CEMP-no stars, a subset of carbon enhanced metal poor (CEMP) stars ($rm [C/Fe]geq0.7$ and $rm [Fe/H]lesssim-1$) have been discovered in ultra-faint dwarf (UFD) galaxies, with $M_{rm vir} sim 10^8$ Msun and $M_{ast}sim10^3-10^4$ Msun at $z=0$, as well as in the halo of the Milky Way (MW). These CEMP-no stars are local fossils that may reflect the properties of the first (Pop~III) and second (Pop~II) generation of stars. However, cosmological simulations have struggled to reproduce the observed level of carbon enhancement of the known CEMP-no stars. Here we present new cosmological hydrodynamic zoom-in simulations of isolated UFDs that achieve a gas mass resolution of $m_{rm gas}sim60$ Msun. We include enrichment from Pop~III faint supernovae (SNe), with $ E_{rm SN}=0.6times10^{51}$ erg, to understand the origin of CEMP-no stars. We confirm that Pop~III and Pop~II stars are mainly responsible for the formation of CEMP and C-normal stars respectively. New to this study, we find that a majority of CEMP-no stars in the observed UFDs and the MW halo can be explained by Pop~III SNe with normal explosion energy ($ E_{rm SN}=1.2times10^{51}$~erg) and Pop~II enrichment, but faint SNe might also be needed to produce CEMP-no stars with $rm [C/Fe]gtrsim2$, corresponding to the absolute carbon abundance of $rm A(C)gtrsim6.0$. Furthermore, we find that while we create CEMP-no stars with high carbon ratio $rm [C/Fe]approx3-4$, by adopting faint SNe, it is still challenging to reproduce CEMP-no stars with extreme level of carbon abundance of $rm A(C)approx 7.0-7.5$, observed both in the MW halo and UFDs.
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