Rapidly Rotating Massive Pop III stars: A Solution for High Carbon Enrichment in the Early Galaxy

Very metal-poor (VMP) stars ([Fe/H]$< -2$) of mass $lesssim 0.8, M_odot$ are thought to be the fossil records of the nucleosynthesis of the earliest generation of massive stars that were present in the early Galaxy. A large fraction of VMP stars are found to be enhanced in C relative to Fe ([C/Fe]$>0.7$) and are referred to as carbon-enhanced metal-poor (CEMP) stars. A subclass of CEMP stars with a low enrichment of heavy elements are called CEMP-no stars and are thought to have formed from the interstellar medium (ISM) polluted by the supernova ejecta of the very first generation (Pop III) massive stars. Although theoretical models of supernova explosions can explain the relative abundance pattern reasonably well, the very high enrichment of C ([C/H]$gtrsim -2.5 $) observed in many of the CEMP-no stars is difficult to explain when reasonable values of dilution of the supernova ejecta with the ISM are adopted. We explore rapidly rotating models of Pop III stars that undergo efficient mixing and reach the so-called quasi-chemically homogeneous (QCH) state. We find that rapidly rotating models that reach the QCH state can eject substantial amounts of C in the wind. The resulting dilution of the wind ejecta in the ISM can naturally explain the high C enrichment observed in CEMP-no stars. We find that rapidly rotating massive Pop III stars are a promising site for explaining the origin of CEMP-no stars. This also suggests that a significant number of Pop III stars were rapid rotators.