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 stars, selected from the Sloan Digital Sky Survey and the Sloan Extension for Galactic Understanding and Exploration, with predictions from asymptotic giant-branch (AGB) mass-transfer models. We consider two initial mass functions (IMFs)-a Salpeter IMF, and a mass function with a characteristic mass of 10 solar mass. These comparisons indicate good agreement between the observed CEMP frequencies for stars with [Fe/H] > -1.5 and a Salpeter IMF, but not with an IMF having a higher characteristic mass. Thus, while the adopted AGB model works well for low-mass progenitor stars, it does not do so for high-mass progenitors. Our results imply 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 corrected 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. [abridged]