Distance and the initial mass function of young open clusters in the η Carina Nebula: Tr14 and Tr16

We present new UBVI _c CCD photometry of the young open clusters Trumpler 14 (Tr14) and Trumpler 16 (Tr16) in the η Carina Nebula. We also identify the optical counterpart of Chandra X-ray sources and Two Micron All Sky Survey point sources. The members of the clusters were selected from the proper-motion study, spectral types, reddening characteristics, and X-ray or near-IR excess emission. An abnormal reddening law R _{V, cl} = 4.4 0.2 was obtained for the stars in the η Carina Nebula using the 141 early-type stars with high proper-motion membership probability (P _μ ≧ 70%). We determined the distance to each cluster and conclude that Tr14 and Tr16 have practically the same distance modulus of V ₀ - M _V = 12.3 0.2mag (d = 2.9 0.3kpc). The slope of the initial mass function was determined to be Γ = -1.3 0.1 for Tr14, Γ = -1.3 0.1 for Tr16, and Γ = -1.4 0.1 for all members in the observed region for the stars with log m≧0.2. We also estimated the age of the clusters to be about 1-3Myr from the evolutionary stage of evolved stars and low-mass pre-main-sequence stars.