2011ApJ...726...27P

We derive a semi-empirical galactic initial mass function (IMF) from observational constraints. We assume that the IMF, ψ(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 m_ch(∼ the peak mass of the IMF), and the lower and upper limits on the mass, m_ℓ and m_u(taken to be 0.004 and 120 M_☉, respectively): ψ(m)dln m ∝ m ^–Γ{1 - exp [ - (m/m_ch)^γ+Γ]}dln m. The values of γ and m_ch 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 γ = 0.51 and m_ch= 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.