Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.mso.anu.edu.au/~akarakas/download/Renda_etal2004.pdf Äàòà èçìåíåíèÿ: Tue Nov 14 07:49:58 2006 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 05:34:03 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: stellar evolution

Mon. Not. R. Astron. So c. 000, 1­6 (2004)

Printed 9 July 2004

A (MN L TEX style file v2.2)

On the origin of fluorine in the Milky Way
Agostino Renda1 , Yeshe Fenner1 , Brad K. Gibson1 , Amanda I. Karakas2,3, John C. Lattanzio2, Simon Campbell2, Alessandro Chieffi Katia Cunha6, Verne V. Smith7
1 2

1,2,4,5

,

Centre for Astrophysics & Supercomputing, Swinburne University, Hawthorn, Victoria, 3122, Australia Centre for Stel lar & Planetary Astrophysics, School of Mathematical Sciences, Monash University, Clayton, Victoria 3800, Australia 3 Institute for Computational Astrophysics, Department of Astronomy & Physics, Saint Mary's University, Halifax, Nova Scotia B3H 3C3, Canada 4 Istituto di Astrofisica Spaziale e Fisica Cosmica (CNR), Via Fosso del Cavaliere, 00133 Roma, Italia 5 INAF Osservatorio Astronomico di Roma, Via Frascati 33, 00040 Monteporzio Catone, Italia 6 Observat´ orio Nacional, Rua General Jos´ Cristino 77, 20921 400 S~ Cristov~ Rio de Janeiro, Brazil e ao ao, 7 Department of Physics, University of Texas at El Paso, El Paso, TX 79968, U.S.A.

Accepted. Received; in original form

ABSTRACT

The main astrophysical factories of fluorine (19 F) are thought to be Type II supernovae, Wolf­Rayet stars, and the asymptotic giant branch (AGB) of intermediate mass stars. We present a model for the chemical evolution of fluorine in the Milky Way using a semi-analytic multi-zone chemical evolution model. For the first time, we demonstrate quantitatively the impact of fluorine nucleosynthesis in Wolf­Rayet and AGB stars. The inclusion of these latter two fluorine production sites provides a possible solution to the long-standing discrepancy between model predictions and the fluorine abundances observed in Milky Way giants. Finally, fluorine is discussed as a possible probe of the role of supernovae and intermediate mass stars in the chemical evolution history of the globular cluster Centauri. Key words: galaxies: evolution ­ stars: abundances ­ stars: evolution

1

INTRODUCTION
19

The three primary astrophysical factories for fluorine ( F) production have long been thought to be Type II Supernovae (SNe II), Wolf­Rayet (WR) stars, and asymptotic giant branch (AGB) stars (e.g. Woosley & Weaver 1995; Meynet & Arnould 2000; Forestini et al. 1992; Mowlavi, Jorissen & Arnould 1998, respectively). Previous attempts to model the Galactic production and evolution of 19 F have been restricted to explore the role of SNe II alone (e.g. Timmes, Woosley & Weaver 1995; Alib´ Labay & Canal 2001). es, The above problem has now been ameliorated by the release of the first detailed yield predictions for fluorine production from WR and AGB stars. We are now in a position to incorporate these yields into a Galactic chemical evolution framework, in order to assess the respective contributions of the three putative fluorine production sites. To do so, we will make use of GEtool, a semi-analytical multi-zone Galactic chemical evolution package which has been calibrated with

extant observational data for the Milky Way (Fenner & Gibson 2003; Gibson et al. 2003).

arenda,yfenner,bgibson@astro.swin.edu.au c 2004 RAS

Specifically, in what follows, we compare the model fluorine distribution in the Milky Way with the abundances observed by Jorissen, Smith & Lambert (1992) in near-solar metallicity giants. Further, our model predictions are contrasted with new fluorine determinations for giants in the Large Magellanic Cloud (LMC) and Centauri (Cunha et al. 2003). In addition, new results for more Centauri giants from Smith et al. (2004) are included. The latter two systems are likely to have had very different star formation and chemical evolution histories from those of the Milky Way, but despite these obvious differences, a comparison against these new data can be valuable. In Section 2, we provide a cursory overview of the three traditional 19 F nucleosynthesis sites; the chemical evolution code in which the nucleosynthesis products from these factories have been implemented is described in Section 3. Our results are then presented and summarised in Sections 4 and 5, respectively.


