Observational evidence exists for the formation of gas giant planets on wide orbits around young stars by disk gravitational instability , but the roles of disk instability and core accretion for forming gas giants on shorter period orbits are less clear .
The controversy extends to population synthesis models of exoplanet demographics and to hydrodynamical models of the fragmentation process .
The latter refers largely to the handling of radiative transfer in three dimensional ( 3D ) hydrodynamical models , which controls heating and cooling processes in gravitationally unstable disks , and hence dense clump formation .
A suite of models using the \beta cooling approximation is presented here .
The initial disks have masses of 0.091 M _ { \odot } and extend from 4 to 20 AU around a 1 M _ { \odot } protostar .
The initial minimum Toomre Q _ { i } values range from 1.3 to 2.7 , while \beta ranges from 1 to 100 .
We show that the choice of Q _ { i } is equal in importance to the \beta value assumed : high Q _ { i } disks can be stable for small \beta , when the initial disk temperature is taken as a lower bound , while low Q _ { i } disks can fragment for high \beta .
These results imply that the evolution of disks toward low Q _ { i } must be taken into account in assessing disk fragmentation possibilities , at least in the inner disk , i.e. , inside about 20 AU .
The models suggest that if low Q _ { i } disks can form , there should be an as yet largely undetected population of gas giants orbiting G dwarfs between about 6 AU and 16 AU .