An Effective Initial Mass Function for Galactic Disks

We derive a semi-empirical effective galactic initial mass function (IMF), which represents the IMF averaged over the age of the galactic disk, from observational constraints. We assume that the star formation rate in a galaxy can be expressed as the product of the IMF,psi(m), which is a smooth function of mass m (in units of solar mass), and a time and space dependent rate zeta(sub *1). The mass dependence of the proposed IMF is determined by four parameters: the low-mass slope gamma, the high-mass slope -Gamma, the characteristic mass m(sub ch) at which the IMF turns over, and the upper limit on the mass, m(sub u).