Fluorine in the Solar Neighborhood: Chemical Evolution Models”

Fluorine in the Solar Neighborhood: Chemical Evolution Models”

E. Spitoni email to: spitoni@oats.inaf.it1 Dipartimento di Fisica, Sezione di Astronomia, Università di Trieste, via G.B. Tiepolo 11, I-34131, Trieste, Italy 12I.N.A.F. - Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, I-34131, Trieste, Italy 2    F. Matteucci 1 Dipartimento di Fisica, Sezione di Astronomia, Università di Trieste, via G.B. Tiepolo 11, I-34131, Trieste, Italy 12I.N.A.F. - Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, I-34131, Trieste, Italy 23I.N.F.N. - Sezione di Trieste, Via Valerio 2, I-34100 Trieste, Italy 3    H. Jönsson 4Lund Observatory, Department of Astronomy and Theoretical Physics, Lund University, Box 43, SE-22100 Lund, Sweden 4    N. Ryde 4Lund Observatory, Department of Astronomy and Theoretical Physics, Lund University, Box 43, SE-22100 Lund, Sweden 4    D. Romano 5I.N.A.F. - Osservatorio Astronomico di Bologna, Via Gobetti 93/3, I-40129 Bologna5
Received xxxx / Accepted xxxx
Key Words.:
Galaxy: abundances - Galaxy: evolution - ISM: general
Abstract

Context:In the light of the new observational data related to fluorine abundances in the solar neighborhood stars, we present here chemical evolution models testing different fluorine nucleosynthesis prescriptions with the aim to best fit those new data.

Aims:We consider chemical evolution models in the solar neighborhood testing different nucleosynthesis prescriptions for fluorine production with the aim of reproducing the observed abundance ratios [F/O] vs. [O/H] and [F/Fe] vs. [Fe/H]. We study in detail the effects of different stellar yields on the fluorine production.

Methods:The adopted chemical evolution models are: i) the classical “two-infall” model which follows the chemical evolution of halo-thick disk and thin disk phases, ii) and the “ one-infall” model designed only for the thin disk evolution. We tested the effects on the predicted fluorine abundance ratios of different nucleosynthesis yield sources: AGB stars, Wolf-Rayet stars, Type II and Type Ia supernovae, and novae.

Results:The fluorine production is dominated by AGB stars but the Wolf-Rayet stars are required to reproduce the trend of the observed data in the solar neighborhood by Jönsson et al. (2017a) with our chemical evolution models. In particular, the best model both for the “two-infall” and “one-infall” cases requires an increase by a factor of two of the Wolf-Rayet yields given by Meynet & Arnould (2000). We also show that the novae, even if their yields are still uncertain, could help to better reproduce the secondary behavior of F in the [F/O] vs. [O/H] relation.

Conclusions:The inclusion of the fluorine production by Wolf-Rayet stars seems to be essential to reproduce the observed ratio [F/O] vs [O/H] in the solar neighborhood by Jönsson et al. (2017a). Moreover, the inclusion of novae helps substantially to reproduce the observed fluorine secondary behavior.

1 Introduction

The aim of this paper is to study the evolution of fluorine (F) abundance in the solar neighborhood, by means of a detailed chemical evolution model. The origin of fluorine is still uncertain and widely debated in literature. The production of the only stable isotope, F, is strictly linked to the physical conditions in stars. In particular, we can identify several stellar sites for fluorine production:

  1. [i)]

  2. Asymptotic giant branch (AGB) stars. For solar metallicity the main process of F production is related to nuclear reaction on N including , neutron, and proton captures. On the other hand, at lower metallicity the F production depends on C (Cristallo et al. 2014).

  3. Wolf-Rayet (W-R) stars can be important producers of fluorine which is injected into ISM by their strong stellar winds. Also here, the chain of reactions leading to F production starts from N, which is normally produced during the CNO cycle as a secondary element. However, in massive stars N can be produced as a primary element if they suffer strong rotation, which produces effects similar to those to the dredge-up mechanism in AGB stars. In this case, however, the primary N production is limited only to very metal poor stars (Z) as shown by Meynet & Maeder (2002). The difference secondary/primary N is important, since in the case of secondary N the F behavior would also follow that of a secondary element, namely depending on the original stellar metallicity.

  4. Type II supernovae (SNe II). These SNe can produce F via the neutrino () process. In fact, although neutrinos are characterized by small cross sections, the great amount of them released during the core-collapse turns Ne in the outer envelopes of the collapsing star into F (Woosley & Haxton 1988).

