The Fragmentation in a Protoplanetary Disk and the Properties of the Resultant Self-Gravitating Clumps

We study the fragmentation properties in the protoplanetary disk and properties of the resultant self-gravitating clumps using our newly constructed disk model. Our disk model includes the mass inflall term from a molecular cloud core and the photoevaporation winds effect. We adopt the conventional fragmentation criterion to judge whether a protoplanetary disk can fragment. In this work, we follow our previous work to investigate the properties of the resultant self-gravitating clumps. In our calculation, the initial masses of the resultant self-gravitating clumps lie in the range of tens of M J to more than one hundred of M J , where M J is the Jupiter mass. These initial masses can seemingly account for the masses of extrasolar planets in magnitude. We also calculate the subsequent gas accretion of clumps in 1.27 × 10 4 yr after the formation of self-gravitating clumps. We find that the subsequent gas accretion of self-gravitating clumps is very efficient, and the clump masses grow to hundreds of M J and the physical radii R c of clumps increase to about 10 AU. Additionally, we also calculate the orbital migration of clumps. We find that most clumps have short migration timescale to be accreted onto the protostar, and only a small fraction of clumps have long migration timescale (>10 6 yr) to successfully become gas giant planets. These results are consistent with previous studies.