Probing the first generations of massive stars through fluorine in CEMP-no stars

Abstract

We investigate whether the first discovered fluorine-rich CEMP-no star, CS 29498$-$043, can be explained by a very metal-poor rotating massive star. We consider single rotating stellar models of 20 $M_{\odot}$ at a metallicity of $Z = 10^{-5}$, exploring initial rotation rates from $\upsilon_{\rm ini}/\upsilon_{\rm crit} = 0$ to $0.7$ in increments of $0.1$ ($0<\upsilon_{\rm ini}<644$ km s$^{-1}$). Rotational mixing enhances the production of light elements in the H--He layers, including fluorine. The ejected material can be nitrogen-rich without being fluorine-rich, whereas fluorine-rich ejecta are always predicted to be nitrogen-rich. The model providing the best fit to the abundances of CS 29498$-$043 is the $\upsilon_{\rm ini}/\upsilon_{\rm crit} = 0.6$ model ($\upsilon_{\rm ini} = 547$ km s$^{-1}$), which reproduces C, N, O, Na, Mg, and Al within the observational uncertainties. However, the predicted [F/Fe] $=2.8$ exceeds the observed value of [F/Fe] $=2.0 \pm 0.4$. By simultaneously varying the $^{15}$N($\alpha,\gamma$)$^{19}$F and $^{19}$F($\alpha,p$)$^{22}$Ne reaction rates within their acceptable ranges, the [F/Fe] ratio in the $\upsilon_{\rm ini}/\upsilon_{\rm crit} = 0.6$ model can be reduced to 2.2, providing a plausible solution to the abundance pattern of CS 29498$-$043. Our results support the hypothesis that fluorine-rich CEMP-no stars may originate from material enriched by a single, metal-poor, rotating massive star. A potential observational test of this scenario may be to check whether the nitrogen and fluorine abundances observed at the surface of CEMP-no stars are correlated.