  5. Novae can also in principle be F producers (José & Hernanz 1998), although the yields are still uncertain. In classical novae the reaction chain OFNe is the mechanism involved in the synthesis of F through the production of the short-lived, -unstable nucleus Ne, which is partially transferred by convection toward the outer cooler layers of the envelope, where it decays into F.

Recently, new observational data (related to 49 K giants with temperatures low enough to show an HF line at 2.3 m) by Jönsson et al. (2017a) showed that the -process is not the main contributor of fluorine production in the solar vicinity, at variance with theoretical predictions. Jönsson et al. (2017b) estimated the kinematic probability that stars belong to the thin disk, thick disk, and/or halo. They showed that the majority of the observed stars are part of the Galactic thin disk

The observed [F/Fe] vs. [Fe/H] and [F/O] vs. [O/H] ratio both follow and increasing trend, in contrast to what would expect if the -process was the dominant fluorine nucleosynthesis source in the solar vicinity, constraining its possible contribution to the cosmic fluorine budget. This tension between data and the -process in the solar neighborhood, is confirmed by the observed secondary relation between fluorine and oxygen in Jönsson et al. (2017a). This observed secondary behavior can constrain the stellar models of AGB and W-R stars. Hence, AGB stars, W-R stars, SNe Ia, novae, and explosive nucleosynthesis in SNe II without process, are the possible fluorine production sites to be tested in detail chemical evolution models for the solar neighborhood.

In this paper, we present chemical evolution models designed to reproduce the data by Jönsson et al. (2017a) in the solar neighborhood testing different nucleosynthesis prescriptions for the fluorine yields. We will present results related both to an update version of the classical “two-infall” model introduced by Chiappini et al. (1997) in which we follow the evolution of the halo-thick disk and thin disk phases, and to a detailed chemical evolution model which follows only the thin disk evolution. The F production sources considered in this paper are: AGB stars (Karakas 2010), massive stars (Kobayashi et al. 2006) and W-R stars (Meynet & Arnould 2000). We will also discuss the case of novae as possible sources for F production adopting the nucleosynthesis yields by José & Hernanz (1998).

Previous papers (Meynet & Arnould 2000, Renda et al. 2004, Kobayashi et al. 2011a) have computed fluorine evolution in the Galaxy. For the first time, Meynet & Arnould (2000) showed that W-R stars could be significant contributors to the solar system abundance of fluorine using a simple model for the chemical evolution. In Renda et al. (2004) the impact of fluorine nucleosynthesis, in both W-R and AGB stars, were considered in chemical evolution model and concluded that the contribution of W-R stars is necessary to reproduce the F abundance in solar vicinity. Kobayashi et al. (2011a) found that the main effect of -process of core-collapse supernovae on the evolution of fluorine in the solar neighborhood, is the presence of a plateau at high [F/O] values for [O/H] -1.2 in the [F/O] vs [O/H] relation. As underlined above, this plateau is in contrast with the most recent observational data by Jönsson et al. (2017a). Novae have never been included so far in chemical models predicting fluorine.

The paper is organized as follows: in Section 2 we describe the chemical evolution models for the solar vicinity adopted in this paper, in Section 3 the nucleosynthesis prescriptions are described. In Section 4 our results concerning the fluorine abundances in the solar neighborhood predicted by our chemical evolution models are reported. In Section 5, we discuss the effects of the novae nucleosynthesis on fluorine production. In Section 6 we draw our main conclusions.





Models AGB stars SNe Ia SNe II Wolf Rayet stars
Karakas (2010) Iwamoto et al. (1999) Kobayashi et al. (2006) Meynet & Arnould (2000)



F1
yes yes yes no


F2
no yes yes no





F3
yes 1.5 yes yes no


F4 yes 2 yes yes no


F5 yes 3 yes yes no

F6 no no no yes








F7
yes yes yes yes



F8 yes yes yes yes 2


F9
yes 2 yes yes yes


















Table 1: The list of the models described in this work in which we considered different contributions for the fluorine production. In this Table we report only the different nucleosynthesis yields adopted for the fluorine.

2 The chemical evolution models for the solar neighborhood

In this Section, we describe the main characteristics of the adopted chemical evolution models for the solar neighborhood in this work:

  1. The classical “two-infall” model of Chiappini et al. (1997, 2001). It is assumed that the Galaxy formed by two independent infalls of primordial gas. In the first episode, occurred on short time-scales, the halo-thick disk components have been formed, while in the second one the thin disk was created on longer time-scales.

  2. Following Matteucci & François (1989) approach, we use the “one-infall” chemical evolution model only for the thin disk evolution in the solar neighborhood.

