Abstract We investigate a few issues regarding fragmentation in the disk instability model for giant planet formation—specifically, initial clump mass (M p), fragmentation region, and fragmentation starting time, ending time, and duration. By running calculations over a wide parameter space and using an evolutionary model of protoplanetary disks, we study dependence on properties of the parent cloud core of the protostar+disk system. We investigate evolution of M p–R relationship for clumps forming at different times during the disk evolution. We find that, in general, for the same radius, M p changes slightly with time, first decreasing and then increasing. In different disks, for the same radius, M p does not change significantly with ω, decreases with M MCC, and increases with T MCC, where ω, M MCC, and T MCC are angular velocity, mass, and temperature of a parent core. Fragmentation might occur most probably at 20–200 au, at 200–450 au with less probability, and at >450 au with small probability. M p might be most probably between 3–35M J, between 35–80M J with less probability, and >80M J with small probability. The ranges of the fragmentation starting time, ending time, and duration are (1–3) × 105 yr, ( 2 – 25 ) × 10 5 yr , and ( 0.1 – 25 ) × 10 5 yr , respectively. We derive an analytical formula that shows dependence of M p on disk properties and can be used to understand numerical calculations. We tentatively use our calculations to understand exoplanet observations.
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