An Investigation Of Fragmentation In The Disk Instability Model For Giant Planet Formation

Up to this point,two theories for giant planet formation have been suggested:the core accretion model and the disk instability model.Here,our interest is in the disk instability model,a gravitationally unstable disk fragments into self-gravitating dense clumps.They then contract to form gas giant planets.The first step of giant planet formation in the disk instability model is fragmentation.One characteristic mass of planets is the initial clump mass.The critical issue for disk instability is when and where fragmentation might occur in protoplanetary disks.We investigate a few issues about fragmentation in the disk instability model for giant planet formation,specifically,initial clump mass（_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_p-relationship for clumps forming at different times during the disk evolution.We find that in general,for the same radius,_pchanges slightly with time,first decreasing and then increasing.In different disks,for the same radius,_pdoes not change significantly with,decreases with_MCC,and increases with_MCC,where,_MCC,and_MCCare angular velocity,mass,and temperature of a parent core.Fragmentation might occur most probably at20-200AU,at 200-450AU with less probability,and at>450AU with small probability._pmight be most probably between 3-35_J,between 35-80_Jwith less probability,and>80_Jwith small probability.The ranges of the starting time,ending time,and duration are1-3×10⁵yr,2-25×10⁵yrand0.1-25×10⁵yr,respectively.We derive an analytical formula for_pthat shows dependence of_pon disk properties and can be used to understand numerical calculations.We tentatively use our calculations to understand exoplanet observations.