2.1 The “two-infall” model

As stated in Section 2, Jönsson et al. (2017a) data sample is related to thick-disk, thin-disk and halo stars. For this reason, first we want to reproduce those data adopting the classical “two-infall” model capable to trace the chemical evolution of halo-thick disk and thin disk phases.

The Galaxy is assumed to have formed by means of two main infall episodes. The accretion law for a certain element at the time in the solar vicinity is defined as:

(1)

The quantity is the abundance by mass of the element in the infalling gas, while Gyr is the time for the maximum infall on the thin disk, Gyr is the time-scale for the creation of the halo and thick-disk and Gyr is the timescale to build up the thin disk in the solar neighborhood (as suggested by fitting the G-dwarf metallicity distribution). Here, we assume that the abundances show primordial gas compositions. Finally, the coefficients and are obtained by imposing a fit to the observed current total surface mass density in the solar neighborhood. A threshold gas density of 7 Mpc in the star formation process (Kennicutt 1989, 1998, Martin & Kennicutt 2001) is also adopted for the disk.

The most recent observational data by the Gaia-ESO Survey (Recio-Blanco et al. 2014; Rojas-Arriagada et al. 2017), APOGEE (Hayden et al. 2015) and AMBRE (Mikolaitis et al. 2017) confirmed the existence of two distinct sequences corresponding to thick and thin disk stars. In Grisoni et al. (2017) it was shown that the “two-infall” model is able to perfectly reproduce the AMBRE data in the solar neighborhood, when applied to the thick and thin disks without including the halo.

2.2 The “one-infall” model

Because of the fact that the majority of the data presented in Jönsson et al. (2017a) is supposed to be thin disk stars, we also considered a chemical evolution model which only follows the thin disk.

To reproduce the chemical evolution of the thin disk, we adopt an updated version of the “one-infall” chemical evolution model presented by Matteucci & François (1989) using the most recent nucleosynthesis yield of Romano et al. (2010).

Figure 1: The abundance ratio [F/O] as a function of [O/H] in the solar neighbourhood for the “two-infall” chemical evolution model adopting different prescriptions for the channels of the fluorine production. For oxygen we keep Romano et al. (2010, model 15) prescriptions. With the blue line we represent the model F1 of Table 2 where fluorine is assumed to be produced by both AGB stars, SNe Ia and SNe II. With the green line we have the model F2 (contributions to fluorine production only from SNe Ia and SNe II). The models F3, F4, F5 in which the AGB yields are multiplied by factors of 1.5, 2 and 3, respectively (along with SN Ia SN II channels) are drawn with brown, black, and red lines. Observational data by Jönsson et al. (2017a) are indicated with cyan circles.
Figure 2: The abundance ratio [F/Fe] as a function of [Fe/H] in the solar neighbourhood for the “two-infall” chemical evolution model adopting different prescriptions for the channels of fluorine production. Model lines are the ones described in Fig. 1. Observational data of Jönsson et al. (2017a) are indicated with cyan circles, whereas the data taken by Pilachowski & Pace (2015) are presented with gray pentagons.

The infall rate in the thin-disk for a given element at the time , and in the solar vicinity is defined as:

(2)

All model parameters are the same as the thin disk phase of the “two-infall” model described in Section 2.1.

3 Nucleosynthesis prescriptions for O, Fe, and F

In this work our principal aim is to analyze in detail the contribution of the different channels for the production of fluorine in the solar neighborhood, by comparing the predicted abundance ratios [F/Fe] vs [Fe/H] and [F/O] vs [O/H] by our chemical evolution models with the data.

We start our study by considering the set of nucleosynthesis yields of the Romano et al. (2010) best model (their model 15) for O, Fe and F (this set of yields has been adopted by Brusadin et al 2013, Micali et al. 2013, Spitoni et al. 2016).

In particular, these yields are:

  • For low-and intermediate-mass stars (0.8-8 M), we consider the metallicity-dependent stellar yields of Karakas (2010) with thermal pulses. These stars contribute to fluorine, negligibly to O and give no contribution to Fe.

  • For SNe Ia, the adopted nucleosynthesis prescriptions are from Iwamoto et al. (1999). These SNe contribute significantly to Fe and negligibly to O and F.

  • For massive stars (M8 M), which are the progenitors of either SNe II or hypernovae (HNe), depending on the explosion energy, we assume the metallicity-dependent He, C, N and O stellar yields, as computed with the Geneva stellar evolutionary code, which takes into account the combined effect of mass loss and rotation (Meynet & Maeder 2002, Hirschi et al. 2005, Hirschi 2007, Ekström et al. 2008). The Kobayashi et al. (2006) yields not including -nucleosynthesis are considered for fluorine. Jönsson et al. (2017a) compared their new observational data with chemical evolution models by Kobayashi et al. (2011b) in presence of -nucleosynthesis. The model showed a plateau at high [F/O] values at low [O/H] in contrast with the new data. For this reason we have not taken into account this kind of nucleosynthesis in this work.

