Fluorine nucleosynthesis and s-processing in AGB stars driven by magnetic-buoyancy mixing

Asymptotic giant branch (AGB) stars are thought to be among the most important sources of fluorine in our Galaxy. While observations and theory agree at close-to-solar metallicity, stellar models overestimate fluorine production in comparison to heavy elements at lower metallicities. We present predictions for 19F abundance for a set of AGB models with various masses and metallicities, in which magnetic buoyancy induces the formation of the 13C neutron source (the so-called 13C pocket). In our new models, fluorine is mostly created as a consequence of secondary 14N nucleosynthesis during convective thermal pulses, with a minor contribution from the 14N existing in the 13C pocket zone. As a result, AGB stellar models with magnetic-buoyancyinduced mixing show low 19F surface abundances which agree with fluorine spectroscopic observations at both low and near-solar metallicity.


Introduction
The cosmic genesis of fluorine is one of the most intriguing problems in nuclear astrophysics. So far, spectroscopic observations of photospheric F enhancements in intrinsic AGB carbon stars [1,2] and metal-poor extrinsic stars [3,4] offer the sole direct observation of fluorine production. Its envelope abundance indicates a correlation with those of carbon and s-process elements and therefore with the 13 C content produced in the interiors of AGB stars [5]. Recently, it was proposed that a process resulting in the creation of an extended 13 C pocket and, simultaneously, a tiny quantity of 14 N, may solve the issue of 19 F overproduction with respect to s-elements in low-mass metal-poor objects [4].
The formation of a 13 C pocket in AGB stars requires that some partial mixing of protons from the envelope occurs during a third dredge-up (TDU) phenomenon. In latest FRUITY models [6], the buoyant rise of magnetic flux tubes in the region below the envelope is considered to cause a stable mass upflow which induces a downflow of protons for maintaining mass conservation. As a result of such magnetic mixing, deep profiles of low proton abundances are predicted to be formed. Because protons are nearly completely used for the synthesis of 13 C, the low proton concentration significantly reduces the local 14 N formation, thereby limiting 19 F production as well. Here we examine fluorine nucleosynthesis in low-mass AGB stars by computing a new series of stellar models accounting for the formation of a magneticbuoyancy-induced 13 C pocket.

Comparison with observations
In the following, we compare data for intrinsic AGB carbon stars [2,4] and extrinsic CH/Ba stars [4,5] with new FRUITY magnetic models of 1.5 M and 2 M . In left panel of Fig. 1 we report the [F/Fe] ratios of the selected sample as a function of [Fe/H]. Within the observational errors, there is a good agreement, confirming the expected F-enhancement trend with the metallicity. The right panel of Fig. 1 shows the comparison between theoretical predictions of FRUITY magnetic models and spectroscopic observations for [F/s] ratios vs. the average s-element enhancement. In this way, the F enhancement for the extrinsic stars is not affected by uncertainties related to the dilution factor and provides a robust tool for comparison. Theoretical expectations can replicate the quasi-linear decreasing trend of [F/s] with the surface s-process enrichment.
In Fig. 2 we perform a similar comparison at low metallicities. We compared model predictions individually since there is no homogeneous sample of stars with both Ba and La. Magnetic models well reproduce the spread observed at different metallicities for both [F/Ba] and [F/La] ratios as a function of total s-process enhancement. Overall, FRUITY magnetic models show a reduction in fluorine production that is consistent with spectroscopic observations of low-metallicity stars. The extended profile and low proton abundance that characterize FRUITY magnetic models [6] have the dual impact of generating large 13 C pockets and a small amount of primary 14 N. In this scenario, the few available protons make first 13 C through the 12 C(p, γ) 13 C reaction, preventing further proton captures to form 14 N, thus inhibiting the nuclear chain 14 N(n, p) 14 C(α, γ) 18 O(p, α) 15 N(α, γ) 19 F. As a consequence, any fluorine appearing in AGB envelopes in these models is of secondary origin, caused by 14 N concentrations left over after H-shell burning. As an outcome, FRUITY magnetic models have low fluorine enhancements and large s-enhancements, which are in close agreement with observations in very metal-poor AGB stars [7].

Conclusions
The production of fluorine in low-mass AGB stars has been examined in light of new FRUITY stellar models, in which the 13 C neutron source is attributed to magnetic-buoyancy-induced phenomena. On the one hand, the new FRUITY magnetic models exhibit a low net 19 F production. This is due to the low abundance of 14 N in the 13 C pocket, which results in negligible fluorine production during 13 C radiative burning. The 19 F envelope abundance is therefore ascribed only to the amount of the secondary 13 C in the H-shell ashes, which depends on the CNO abundances in the star. On the other hand, mixing induced by magnetic buoyancy leads to extended 13 C pockets so resulting in large surface s-process enrichments. As a whole, new FRUITY magnetic models simultaneously account for both the observed fluorine and the average s-element enhancements in intrinsic AGB carbon stars and extrinsic CH/Ba stars.