2
2 2.1

A. Renda et al.
NUCLEOSYNTHESIS OF Type II Supernovae
19

F

The massive star progenitors to SNe II produce fluorine primarily as the result of spallation of 20 Ne by µ and neutrinos near the collapsed core (Woosley & Haxton 1988; Woosley et al. 1990). A fraction of the 19 F thus created is destroyed by the subsequent shock but most is returned to the ambient Interstellar Medium (ISM). The fluorine yields by neutrino spallation are very sensitive to the assumed spectra of µ and neutrinos (Woosley et al. 2002), which could be nonthermal and deficient on their high-energy tails, lowering the equivalent temperature of the neutrinos in the supernova model (Myra & Burrows 1990). An additional source of 19 F derives from pre-explosive CNO burning in helium shell. However, fluorine production by neutrino spallation is largely dominant, as evident by comparing the models in Woosley & Weaver (1995), the only ones to-date including neutrino process, and recent models which do not include neutrino nucleosynthesis of fluorine (Limongi & Chieffi 2003). Most recently, Heger et al. (2004) suggest that the relevant neutrino cross sections need to be revised downwards; if confirmed, the associated SNe II 19 F yield would decrease by 50%. In light of the preliminary nature of the Heger et al. claim, we retain the conservative choice offered by the Woosley & Weaver (1995) compilation.

For stars more massive than 4 M , the convective envelope is so deep that it penetrates into the top of the hydrogen-burning shell so that nucleosynthesis actually occurs in the envelope of the star. Such "hot-bottom-burning" acts to destroy 19 F, and should be treated self-consistently within the AGB models considered. 2.3 Wolf­Rayet stars

2.2

Asymptotic giant branch stars

The nucleosynthesis pathways for fluorine production within AGB stars involve both helium burning and combined hydrogen-helium burning phases (e.g. Forestini et al. 1992; Jorissen et al. 1992; Mowlavi et al. 1998) and are companions for the nucleosynthesis by slow neutron accretion (s-process) (Mowlavi et al. 1998). Provided a suitable source of protons is available, fluorine can be synthesised via 14 N(, )18 F ( + ) 18 O(p,) 15 N(, ) 19 F. Primary sources of uncertainty in predicting fluorine nucleosynthesis in AGB stars relate to the adopted reaction rates, especially 14 C (, )18 O and 19 F (, p)22 N e, and the treatment of the nucleosynthesis occurring during the convective thermal pulses. Nucleosynthesis during the interpulse periods can also be important if protons from the envelope are partially mixed in the top layers of the He intershell (partial mixing zone), as Lugaro et al. (2004) have recently demonstrated. Nucleosynthesis in this zone may result in a significant increase in the predicted 19 F yields. The magnitude of these systematic uncertainties for stellar models with mass 3 M and metallicities Z = 0.004 - 0.02 are 50%, while for stellar models with mass M = 5 M and metallicity Z = 0.02 the uncertainty is a factor of 5, due to the uncertain 19 F (, p)22 N e reaction rate. Characterising the mass- and metallicity-dependence of the partial mixing zone­19 F relationship needs to be completed before we can assess its behaviour self-consistently within our chemical evolution model of the Milky Way. For the present study, we have adopted the yields presented in Appendix, based upon the Karakas & Lattanzio (2003, and references therein) models, which themselves do not include 19 F nucleosynthesis via partial mixing. This choice is a conservative one, and thus should be considered as a lower limit to the production of 19 F from AGB stars.

Fluorine production in WR stars is tied to its nucleosynthesis during the helium-burning phase. At the end of this phase though, significant fluorine destruction occurs via 19 F(, p)22 Ne. Any earlier synthesised 19 F must be removed from the stellar interior in order to avoid destruction. For massive stars to be significant contributors to net fluorine production, they must experience mass loss on a timescale that allows the removal of 19 F before its destruction. This requirement is met by WR stars. Recently, Meynet & Arnould (2000) studied the role that such stars can play in the chemical evolution of fluorine by adopting updated reaction rates coupled with extreme mass-loss rates in not-rotating stellar models. They pointed out that WR mass-loss is strongly metallicity-dependent, and that the number of WR stars at low metallicities is very small. Their WR yields reflect such metallicity-dependence, with minimal fluorine returned to the ISM at low metallicities, but significant 19 F returned at solar and super-solar metallicities. The WR yields are sensitive to the adopted reaction and mass-loss rates, while rotating models could favour an early entrance into the WR phase for a given mass, decrease the minimum initial mass for a star to go through a WR phase at a given metallicity, and open more nucleosynthetic channels because of the mixing induced by rotation. Therefore, after Meynet & Arnould (2000), we consider the aforementioned WR yields as lower limits.