    In this paper we test also the effects of W-R yields. For W-R stars we assume the F production by the models with mass loss by Meynet & Arnould (2000). These yields do not include oxygen.

    Meynet & Arnould (1993) have suggested that W-R stars could significantly contaminate the Galaxy with F. In their scenario, F is synthesized at the beginning of the He-burning phase from the N left over by the previous CNO-burning core, and is ejected in the interstellar medium when the star enters its WC phase. Since the mass loss depends on stellar metallicity, the F yields are metallicity-dependent.

    For all the elements heavier than oxygen, namely Fe in this study, we assume the Kobayashi et al. (2006) yields.

Figure 3: The abundance ratio [F/O] as a function of [O/H] in the solar neighbourhood for the “two-infall” chemical evolution model testing different prescriptions for the channels of fluorine production. With the blue line we represent the model F1 of Table 1. With the red line we consider also the Wolf-Rayet yield by Meynet & Arnould (2000). Model F6 where only Wolf-Rayet stars contribute to the fluorine production is indicated with the brown line in this plot. The black line is the model F8, similar to the F7 model but with the Wolf-Rayet yields multiplied by a factor of 2. Observational data of Jönsson et al. (2017a) are indicated with cyan circles.
Figure 4: The abundance ratio [F/Fe] as a function of [Fe/H] in the solar neighbourhood for the “two-infall” chemical evolution model adopting different fluorine yields. Model lines are the ones described in Fig. 3. Observational data of Jönsson et al. (2017a) are indicated with cyan circles whereas the data taken by Pilachowski & Pace (2015) are presented with gray pentagons.

4 Results: testing different nucleosynthesis prescriptions for fluorine

In this Section, we show the results related to the different prescriptions for the fluorine yields with the aim of reproducing the observational data by Jönsson et al. (2017a) both for the “two-infall” model and for a model where it is studied only the evolution of the thin disk (“one-infall” model). In Table 1 we present the list of all models tested here varying the fluorine yield prescriptions. For each model (F1..F9) it is indicated the presence of AGB stars with yields by Karakas (2010) in column 2, of Type Ia SNe with yields by Iwamoto et al. (1999) in column 3, of massive stars with yields by Kobayashi et al. (2006) in column 4, and W-R stars with yields by Meynet & Arnould (2000) in column 5. As stated above we started our work analyzing the effects of the nucleosynthesis prescriptions of the best model by Romano et al. (2010) (their model 15) on the [F/O] vs. [O/H] and [F/Fe] vs. [Fe/H] ratios in the light of the new data by Jönsson et al. (2017a). We label this model as F1.

The solar values adopted in this work for oxygen and iron are the Asplund (2009) ones, whereas for fluorine the one computed by Maiorca et al. (2014) is used to be coherent with the Jönsson et al (2017a) work.

Figure 5: The abundance ratio [F/O] as a function of [O/H] in the solar neighbourhood for the “two-infall” chemical evolution model. With the blue line we represent the model F1 of Table 1 where fluorine is assumed to be produced by both AGB stars, SNe Ia and SNe II. Model, similar to the F7 model but with the Wolf-Rayet yields multiplied by a factor of 2 is drawn with the black line. With the magenta is represented the model F9 where the contribution of SNe II and SNe Ia are considered along with W-R stars. In this model the AGB yields are multiplied by a factor of 2. Observational data of Jönsson et al. (2017a) are indicated with cyan circles.

We stress that in this work we analyze in detail only fluorine yields; for the other elements shown in this paper (O,Fe), we use the model 15 prescriptions by Romano et al. (2010), which does not include fluorine though.

4.1 The “two-infall” model results

Jönsson et al. (2017a) compared their new observational data with chemical evolution models by Kobayashi et al. (2011a, 2011b) for thick and thin disk stars where it was considered the contribution of AGB stars and processes to the fluorine production. The main problem of those models is that they are not capable to reproduce the slope of the secondary behavior of the new data presented by Jönsson et al. (2017a).

