Prediction of the protostellar mass spectrum in the Orion near-infrared cluster

A simple analytical accretion model is developed for the protostellar mass spectrum in the infrared cluster in Orion (OMC1/KL region) in which protostellar cores compete for the accretion of the gas of their parent cloud. Unlike coagulation models, this model is a linear model which includes the conservation of the number of accretion nuclei, with no collisional mergers occurring. Gas exhaustion effects are not included, since less than 50 percent of the cloud gas will be accreted before the most massive star powers the formation of a hot H II region or the formation of an energetic stellar wind, thereby freezing the mass spectrum. A mass spectrum is predicted to be of the form dN/d log M approximately equal to 1/M for M greater than or approximately equal to 1 solar mass, independent of the form of the mass spectrum at the beginning of the accretion process. In particular, a runaway growth of the most massive star, with a big gap in mass to the next massive star, is predicted.