Carbon-enhanced metal-poor stars in SDSS/Segue. II. Comparison of CEMP-star frequencies with binary population-synthesis models

We present a comparison of the frequencies of carbon-enhanced metal-poor (CEMP) giant and main-sequence turnoff (MSTO) stars with predictions from binary population-synthesis models involving asymptotic giant-branch (AGB) mass transfer. The giant and MSTO stars are selected from the Sloan Digital Sky Survey and the Sloan Extension for Galactic Understanding and Exploration. We consider two initial mass functions (IMFs)—a Salpeter IMF, and a mass function with a characteristic mass of 10 M _☉. For giant stars, the comparison indicates a good agreement between the observed CEMP frequencies and the AGB binary model using a Salpeter IMF for [Fe/H] > – 1.5, and a characteristic mass of 10 M _☉ for [Fe/H] < – 2.5. This result suggests that the IMF shifted from high- to low-mass dominated in the early history of the Milky Way, which appears to have occurred at a 'chemical time' between [Fe/H] =–2.5 and [Fe/H] =–1.5. The CEMP frequency for the turnoff stars with [Fe/H] < – 3.0 is much higher than the AGB model prediction from the high-mass IMF, supporting the previous assertion that one or more additional mechanisms, not associated with AGB stars, are required for the production of carbon-rich material below [Fe/H] =–3.0. We also discuss possible effects of first dredge-up and extra mixing in red giants and internal mixing in turnoff stars on the derived CEMP frequencies.