Here, we show the results related to the “two-infall” model of Chiappini et al. (1997, 2001) updated by Romano et al. (2010) for the chemical evolution of the solar neighborhood. In Fig. 1 we show the abundance ratio [F/O] as a function of [O/H] in the solar neighbourhood adopting different prescriptions for the channels of fluorine production. First, we consider for F and O the nucleosynthesis yields adopted by the model15 of Romano et al. (2010) (model F1 in Table 1): the ones of Karakas (2010) for AGB stars with thermal pulses, Iwamoto et al. (1999) for Type Ia SNe, and Kobayashi et al. (2006) for massive stars for F and the Geneva stellar evolutionary code for O.

In Fig. 1, model F1 clearly shows the transition between the halo-thick disk phase and the thin disk. Because of the presence of a threshold for the surface gas density in the star formation we have a gap in the star formation history (see Spitoni et al. 2016) in the correspondence of the beginning of the second gas infall.

At variance with the models of Kobayashi et al. (2011a,b) shown in Fig. 3 of Jönsson et al. (2017a), the F1 model shows a decrease of [F/O] abundance values for [O/H] larger than 0.2 dex. This behavior is due to the different prescriptions for the yield of oxygen we adopted. In fact, in Romano et al. (2010) the oxygen produced by massive stars is coming from the Geneva tracks with mass loss and rotation (Meynet & Maeder 2002, Hirschi et al. 2005, Hirschi 2007, Ekström et al. 2008). Model F1 is not able to reproduce the observational trend of Jönsson et al. (2017a) data for over-solar values of [O/H], and the main problem is that we are not capable to reach the high [F/O] observed values.

In Fig. 1, it is also proven that adopting the Romano et al. (2010) best choice for the yields (their model 15) the main contribution to the fluorine is given by AGB stars. In fact, model F2 (see Table 1), in which the fluorine is created only by means of SN Ia and SN II channels, shows a vary small amount of fluorine production: the [F/O] abundance at maximum reaches the value of -0.8 dex.

However, the AGB yields of F are still uncertain. In fact, the recent measurements by Indelicato et al. (2017) and He et al. (2017) of the FO reaction, suggest that the computed yields from AGB-stars should be revised and higher values might be expected. Therefore, in Fig. 1 the effects of increasing by hand the contribution by AGB stars are presented. Multiplying the yields by factors of 1.5, 2 and 3 (models F3, F4, and F5 in Table 1, respectively), we have a better agreement with the data.

This kind of procedure has been widely used in chemical evolution models in the past. For example, in François et al. (2004) best model the Mg yields related to the massive stars of Woosley & Weaver (1995) have been multiplied by a factor of two. More recently, in Maas et al. (2017) phosphorus yields by Kobayashi et al. (2006) have been multiplied by a factor of 2.75 with the aim of reproducing the [P/Fe] vs [Fe/H] abundance ratios in the solar neighborhood as suggested by the new observational stellar data using the chemical evolution model by Cescutti et al. (2012). From Fig. 1 we see that models F4 and F5 are able to:

  • reach the observed high [F/O] ratio values for over-solar [O/H] abundances.

  • trace the observed secondary slope of the data for sub-solar [O/H] values.

The data in Fig. 1 present a change in the slope of the [F/O] vs [O/H] abundance ratios for values larger than [O/H]=0. The secondary behavior of the fluorine is not perfectly reproduced for over-solar values of [O/H], in fact models F3 and F4 show a decrease of the [F/O] abundance ratio for [O/H] 0.

A common problem of models F3, F4, and F5, is that the transition between the halo-thick disk phase and the thin disk has a big impact in the [F/O] vs [O/H] ratios adopting the Romano et al. (2010) model15 set of yields. We will show in the next subsection related to the “one-infall” results (the chemical evolution only for the thin disk), that a better agreement with the data is achieved. We recall here that the majority of the data presented by Jönsson et al. (2017a) are parts of the thin disk system.

However, the predicted fluorine solar values are in agreement with solar ones of Maiorca et al. (2014) as shown in Table 2. In fact, the predicted solar mass fraction for fluorine by the model F4 (AGB yields multiplied by a factor of 2) is 4.91 10; which compares very well to the value of 4.78 10 predicted by Maiorca et al. (2014).

Figure 6: The abundance ratio [F/O] as a function of [O/H] in the solar neighbourhood for the “one-infall” chemical evolution model adopting different nucleosynthesis prescriptions for the fluorine production. Model lines are the ones described in Fig. 1. Observational data of Jönsson et al. (2017a) are indicated with cyan circles whereas the data taken by Pilachowski & Pace (2015) are presented with gray pentagons.
Figure 7: The abundance ratio [F/Fe] as a function of [Fe/H] in the solar neighbourhood for the “one-infall” chemical evolution model. Model lines are the ones described in Fig. 6. Observational data of Jönsson et al. (2017a) are indicated with cyan circles whereas the data taken by Pilachowski & Pace (2015) are presented with gray pentagons.

