Protostellar disk instabilities and the formation of substellar companions

Recent numerical simulations of self-gravitating protostellar disks have su ggested that gravitational instabilities can lead to the production of subs tellar companions. In these simulations, the disk is typically assumed to b e locally isothermal; i.e., the initial, axisymmetric temperature in the di sk remains everywhere unchanged. Such an idealized condition implies extrem ely efficient cooling for outwardly moving parcels of gas. While we have se en disk disruption in our own locally isothermal simulations of a small, ma ssive protostellar disk, no long-lived companions formed as a result of the instabilities. Instead, thermal and tidal effects and the complex interact ions of the disk material prevented permanent condensations from forming, d espite the vigorous growth of spiral instabilities. In order to compare our results more directly with those of other authors, we here present three-d imensional evolutions of an older, larger, but less massive protostellar di sk. We show that potentially long-lived condensations form only for the ext reme of local isothermality, and then only when severe restrictions are pla ced on the natural tendency of the protostellar disk to expand in response to gravitational instabilities. A more realistic adiabatic evolution leads to vertical and radial expansion of the disk but no clump formation. We con clude that isothermal disk calculations cannot demonstrate companion format ion by disk fragmentation but only suggest it at best. It will be necessary in future numerical work on this problem to treat the disk thermodynamics more realistically.