The role of faint population III supernovae in forming CEMP stars in ultra-faint dwarf galaxies

Carbon enhanced metal poor (CEMP)-no stars, a subset of CEMP stars ($\rm [C/Fe]\ge 0.7$ and $\rm [Fe/H]\lesssim -1$) have been discovered in ultra-faint dwarf (UFD) galaxies, with $M_{\rm vir}\approx 10^8{\, \mathrm{ M}_\odot }$ and $M_{\ast }\approx 10^3-10^4{\, \mathrm{ M}_\odot }$ 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 $m_{\rm gas}\approx 60{\, \mathrm{ M}_\odot }$. We include enrichment from Pop III faint supernovae (SNe), with ESN = 0.6 × 1051 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 (ESN = 1.2 × 1051 erg) and Pop II enrichment, but faint SNe might also be needed to produce CEMP-no stars with $\rm [C/Fe]\gtrsim 2$, corresponding to the absolute carbon abundance of $\rm A(C)\gtrsim 6.0$. Furthermore, we find that while we create CEMP-no stars with high carbon ratio $\rm [C/Fe]\approx 3-4$, 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.