In Fig. 2 the same models of the previous Figure are considered but in the terms of [F/Fe] vs [Fe/H], and we compare our models with the data by Jönsson et al. (2017a) along with Pilachowski & Pace (2015) ones (the stars in Pilachowski & Pace 2015 are thin disk, see their Section 2.1). If we consider both data sets the area spread by the data is well covered by the model predictions. On the other hand, the trend shown by solely the data of Jönsson et al. (2017a) - i.e. the abundance ratio [F/Fe] always increases with [Fe/H] - is not reproduced by any models presented so far in this paper.

In Fig 3 we present the model results for the two-infall model where the W-R star yields by Meynet & Arnould (2000) for the fluorine are taken into account. As suggested by Renda et al. (2004) and Jönsson et al. (2017a) a possible source for fluorine production are W-R stars. They might deposit fluorine into the interstellar medium via their strong stellar winds (Meynet & Arnould 2000; Palacios et al. 2005). Just like in the AGB scenario, the fluorine in W-R winds is produced in reactions starting from N, including , neutron, and proton captures. Due to the strong metallicity dependence of the winds of these stars, a possible fluorine production through this channel is expected to start first at slightly sub-solar metallicities and then increase for higher metallicities (Renda et al. 2004).





Fluorine Solar values Maiorca (2014): 4.78 10
2 Infall model 1 Infall model



F1
3.07 10 3.03 10
F2 9.51 10 9.15 10

F3
3.99 10 3.95 10

F4
4.91 10 4.87 10

F5
6.74 10 6.71 10
F6 3.23 10 3.10 10
F7 5.79 10 5.64 10
F8 8.58 10 8.30 10
F9 7.62 10 7.48 10



Table 2: The solar values expressed in mass fraction of fluorine predicted the models reported in Table 1 where different channels for the fluorine production are considered.
Figure 8: The abundance ratio [F/O] as a function of [O/H] in the solar neighbourhood for the “one-infall” chemical evolution model adopting different prescriptions for the channels of fluorine production. The model F6, in which only the contribution for fluorine production is given by W-R stars, is indicated with the brown line. Model F7 in which we adopt Romano et al. (2010) yield including W-R stars by Meynet & Arnould (2000) is with the red line. Model F8 (same of model F7, but with the W-R fluorine yields multiplied by 2, see Table 1) is drawn with the black line. Finally, models F9 (same of model F7, but with the AGB fluorine yields multiplied by 2, see Table 1) is labeled with magenta line. Observational data of Jönsson et al. (2017a) are indicated with cyan circles.

In Fig. 3 we note that model F7 which considers the Romano et al. (2010) yield prescriptions for oxygen, coupled with W-R contribution for the fluorine production, is able to increase the [F/O] vs [O/H] relation for over-solar values of [O/H] in comparison with the “reference” model F1. This leads to a better agreement with the data of Jönsson et al. (2017a), but the slope of the observed secondary behavior is not well reproduced, and the model shows lower [F/O] values at larger [O/H]. The predicted solar mass fraction for fluorine by the model F7 is 5.79 10, therefore still in perfect agreement with Maiorca et al. (2014) value.

In Fig. 3 we also draw the model F8 (see Table 1 for model yield detail) where we tested the metal dependent W-R yield by Meynet & Arnould (2000) for fluorine multiplied by hand by a factor of 2 coupled with the Romano et al. (2010) yield. We note that this model is capable to perfectly reproduce the observed data. The predicted solar mass fraction for fluorine by the model F8 is 8.58 10 (see Table 2), definitely a larger value than the one predicted by Maiorca et al. (2014), but still within a factor of two.

In summary, from Table 2 we see that the solar fluorine abundance value reached by the model F7 is in agreement with the Maiorca et al. (2014) value, whereas the model F8 (W-R fluorine yields multiplied by a factor of two) shows, as expected, a larger value but within a factor of two.

We also show the effects of considering fluorine as produced only by W-R stars (model F6). We note that W-R stars contribute to increase the fluorine production in the whole range of [O/H]. The main feature of model F6 is that it shows the secondary behavior slope observed in the Jönsson et al. (2017a) stellar sample for [O/H] over-solar values. Concerning the [F/Fe] vs. [Fe/H] abundance ratios, in Fig 4 are reported the same models described above and shown in Fig. 3.

We see that models including the W-R contribution for the fluorine provide a better fit to the observed data set of Jönsson et al. (2017a) and Pilachowski & Pace (2015) compared to the models presented in Fig. 2 without this contribution.