3

THE MODEL

In this study we employ GEtool, our semi-analytical multizone chemical evolution package to model a sample Milky Way-like disk galaxy (Fenner & Gibson 2003; Gibson et al. 2003). A dual­infall framework is constructed in which the first infall episode corresponds to the formation of the halo, and the second to the inside-out formation of the disk. A Kroupa, Tout & Gilmore (1993) initial mass function (IMF) has been assumed, with lower and upper mass limits of 0.08 M and 120 M , respectively. Stellar yields are one of the most important features in galactic chemical evolution models, yet questions remain concerning the precise composition of stellar ejecta, due to the uncertain role played by processes including mass loss, rotation, fallback, and the location of the mass cut, which separates the remnant from the ejected material in SNe. The SNe II yields are from Woosley & Weaver (1995); the yields for stars more massive than 60 M are assumed to be mass-independent. Such assumption is made to avoid extreme extrapolation from the most massive star in the Woosley & Weaver models (40 M ) to the upper end of the IMF (120 M ), and has negligible effect on the results, given the shape of the adopted IMF. We have halved the iron yields shown in Woosley &
c 2004 RAS, MNRAS 000, 1­6


The origin of fluorine in the Milky Way
-2 -4 -6 -8 10 20 30 a 40

3

-2 -4 -6 -8 20 40 60 80 b

-2 -4 -6 c -8 2 4 6

Figure 1. Fluorine yields from a) SNe I I (Wo osley & Weaver 1995), b) WR (Meynet & Arnould 2000), and c) AGB stars (App endix).

Weaver (1995), as suggested by Timmes et al. (1995). The Type Ia (SNe Ia) yields of Iwamoto et al. (1999) were also employed. We adopted the metallicity-dependent yields of Renzini & Voli (1981) for single stars in the mass range 1 - 8 M . For the purposes of this work, which focuses on fluorine, the choice of the Renzini & Voli yield set does not affect the results. Metalllicity-dependent stellar lifetimes have been taken from Schaller et al. (1992). We have constructed three Milky Way (MW) model variants that differ only in their respective treatments of 19 F production: 1) MWa assumes that SNe II are the only source of 19 F; 2) MWb includes yields from both SNe II and WR stars; 3) MWc includes all three sources of fluorine SNe II, WR, and AGB stars. We end by noting that within our adopted dual­infall framework for the chemical evolution of the Milky Way, our model is constrained by an array of observational boundary conditions, including the present-day star and gas distributions (both in density and metallicity), abundance ratio patterns, age-metallicity relation, and G-dwarf distribution (Gibson et al. 2003). While the modification of any individual ingredient within model framework will have an impact, to some degree, upon the predicted chemical evolution, this can only eventuate at the expense of one or more of the aforementioned boundary conditions that we require our model to adhere to. Within our framework, yield uncertainties will dominate the systematic uncertainties for the predicted evolution of 19 F.

1) SNe II 19 F yields are taken from Woosley & Weaver (1995) and assumed to be mass-independent for stellar masses in excess of 60 M . 2) WR 19 F yields are taken from Meynet & Arnould (2000) for stellar masses in the range 25 - 120 M : each star within this range is assumed to evolve through the WR stage. Such simplifying assumption could overestimate the WR contribution to fluorine, even though the adopted WR yields are themselves lower limits (Section 2.3). The WR fluorine contribution has been added to the corresponding SNe II contribution (which comes from a different stage of the stellar evolution). 3) AGB 19 F and oxygen yields in the 1 - 6.5 M mass range have been derived from stellar models constructed with the Mount Stromlo Stellar Structure Code (Frost & Lattanzio 1996; Karakas et al. 2002), and are presented in Appendix. The post-processing nucleosynthesis models with 74 species and time-dependent diffusive convective mixing are described in detail in Frost et al. (1998) and Karakas & Lattanzio (2003). To ensure internal consistency, we have also employed the AGB oxygen yields in lieu of those of Renzini & Voli (1981), within this mass range. The above fluorine yields are shown in Figure 1. In Figure 2, the yields are expressed as [F/O]1 and [F/O] I M F , the latter corresponding to the mean [F/O] yields for SNe II and AGB stars, weighted by the IMF over the SNe II and AGB mass range, respectively. We have not shown a comparable entry for the WR stars as a self-consistent treatment of the oxygen production was not included in Meynet & Arnould (2000). Here, oxygen has been used as the normalisation to make easier the comparison with the observations, especially in Centauri, though oxygen can be synthesised in various stellar sites, and its yields can be affected by different reaction rates and modeling of helium cores, semiconvection, convective boundary layers, and mass-loss (e.g. Woosley et al. 2002; Dray et al. 2003).

