An initial mass function for individual stars in galactic disks. I. Constraining the shape of the initial mass function

Abstract

We derive a semi-empirical galactic initial mass function (IMF) from observational constraints. We assume that the IMF, φ(m), is a smooth function of the stellar mass m. The mass dependence of the proposed IMF is determined by five parameters: the low-mass slope γ, the high-mass slope - γ (taken to be -1.35), the characteristic mass mch (∼ the peak mass of the IMF), and the lower and upper limits on the mass, ml and mu (taken to be 0.004 and 120M⊙, respectively): φ(m)dlnm α m-Γ{1 - exp[-(m/mch) γ+Γ]}d lnm. The values of γ and mch are derived from two integral constraints: (1) the ratio of the number density of stars in the range m = 0.1-0.6 M⊙ to that in the range m = 0.6-0.8 M⊙ as inferred from the mass distribution of field stars in the local neighborhood and (2) the ratio of the number of stars in the range m = 0.08-1 M⊙ to the number of brown dwarfs in the range m = 0.03-0.08 M⊙ in young clusters. The IMF satisfying the above constraints is characterized by the parameters? = 0.51 and mch = 0.35 M⊙ (which corresponds to a peak mass of 0.27 M ⊙). This IMF agrees quite well with the Chabrier IMF for the entire mass range over which we have compared with data, but predicts significantly more stars with masses <0.03 M⊙; we also compare with other IMFs in current use and give a number of important parameters implied by the IMFs. © 2011. The American Astronomical Society. All rights reserved. Printed in the U.S.A.