Context. The chemical evolution of fluorine is still a matter of debate in Galactic archaeology, especially at low metallicities, where it is particularly challenging to obtain the corresponding chemical abundances from observations. Aims. We present here the first detailed theoretical study of the chemical evolution of fluorine at low metallicities using a stochastic chemical evolution model for the Galactic halo, in light of the most recent data for fluorine, which include observations at lower metallicities down to [Fe/H]∼ −4 dex, more than a factor of 10 lower than previous detections. Methods. We employed a state-of-the-art stochastic chemical evolution model to follow the evolution in the Galactic halo, which has been shown to reproduce the main observables in this Galactic component and the abundance patterns of CNO and neutron-capture elements, and we implemented nucleosynthesis prescriptions for fluorine, focusing on the chemical evolution of this element. Results. By comparing recent observations with model predictions, we confirm the importance of rotating massive stars at low metallicities to explain both the [F/Fe] versus [Fe/H] and [F/O] versus [O/H] diagrams. In particular, we show that we can reach a high [F/Fe] of ∼2 dex at an [Fe/H] of approximately −4 dex, in agreement with recent observations at the lowest metallicities. Conclusions. With a stochastic chemical evolution model for the Galactic halo, we confirm the importance of rotating massive stars as fluorine producers, as suggested in previous studies that used chemical evolution models for the Galactic disc. We also expect an important production of F at high redshifts, in agreement with recent detections of super-solar N by JWST. Further data for fluorine at low metallicities, and also at high redshifts, are needed to put further constraints on the chemical evolution of fluorine and for comparison with our theoretical predictions.
