The Initial mass function and stellar birthrate in the solar neighborhood

We examine the initial mass function (IMF) and time history of the stellar birthrate in the solar neighborhood assuming a time-independent IMF. The present-day mass function is constructed from the luminosity function, and a discussion of all the relevant observational quantities (luminosity function, mass-luminosity relation, scale heights, correction for non--main-sequence stars, and correction for main-sequence brightening) and the associated uncertainties is given. The observed total mass is not in serious disagreement with the dynamical mass (Oort limit) when the uncertainties are considered, and so there is no strong evidence for a local ''missing mass'' problem. The primary constraint on the birthrate history is the requirement that the derived IMF not exhibit an unphysical discontinuity at the mass where the main-sequence lifetime equals the age of the galactic disk. Considering the above uncertainties, the average past birthrate may be at most about 5 times larger or 3 times smaller than the present bithrate according to this constraint, and we favor a variation of less than a factor of 2. A discussion of 12 secondary constraints on the birthrate history is given, and it is concluded that these constraints are either consistent with the continuity constraint or else indeterminate. Ther is, inmore » particular, no evidence for a birthrate which depends on the square of the mean gas density. If the birthrate depends on some power of the mean gas density, the exponent must be small (< or approx. =0.5). Theoretical models for the birthrate history are also examined. Tables of various useful quantities such as cumulative number and mass distributions, present birthrates, and mass consumption rates are given.« less