The influence of the turbulent perturbation scale on prestellar core fragmentation and disk formation
The collapse of weakly turbulent prestellar cores is a critical stage in the process of star formation. Being highly non-linear and stochastic, the outcome of collapse can only be explored theoretically by performing large ensembles of numerical simulations. Standard practice is to quantify the initial turbulent velocity field in a core in terms of the amount of turbulent energy (or some equivalent) and the exponent in the power spectrum (n \equiv -d log Pk /d log k). In this paper, we present a numerical study of the influence of the details of the turbulent velocity field on the collapse of an isolated, weakly turbulent, low-mass prestellar core. We show that, as long as n > 3 (as is usually assumed), a more critical parameter than n is the maximum wavelength in the turbulent velocity field, λ_MAX. This is because λ_MAX carries most of the turbulent energy, and thereby influences both the amount and the spatial coherence of the angular momentum in the core. We show that the formation of dense filaments during collapse depends critically on λ_MAX, and we explain this finding using a force balance analysis. We also show that the core only has a high probability of fragmenting if λ_MAX > 0.5 R_CORE (where R_CORE is the core radius); that the dominant mode of fragmentation involves the formation and break-up of filaments; and that, although small protostellar disks (with radius R_DISK <= 20 AU) form routinely, more extended disks are rare. In turbulent, low-mass cores of the type we simulate here, the formation of large, fragmenting protostellar disks is suppressed by early fragmentation in the filaments.