Protostellar Disks: Formation, Fragmentation, and the Brown Dwarf Desert

We argue that gravitational instability of typical protostellar disks is not a viable mechanism for the fragmentation into multiple systems (binary stars, brown dwarf companions, or gas giant planets) except at periods above roughly 20,000 yr. Our conclusion is based on a comparison between prior numerical work on disk self-gravity by Gammie and our own analytical models for the dynamical and thermal state of protostellar disks. For this purpose we first develop a simple theory for the initial conditions of low-mass star formation, accounting for the effect of turbulence on the characteristic mass, accretion rate, and angular momentum of collapsing cores. We also present formulae for the probability distribution of these quantities for the case of homogeneous Gaussian turbulence. However, our conclusions are not sensitive to this parameterization. Second, we examine the criterion for fragmentation to occur during star formation, concentrating on the self-gravitational instabilities of protostellar accretion disks in their main accretion phase. Self-gravitational instabilities are strongly dependent on the thermal state of the disk, and we find that the combination of viscous heating and stellar irradiation quenches fragmentation due to Toomre's local instability. Simulations by Matsumoto & Hanawa, which do not include detailed thermal evolution, predict fragmentation in an early phase of collapse. But, fragments born in this phase are on tight orbits and are likely to merge later due to disk accretion. Global instability of the disk may be required to process mass supply, but this is also unlikely to produce fragments. We conclude that numerical simulations that predict brown dwarf formation by disk fragmentation but do not account for irradiation are unrealistic. Our findings help to explain the dearth of substellar companions to stellar-type stars: the brown dwarf desert.