Observations indicate that massive stars in the Galaxy form in regions of very high surface density , \Sigma \sim 1 g cm ^ { -2 } .
Clusters containing massive stars and globular clusters have a column density comparable to this .
The total pressure in clouds of such a column density is P / k \sim 10 ^ { 8 } -10 ^ { 9 } 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 high densities in regions of massive star formation lead to typical time scales for the formation of a massive star of about 10 ^ { 5 } 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 \rho \propto r ^ { -1.5 } , the protostellar accretion rate grows with time as \dot { m } _ { * } \propto 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 20 M _ { \odot } .
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 ( H _ { 2 } O ) .
In the Appendixes , we discuss the pressure in molecular clouds and we argue that “ logatropic ” models for molecular clouds are incompatible with observation .