An examination of the M = 1 instability in a low-mass protoplanetary disk

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Gravitational Fields, Protoplanets, Solar Interior, Solar Rotation, Stellar Models, Boundary Conditions, Corotation, Energy Transfer, Entropy, Momentum Transfer

Scientific paper

We show that different physical mechanisms drive the m = 1 gravitational instability for high and low disk masses. For high disk masses, sling amplification is dominant. For low disk masses, swing amplification and the indirect potential are both important. In any case, the m = 1 mode is sensitive to the outer boundary condition. The dependence of the swing amplification on Toomre's Q parameter is somewhat reduced by the fact that the distance between the corotation point and the outer disk edge decreases as the disk mass decreases. The maximum nebula mass derived by Shu et al. (1990), which was obtained analytically by considering only the sling mechanism, decreases when other effects are included. We suggest that this mass depends on onset of local, rather than global, gravitational stability.

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