4

RESULTS

In Figure 3, the evolution of [F/O], A(O), the gas infall rate inf all , the star formation rate (SFR), the SNe II rate and the gas-phase global metallicity Z of the three models at the solar neighbourhood are summarised. The empirical SFR history derived by Bertelli & Nasi (2001) is shown as a thick solid line in Figure 3d, while the shaded region corresponds to the range of values suggested by Rana (1991). A conservative range of estimated SNe II rates is also shown in Figure 3e (Cappellaro, Evans & Turatto 1999).2 . Figure 4

3.1

Fluorine yields
19

We now summarise the "Milky Way" models.

F yields employed in our three

Hereafter, [X/Y]= log10 (X/Y)-log10 (X/Y) and A(X)= 12 + log10 (nX /nH ). An accurate determination of photospheric solar abundances requires detailed mo deling of the solar granulation and accounting for departures from lo cal thermo dynamical equilibrium (e.g. Allende Prieto, Lamb ert & Asplund 2001). We adopt the solar fluorine abundance suggested by Cunha et al. (2003), and the solar iron and oxygen abundances from Holweger (2001). 2 The range of values shown in Figure 3e is derived from the sample of S0a ­ Sb galaxies in Capp ellaro et al. (1999) - 0.42 ± 0.19 SNu, where 1 SNu= 1 SN(100 yr)-1 (1010 LB )-1 ), assuming LB W = 2 â 1010 LB and a galactic radial extent of 15 kp c. M

1

c 2004 RAS, MNRAS 000, 1­6


4

A. Renda et al.
1 a 0 -1 -2 -3 10 20 30 40 0 -1 5 -2 -3 -6 -4 -2 0 9 8.5 8 b 2 1 0 -1 2 0.2 1 0 -1 0.02 0 -0.2 -0.4 -0.6 -0.8 2 4 6 -6 -4 -2 0 5 10 c 0.015 0.01 0.005 f 0 0 5 10 d 7.5 1 c 10 15 a 8 6 4 2 0 -1 -1.5 -2 b -2.5 e -3 d

Figure 2. [F/O] and [F/O] I M F for SNe I I and AGB yields (upp er and lower panels, resp ectively). Here, A(19 F) = 4.55 (see discussion in Cunha et al. 2003) and A(O) = 8.736 (e.g. Holweger 2001). The shaded regions in Figures 2a and 2b show the observed [F/O] in Cen giants (Cunha et al. 2003). The [F/O] I M F are weighted by the IMF over the SNe I I (11 - 40M ) and AGB (1 - 6.5 M ) mass range, resp ectively. In Figure 2d, b oth [F/O]AGB I M F and [F/O]S N e I I I M F are shown (closed b oxes and op en triangles, resp ectively).

Figure 3. Predicted evolution in the solar neighb ourho o d of a) the gas infall rate inf all , b) A(O), c) [F/O], d) star formation rate (SFR), e) SNe I I rate, and f ) metallicity Z (MWa, solid line; MWb, dotted; MWc, short-dashed). The SFR history at the solar neighb ourho o d obtained by Bertelli & Nasi (2001) is also shown as a thick solid line in panel `d', while the shaded region shows the range of values suggested by Rana (1991). A range of values corresp onding to the estimated SNe I I rate is shown in panel `e' (Capp ellaro et al. 1999).

