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 .