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Doppler surveys have shown that more massive stars have significantly higherfrequencies of giant planets inside $\sim$ 3 AU than lower mass stars,consistent with giant planet formation by core accretion. Direct imagingsearches have begun to discover significant numbers of giant planet candidatesaround stars with masses of $\sim$ 1 $M_\odot$ to $\sim$ 2 $M_\odot$ at orbitaldistances of $\sim$ 20 AU to $\sim$ 120 AU. Given the inability of coreaccretion to form giant planets at such large distances, gravitationalinstabilities of the gas disk leading to clump formation have been suggested asthe more likely formation mechanism. Here we present five new models of theevolution of disks with inner radii of 20 AU and outer radii of 60 AU, forcentral protostars with masses of 0.1, 0.5, 1.0, 1.5, and 2.0 $M_\odot$, inorder to assess the likelihood of planet formation on wide orbits around starswith 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 theinner disks to $\sim 1.6$ in the outer disks. These five models show that diskinstability 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 orbitswith 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 theprotostar (and protoplanetary disk) are increased. In particular, diskinstability appears to be a likely formation mechanism for the HR 8799 gasgiant planetary system.

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