Cluster formation in protostellar outflow-driven turbulence

Most, perhaps all, stars go through a phase of vigorous outflow during formation. We examine, through three-dimensional MHD simulation, the effects of protostellar outflows on cluster formation. We find that the initial turbulence in the cluster-forming region is quickly replaced by motions generated by outflows. The protostellar outflow-driven turbulence (protostellar turbulence for short) can keep the region close to a virial equilibrium long after the initial turbulence has decayed away. We argue that there exist two types of turbulence in star-forming clouds: a primordial (or interstellar) turbulence and a protostellar turbulence, with the former transformed into the latter mostly in embedded clusters such as NGC 1333. Since the majority of stars are thought to form in clusters, an implication is that the stellar initial mass function is determined to a large extent by the stars themselves, through outflows that individually limit the mass accretion onto forming stars and collectively shape the environments ( density structure and velocity field) in which most cluster members form. We speculate that massive cluster-forming clumps supported by protostellar turbulence gradually evolve toward a highly centrally condensed pivotal state, culminating in rapid formation of massive stars in the densest part through accretion.