We conclude this Subsection focused on the two-infall model results, presenting in Fig. 5 the effects of varying AGB fluorine yields by hands in presence of W-R fluorine contribution. In model F9 (see Table 1) the AGB yields are multiplied by a factor of two along with W-R yields by Meynet & Arnould (2000). In this way we have a better agreement with data compared to reference model F1.

Without any modification of W-R fluorine yields we find a slight decreasing trend in the [F/O] vs [O/H] relation for over-solar [O/H] values but still in agreement with Jönsson et al. (2017a) data. Moreover the predicted fluorine solar mass fraction is 7.62 10, therefore in better agreement with the Maiorca et al. (2014) one.

Figure 9: The abundance ratio [F/Fe] as a function of [Fe/H] in the solar neighbourhood for models F6-F7-F8-F9 applied to the “one-infall” chemical evolution model. Model lines are the same of Fig. 8. Observational data of Jönsson et al. (2017a) are indicated with cyan circles whereas the data taken by Pilachowski & Pace (2015) are presented with gray pentagons.

4.2 The “one-infall” model results

In this Subsection we present the results of chemical evolution models for the thin disk of the Galaxy in the solar neighborhood (the one infall model). In Fig. 6 models F1, F2, F3, F4 and F5 are shown (see Table 1 for model detail). In this Figure it is evident a “smoother” chemical evolution compared to the “two-infall” case. This is due to the absence of any gap in the star formation history which is a peculiar feature of the two-infall model (during the transition between the halo-thick disk phase) and the thin disk one.

Figure 10: The abundance ratio [F/O] as a function of [O/H] in the solar neighbourhood for the “one-infall” (left panel) and “two-infall” (right panel) chemical evolution models taking into account the effects of the novae. We consider for fluorine the maximum yield by José & Hernandez (1998, model ONe7) related to ONe White dwarf with masses of 1.35 M). With the blue line the reference F7 model is reported. The model with the “maximum” F novae yield is labeled with the pink line. Models with “maximum” F nova yield multiplied by factor of 5 and 10 are drawn with orange and purple lines, respectively.

As anticipated in Subsection 6.1, the “one-infall” model results are able to better reproduce the Jönsson et al. (2017a) abundance ratios. The same models of Fig. 6 are shown in terms of [F/Fe] vs [Fe/H] in Fig. 7.

In Fig. 7 if we consider both data sets, the area spread by the data is well covered by model predictions. On the other hand, the increase of [F/Fe] for larger values of [Fe/H] shown by the data of Jönsson et al. (2017a) alone, is not reproduced by any model. Moreover, as it can be seen in Table 2, the solar values predicted by the “one-infall” model are not so different from the ones by the two-infall one, although only slightly smaller.

In Fig. 8 we show the effects on the relations [F/O] vs. [O/H] of including the Wolf-Rayet stars contribution to the fluorine production on the “one-infall” chemical evolution model for the thin disk in terms of [F/O] vs. [O/H] abundance ratios. The model which best fits the data is model F8 which perfectly reproduces the change of slope of the data. In fact, the predicted knee by this model is located around the solar value of [O/H], in agreement with the data.

As for the two-infall case, the model F8 shows a higher solar value for the fluorine compared with the Maiorca et al. (2014) value (see Table 2).

Moreover, in Fig. 8 we show the model F9 applied to the “one-infall” chemical evolution, in which we multiplied by a factor of two the AGB yields for fluorine along with the W-R yield of Meynet & Arnould (2000). Also in this case, the model F9 applied to the “one-infall” chemical evolution model leads to a better fit of the data compared with the case when we considered it for the two-infall model. Even if this model predicts a decreasing trend for [F/O] vs [O/H] for over-solar [O/H] values, the model line is within the observed error bars. As reported in Table 2 this model predicts a fluorine solar value better in agreement with the Maiorca et al. (2014) value compared to the model F8.

In Fig. 9 models with W-R fluorine contribution are reported for the [F/Fe] vs [Fe/H] relation. Again, if we consider Pilachowski & Pace (2015) and Jönsson et al. (2017a) the best model is the F8. However this model it is not able to reproduce the trend shown by the data by Jönsson et al. (2017a). In conclusions, as shown for the two-infall case, we confirm that:

  • Increasing by hand the AGB fluorine yields leads to a better fit of [F/O] vs [O/H] abundance ratios for sub-solar values of [O/H], but the secondary behavior at higher [O/H] is not reproduced adopting the nucleosynthesis yields of model15 of Romano et al. (2010).