then shows the the evolution of [F/O] versus A(O) (panel a), and the evolution of [F/O] versus [O/Fe] (panel b), compared against the IMF-weighted SNe II yields (recall Figure 2). The MWa model provides a satisfactory reproduction of the estimated star formation history and SNe II rate in the solar neighbourhood (Figures 3d and 3e). This model, whose only fluorine source is SNe II, underproduces fluorine with respect to the abundances measured in K and M Milky Way giants observed by Jorissen et al. (1992) and reanalysed by Cunha et al. (2003) (Fig. 4a). Fig. 4a does not show the s-process enriched AGB stars of spectral types MS, S, or C in Jorissen et al. (1992), where freshly synthesised fluorine could be mixed to the stellar surface. Such inclusion of selfpolluted 19 F-rich stars could obscure any metallicity trend. The results of the MWa and MWb models show that the additional contribution from WR stars increases [F/O] by up to factor of 2 by the present-day, but it is negligible in excess of 9 Gyr (Figure 3c). The addition of both WR and AGB sources within the MWc model leads to a present-day [F/O] that is 0.4 dex greater than in the MWa case. Further, and perhaps more important, AGB stars are now shown to deliver significant amounts of fluorine to the ISM during the early epochs of the Milky Way's evolution. Such a result is entirely con-

sistent (and expected) given the metallicity-dependence of the AGB yields; said yields possess [F/O] ratios which are greater at lower metallicities (recall Figure 2). We can conclude that it is only the addition of both the WR and AGB contributions which allow for a significant improvement in the comparison between galactic models incorporating fluorine evolution and the observational data.

5

DISCUSSION

Given these assumptions, the estimated SNe I I rate at the solar neighb ourho o d is necessarily uncertain.

We have studied the Galactic chemical evolution of fluorine, for the first time using new grids of stellar models which provide self-consistent predictions of fluorine nucleosynthesis for stars in both the WR and AGB phases of stellar evolution. We have shown that the WR contribution is significant at solar and super-solar metallicities because of the adopted metallicity-dependent mass-loss prescription employed in the stellar models. In contrast, the contribution of AGB stars to fluorine production peaks during the early epochs of the Galaxy's evolution (again due to the metallicity-dependent behaviour of the AGB models). In combination, the addition of the WR and AGB yields leads to a significant improvement in the galactic chemical evolution models when compared against observations. The comparison between our MW models and the fluorine abundances in LMC and Cen giants (Cunha et al. 2003) is not straightforward, as the latter two have star forc 2004 RAS, MNRAS 000, 1­6


The origin of fluorine in the Milky Way

5

0

-0.2

sections alluded to in Section 2.1 be confirmed (Heger et al. 2004), the concurrent factor of 2 reduction in SNe II 19 F production would improve the agreement of the model with the observed F/O ratio in Cen giants. This would consequently strengthen our conclusions which already support a picture whereby these giants have been polluted by earlier generations of SNe II ejecta.

-0.4

-0.6 7.8 8 8.2 8.4 8.6 8.8 0.6 0.4 0.2 0

ACKNOWLEDGMENTS We acknowledge the financial support of the Australian Research Council through its Discovery Pro ject and Linkage International schemes, and the Victorian Partnership for Advanced Computing through its Expertise Grant program. We thank Maria Lugaro for discussion and help, and the referee, Marcel Arnould, for his comments. We also acknowledge the efforts of toothpaste manufacturers around the world in highlighting the importance of fluorine production throughout the Universe.

a 0.5

b

0

-0.5

-1

7

7.5

8

8.5

9

1

0.5

0

-0.5

REFERENCES
Figure 4. (a): [F/O] as a function of A(O) for the MW mo dels (MWa, solid line; MWb, dotted; MWc, short-dashed). Also shown are the values observed in Milky Way, LMC, and Cen giants (crosses, b oxes and hexagons, resp ectively). (b): [F/O] as a function of [O/Fe], compared with the IMF-weighted [O/Fe] yields for SNe I I (op en triangles). Within the op en triangles, `0' corresp onds to Z=0; `1', to Z=1.9â10-6 ; `2', to Z=1.9â10-4 ; `3', to Z=1.9â10-3 ; `4', to Z=1.9â10-2 . The upp er panels represent enlargements of the framed regions delineated in the corresp onding b ottom panels.

