A THEORY OF THE INITIAL MASS FUNCTION FOR STAR-FORMATION IN MOLECULARCLOUDS

We present a class of models for the initial mass function (IMF) for s tars forming within molecular clouds. This class of models uses the id ea that stars determine their own masses through the action of powerfu l stellar outflows. This concept allows us to calculate a semiempirica l mass formula (SEMF), which provides the transformation between initi al conditions in molecular clouds and the final masses of forming star s. For a particular SEMF, a given distribution of initial conditions p redicts a corresponding IMF. In this paper, we consider several differ ent descriptions for the distribution of initial conditions in star-fo rming molecular clouds. First, we consider the limiting case in which only one physical variable-the effective sound speed-determines the in itial conditions. In this limit, we use observed scaling laws to deter mine the distribution of sound speed and the SEMF to convert this dist ribution into an IMF, Next, we consider the opposite limit in which ma ny different independent physical variables play a role in determining stellar masses. In this limit, the central limit theorem shows that t he IMF approaches a log-normal form. Realistic star-forming regions co ntain an intermediate number of relevant variables; we thus consider i ntermediate cases between the two limits. Our results show that this p icture of star formation and the IMF naturally produces stellar mass d istributions that are roughly consistent with observations. This paper thus provides a calculational framework to construct theoretical mode ls of the IMF.