The Formation of Massive Stars from Turbulent Cores

Observations indicate that massive stars in the Galaxy form in regions of very high surface density, Σ ∼ 1 g cm−2. Clusters containing massive stars and globular clusters have a column density comparable to this. The gas pressure in clouds of such a column density is P/k ∼ 108 − 109 K cm−3, far greater than that in the diffuse interstellar medium or the average in giant molecular clouds. Observations show that massive star-forming regions are supersonically turbulent, and we show that the molecular cores out of which individual massive stars form are as well. The protostellar accretion rate in such a core is approximately equal to the instantaneous mass of the star divided by the free-fall time of the gas that is accreting onto the star (Stahler, Shu, & Taam 1980). The star-formation time in this Turbulent Core model for massive star formation is several times the mean free-fall time of the core out of which the star forms, but is about equal to that of the region in which the core is embedded. The typical time for a massive star to form is about 105 yr. The corresponding accretion rate is high enough to overcome the radiation pressure due to the luminosity of the star. For the typical case we consider, in which the cores out of which the stars form have a density structure ρ ∝ r−1.5, the protostellar accretion rate grows with time as ṁ∗ ∝ t. We present a new calculation of the evolution of the radius of a protostar and determine the protostellar accretion luminosity. At the high accretion rates that are typical in regions of massive star formation, protostars join the main sequence at about 20M⊙. We apply these results to predict the properties of protostars thought to be powering several observed hot molecular cores, including the Orion hot core and W3(H2O). In the Appendixes, we discuss the pressure in molecular clouds and we demonstrate that “logatropic” models for molecular clouds are incompatible with observation. Subject headings: hydrodynamics — ISM: clouds — stars: formation