mation (and therefore chemical evolution) histories different from that of the MW. However, it is interesting to speculate on the possible origin of fluorine in Cen, given the unique nature of this "globular cluster" (e.g. Smith 2003). Specifically, Cen is the most massive Galactic cluster, and unlike most globulars, possesses a significant spread in metallicity ( 1.5 dex) amongst its stellar population. It has been suggested that Cen is actually the remnant core of a tidallydisrupted dwarf galaxy (Bekki & Freeman 2003). Such a scenario could naturally drive radial gas inflows to the dwarf nucleus, potentially triggering starbursts. Interestingly, SNe II ejecta are characterised by low [F/O] I M F (Figure 2c) and high [O/Fe] I M F (Figure 4b), whereas AGB ejecta have higher [F/O] I M F (Figure 2d). The observed Cen giants have primarily low [F/O] (Figures 2a ­ 2b, 4a ­ 4b) and high [O/Fe] (Figure 4b) values, consistent with a picture in which their interiors have been polluted by the ejecta of an earlier generation of SNe II, but not from a comparable generation of AGB. Given that the observed oxygen abundance in such Cen giants is similar to that seen in comparable LMC and MW giants (Figure 4a), this would suggest that the chemical enrichment of Cen proceeded on a short timescale (to avoid pollution from the lower mass progenitors to the AGB stars) and in an inhomogeneous manner (given the significant scatter in observed fluorine abundances), as discussed previously by Cunha et al. (2003). Should the (downward) revised neutrino cross
c 2004 RAS, MNRAS 000, 1­6

Alib´ A., Labay J., Canal R., 2001, A&A, 370, 1103 es Allende Prieto C., Lambert D.L., Asplund M., 2001, ApJ, 556, L63 Bekki K., Freeman K.C., 2003, MNRAS, 346, L11 Bertelli G., Nasi E., 2001, AJ, 121, 1013 Cappellaro E., Evans R., Turatto M., 1999, A&A, 351, 459 Cunha K., Smith V.V., Lambert D.L., Hinkle K.H., 2003, AJ, 126, 1305 Dray L.M., Tout C.A., Karakas A.I., Lattanzio J.C., 2003, MNRAS, 338, 973 Fenner Y., Gibson B.K., 2003, PASA, 20, 189 Forestini M., Goriely S., Jorissen A., Arnould M., 1992, A&A, 261, 157 Frost C.A., Lattanzio J.C., 1996, ApJ, 473, 383 Frost C.A., Cannon R.C., Lattanzio J.C., Wood P.R., Forestini M., 1998, A&A, 332, L17 Gibson B.K., Fenner Y., Renda A., Kawata D., Lee H.-c., 2003, PASA, 20, 401 Heger A., Kolbe E., Haxton W.C., Langanke K., MartinezPinedo G., Woosley S.E., 2004 (astro-ph/0307546) Holweger H., 2001, in Wimmer-Schweingruber R.F. ed, American Institute of Physics Conference Series, Vol. 598: "Solar and Galactic Composition", p. 23 Iglesias C.A., Rogers F.J., 1996, ApJ, 464, 943 Iwamoto K., Brachwitz F., Nomoto K., Kishimoto N., Umeda H., Hix W.R., Thielemann F.-K., 1999, ApJS, 125, 439 Jorissen A., Smith V.V., Lambert D.L., 1992, A&A, 261, 164 Karakas A.I., Lattanzio J.C., Pols O.R., 2002, PASA, 19, 515 Karakas A.I., Lattanzio J.C., 2003, PASA, 20, 279 Kroupa P., Tout C.A., Gilmore G., 1993, MNRAS, 262, 545 Limongi M., Chieffi A., 2003, ApJ, 592, 404 Lugaro M., G¨ orres J., Wiescher M., Ugalde C., Karakas A.I., Lattanzio J.C., Cannon R., 2004, submitted Meynet G., Arnould M., 2000, A&A, 355, 176 Mowlavi N., Jorissen A., Arnould M., 1998, A&A, 334, 153


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sources of uncertainty in predicting fluorine nucleosynthesis in AGB stars relate to the adopted reaction rates, especially 14 C (, )18 O and 19 F (, p)22 N e, and the treatment of the nucleosynthesis occurring during the convective thermal pulses and the interpulse periods (Lugaro et al. 2004; see also Section 2.2).

