We investigate structure of self-gravitating disks , their fragmentation and evolution of the fragments ( the clumps ) using both analytic approach and three-dimensional radiation hydrodynamics simulations starting from molecular cores .
The simulations show that non-local radiative transfer determines disk temperature .
We find the disk structure is well described by an analytical model of quasi-steady self-gravitating disk with radial radiative transfer .
Because the radiative process is not local and radiation from the interstellar medium can not be ignored , the local radiative cooling would not be balanced with the viscous heating in a massive disk around a low mass star .
In our simulations , there are cases in which the disk does not fragment even though it satisfies the fragmentation criterion based on disk cooling time ( Q \sim 1 and \Omega t _ { cool } \sim 1 ) .
This indicates that at least the criterion is not sufficient condition for fragmentation .
We determine the parameter range for the host cloud core in which disk fragmentation occurs .
In addition , we show that the temperature evolution of the center of the clump is close to that of typical first cores and the minimum initial mass of clumps to be about a few Jupiter mass .