  • Models which take into account W-R metallicity dependent yields for fluorine by Meynet & Arnould (2000) are capable to better fit the observed data.

  • The best models are the F8 and F9 ones.

5 Testing the novae as possible sources for F production

In the last section we focus on the effects of nova nucleosynthesis on the fluorine production. In principle this source could help to reproduce the secondary behavior of fluorine observed by Jönsson et al. (2017a) in the [F/O] vs [O/H] at high [O/H] values.

We tested that the inclusion of the nova yields by José & Hernanz (1998) on the model F7 (see Table 1) has a negligible effect on the chemical evolution of fluorine. In any case, as an exercise, we present in Fig. 10 the model with the “maximum” fluorine yield by novae, showing the model F7 in the [F/O] vs [O/H] relation, including F produced by novae originated in ONe white dwarf (W-D) of 1.35 M (model ONe7 of José & Hernanz 1998). Although this W-D model leads the maximum production of F in novae, we are aware that these objects are extremely rare in nature. In the same Figure we present model results in which the fluorine nova yields are multiplied by factors of 3 and 5, respectively.

It is quite interesting to note that in this way we are able to trace perfectly the secondary trend at high [O/H] values. However, we remind the reader that nova yields are still very uncertain. It is worth noting that Li synthesized in a nova outburst as inferred from recent observations (Tajitsu et al. 2015, Izzo et al. 2015) exceeds by far the one expected from the theoretical models of José & Hernanz (1998). This fact suggests that there is also room for a significant revision of F yield from novae.

6 Conclusions

In this article we studied in detail the effects of different nucleosynthesis prescriptions for the fluorine production on the chemical evolution models for the solar neighborhood with the aim of reproducing the observational data by Jönsson et al. (2017a). Our main conclusions can be summarized as follows:

  • The role played by Wolf-Rayet stars in the fluorine production seems to be essential to reproduce the new observed ratios in the solar neighborhood [F/O] vs [O/H] by Jönsson et al. (2017a). This confirms previous suggestions by Renda et al. (2004).

  • We obtain a better agreement with the observed fluorine abundances when we consider the “one-infall” chemical evolution model, relative only to the thin disk.

  • The best “one-infall” model reproducing the observed abundance ratios [F/O] vs [O/H] for the thin disk requires the nucleosynthesis prescriptions of the model 15 of Romano et al. (2010) along with the Wolf-Rayet fluorine yields by Meynet & Arnould (2000) multiplied by a factor of two. On the other hand, this model predict a solar value higher than the one of Maiorca et al. (2014).

  • Considering the AGB yields by Karakas et al. (2010) multiplied by a factor of two along with Meynet & Arnould (2000) Wolf-Rayet yields leads to a good fit of the [F/O] vs [O/H] data and predict a solar value in agreement with Maiorca et al. (2014) value.

  • Concerning the [F/Fe] vs [Fe/H] relation, the models presented here are in agreement with the collection of data composed by Jönsson et al. (2017a) and Pilachowski & Pace (2015). The data by Jönsson et al. (2017a) show that [F/Fe] abundances increase with [Fe/H]. This trend is not found by our models for [Fe/H] values larger than -0.3 dex. We want to underline that there are still huge uncertainties concerning the nucleosynthesis of F, and this could be the reason of the discrepancy.

  • More detailed data for fluorine in the solar neighborhood are required at low metallicities, i.e for [O/H] values smaller than -0.4 dex, to confirm the importance of W-R stars in the fluorine production, as we conclude in this paper. In fact, we predict that the inclusion of the fluorine produced by W-R star would affect the [F/O] vs [O/H] ratio also at small [O/H] values leading to a roughly flat [F/O] ratio for [O/H] smaller that -0.5 dex.

  • We also show that the novae, even if their yields are still uncertain could help to better reproduce the secondary behavior of F in the [F/O] vs. [O/H] relation in presence of W-R stars fluorine contribution.

Acknowledgments

We thank the anonymous referee for the suggestions that improved the paper. E. Spitoni and F. Matteucci thank the financial support by FRA2016 - University of Trieste. N. Ryde acknowledges support from the Swedish Research Council, VR (project number 621-2014-5640), Funds the Royal Physiographic Society of Lund. (Stiftelsen Walter Gyllenbergs fond and Märta och Erik Holmbergs donation), and from the project grant “The New Milky” from the Knut and Alice Wallenberg foundation. H. Jönsson acknowledges the support by the Lars Hierta Memorial Foundation, Helge Ax:son Johnsons stiftelse, and Stiftelsen Olle Engkvist Byggmästare.

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