Myra E.S., Burrows A., 1990, ApJ, 364, 222 Rana N.C., 1991, ARA&A, 29, 129 Renzini A., Voli M., 1981, A&A, 94, 175 Russell S.C., Dopita M.A., 1992, ApJ, 384, 508 Schaller G., Schaerer D., Meynet G., Maeder A., 1992, A&AS, 96, 269 Smith V.V., 2003, in McWilliam A., Rauch M. eds, Carnegie Observatories Astrophysics Series, Vol. 4: "Origin and Evolution of the Elements", (Pasadena: Carnegie Observatories, http:// www.ociw.edu/ociw/symposia/series/ symposium4/proceedings.html) Smith V.V., Cunha K., Hinkle K.H., Blum R.D., 2004, submitted Timmes F.X., Woosley S.E., Weaver T.A., 1995, ApJS, 98, 617 Vassiliadis E., Wood P.R., 1993, ApJ, 413, 641 Woosley S.E., Haxton W.C., 1988, Nature, 334, 45 Woosley S.E., Hartmann D.H., Hoffman R.D., Haxton W.C., 1990, ApJ, 356, 272 Woosley S.E., Weaver T.A., 1995, ApJS, 101, 181 Woosley S.E., Heger A., Weaver T.A., 2002, Rev. Mod. Phys., 74, 1015
A This paper has been typeset from a TEX/ L TEX file prepared by the author.

APPENDIX A: ASYMPTOTIC GIANT BRANCH 19 F AND 16,17,18 O YIELDS The yields employed here have been derived via the following: Y
19 F , O

(Z ) = X
i19 F, O

Y

net19 F, O

+
r em

(Z ) â [m - m

(Z )].

(A1)

Here, Y19 F, O (Z ) is the overall yield, Xi19 F, O (Z ) is the initial mass fraction of the element within a star of mass m and metallicity Z , [m - m rem (Z )] is the total mass ejected during the stellar lifetime, and Ynet19 F, O is the net yield. We calculate XiO and YnetO as, respectively: X Y
netO iO

=X

i16 O

+X

i17 O

+X

i18 O

; .

(A2) (A3)

=Y

net16 O

+Y

net17 O

+Y

net18 O

The yields are the result of full evolutionary calculations using the Mount Stromlo Stellar Structure Code (e.g. Karakas & Lattanzio 2003). We use the standard Reimers massloss formula on the first giant branch and the Vassiliadis & Wood (1993) formula during the AGB evolution. Opacities are from OPAL (Iglesias & Rogers 1996). The models with Z = 0.02 and 0.0001 used scaled solar abundances, whereas those for Z = 0.004 and 0.008 are appropriate to the Small and Large Magellanic Clouds, respectively, and are taken from Russell & Dopita (1992). Numerical problems during the third dredge-up are handled in the way described in Frost & Lattanzio (1996). A mixing length of 1.75 pressure scale-heights has been used. A main uncertainty in the predicted yields for fluorine is the occurrence and dimension of the partial mixing zone. Note that this partial mixing zone was ignored in the models presented here. Primary
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The origin of fluorine in the Milky Way
Table A1. AGB
19

7

F and

16,17,18

O yields (M ).

Z 0.0001 m 1.0 1.25 1.75 2.0 2.25 2.5 3.0 4.0 5.0 Z 0.004 m 1.0 1.25 1.5 1.75 1.9 2.25 2.5 3.0 3.5 4.0 5.0 6.0 Z 0.008 m 1.0 1.25 1.5 1.75 1.9 2.25 2.5 3.5 4.0 5.0 6.0 Z 0.02 m 1.0 1.25 1.5 1.75 1.9 2.0 2.25 3.0 3.5 4.0 5.0 6.0 6.5 m r em 0.57309 0.578 0.60 0.63 0.636 0.64 0.65 0.682 0.716 0.791 0.878 0.929 0.964 m r em 0.5998 0.61 0.63 0.64 0.64 0.65 0.67 0.77 0.84 0.89 0.95 m r em 0.63 0.64 0.646 0.65 0.65 0.66 0.68 0.73 0.82 0.86 0.91 0.97 m r em 0.65 0.65 0.67 0.70 0.72 0.737 0.820 0.868 0.924

