= Fragment survival in a self-gravitating planetary disk
A fragment formed by <gravitational instability of an astrophysical disk> must remain bound after it forms. Its own <gravity> competes with the surrounding tidal field, while heating, cooling and <accretion> change its size and internal support.
For a low-mass clump on a <circular orbit> around a dominant <star>, its <Hill radius> estimates the region over which its attraction can resist the local stellar tide. Cooling and contraction can make a fragment more compact, whereas inward migration can shrink that tidal region. A calculation demonstrating initial fragmentation therefore does not alone establish a long-lived giant <planet>: survival requires the subsequent thermal and orbital evolution as well.
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