We model the formation of high-mass stars , specifying the accretion rate in terms of the instantaneous and final mass of the star , the ambient pressure of the star-forming region and the form of polytropic pressure support of the pre-stellar gas core .
The high pressures typical of Galactic regions of massive star formation allow a 100 \ > { M _ { \odot } } star to form in \sim 10 ^ { 5 } \ > { yr } with a final accretion rate \sim 10 ^ { -3 } \ > { M _ { \odot } \ > yr ^ { -1 } } .
By modeling protostellar evolution we predict the properties of several nearby massive protostars .
We model cluster formation by applying this theory to many stars .
We use the observed intensity of outflows from protoclusters to estimate the star formation rate , finding that clusters take at least several free-fall times to form ; for a cluster similar to the Orion Nebula Cluster , we predict a formation timescale \sim 1 \times 10 ^ { 6 } \ > { yr } .