_\odot$ to 0.21 $M_\odot$, with initial Toomre $Q$ stability values ranging from 1.1 in the inner disks to $\sim 1.6$ in the outer disks. These five models show that disk instability is capable of forming clumps on time scales of $\sim 10^3$ yr that, if they survive for longer times, could form giant planets initially on orbits with semimajor axes of $\sim$ 30 AU to $\sim$ 70 AU and eccenticities of $\sim$ 0 to $\sim$ 0.35, with initial masses of $\sim 1 M_{Jup}$ to $\sim 5 M_{Jup}$, around solar-type stars, with more protoplanets forming as the mass of the protostar (and protoplanetary disk) are increased. In particular, disk instability appears to be a likely formation mechanism for the HR 8799 gas giant planetary system.