Xi19 F 2.31800e-09 Ynet 19 FAGB 0.51379E-08 0.21202E-06 0.54275E-05 0.10527E-04 0.13578E-04 0.45574E-05 0.62016E-07 0.27367E-08 -0.34142E-08 Xi19 F 1.69218E-07 Ynet 19 FAGB 0.94462E-09 0.62277E-08 0.22912E-07 0.17284E-06 0.49608E-06 0.38720E-05 0.80892E-05 0.68954E-05 0.76727E-06 0.55804E-07 -0.65262E-06 -0.84234E-06 Xi19 F 3.25423E-07 Ynet 19 FAGB 0.23717E-08 0.11401E-07 0.20168E-07 0.90125E-07 0.18749E-06 0.14941E-05 0.30357E-05 0.22972E-05 0.66878E-06 -0.12324E-05 -0.16173E-05 Xi19 F 4.63728E-07 Ynet 19 FAGB 0.36025E-08 0.15858E-07 0.25014E-07 0.29957E-07 0.28199E-07 0.27049E-07 0.12064E-06 0.34981E-05 0.49320E-05 0.14844E-05 0.86376E-06 -0.22147E-05 -0.24583E-05

Xi16 O 4.44786e-05 Ynet 16 OAGB 0.52869E-05 0.69519E-04 0.31623E-03 0.41221E-03 0.51952E-03 0.13068E-02 0.13776E-02 0.16630E-02 0.76699E-03 Xi16 O 1.28324E-03 Ynet 16 OAGB -0.29158E-05 -0.20669E-05 0.19546E-04 0.75738E-04 0.95973E-04 0.14749E-03 0.93431E-04 0.16497E-04 0.62994E-04 0.68820E-05 -0.19071E-02 -0.39748E-02 Xi16 O 2.64027E-03 Ynet 16 OAGB -0.26083E-05 -0.40814E-05 -0.45432E-05 0.22020E-04 0.38094E-04 0.85696E-05 -0.12452E-03 -0.37752E-03 -0.30252E-03 -0.24193E-02 -0.57759E-02 Xi16 O 9.60266E-03 Ynet 16 OAGB -0.61933E-06 -0.22254E-05 -0.32904E-05 -0.54827E-05 -0.10482E-04 -0.17893E-04 -0.20851E-03 -0.11882E-02 -0.17086E-02 -0.16979E-02 -0.39096E-02 -0.83059E-02 -0.97865E-02

Xi17 O 1.93800e-08 Ynet 17 OAGB 0.38546E-07 0.72848E-07 0.60806E-06 0.78911E-06 0.41433E-06 0.74846E-06 0.20197E-05 0.36273E-05 0.19749E-05 Xi17 O 1.41477E-06 Ynet 17 OAGB 0.22240E-06 0.49241E-06 0.15093E-05 0.44914E-05 0.75796E-05 0.11186E-04 0.98989E-05 0.10204E-04 0.43600E-05 0.17349E-05 0.20350E-05 0.10162E-05 Xi17 O 2.72075E-06 Ynet 17 OAGB 0.28610E-06 0.65704E-06 0.19727E-05 0.60267E-05 0.95185E-05 0.16553E-04 0.14976E-04 0.16132E-04 0.14747E-04 0.68396E-05 0.80141E-05 Xi17 O 3.87707E-06 Ynet 17 OAGB 0.34219E-06 0.97603E-06 0.31910E-05 0.90611E-05 0.14418E-04 0.19332E-04 0.44894E-04 0.51877E-04 0.57427E-04 0.55128E-04 0.46522E-04 0.78725E-04 0.98794E-04

Xi18 O 1.08000e-07 Ynet 18 OAGB -0.59145E-08 -0.14220E-07 0.21305E-07 0.66983E-07 0.99055E-07 -0.17541E-07 -0.23173E-06 -0.33571E-06 -0.41578E-06 Xi18 O 7.88419E-06 Ynet 18 OAGB -0.25334E-06 -0.89206E-06 -0.15635E-05 -0.25162E-05 -0.32065E-05 -0.43546E-05 -0.54950E-05 -0.69500E-05 -0.19736E-04 -0.24560E-04 -0.32029E-04 -0.39405E-04 Xi18 O 1.51621E-05 Ynet 18 OAGB -0.39665E-06 -0.15151E-05 -0.28219E-05 -0.45889E-05 -0.53377E-05 -0.74497E-05 -0.90888E-05 -0.14133E-04 -0.23226E-04 -0.61869E-04 -0.75982E-04 Xi18 O 2.16506E-05 Ynet 18 OAGB -0.41416E-06 -0.18066E-05 -0.33975E-05 -0.52622E-05 -0.60505E-05 -0.66536E-05 -0.81507E-05 -0.13306E-04 -0.17219E-04 -0.19531E-04 -0.70118E-04 -0.10882E-03 -0.11879E-03

c 2004 RAS, MNRAS 000, 1­6