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Astron. Astrophys. 348, 211-221 (1999)

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5. Discussion

5.1. Stellar masses

According to standard stellar models the depletion of lithium is a strong function of stellar mass (Pinsonneault et al. 1992). Hence, it is of considerable interest to determine the masses of the stars. This can be done by comparing [FORMULA] and absolute magnitude, [FORMULA], with mass tracks from stellar evolution calculations.

Using the apparent magnitudes given in Table 1 and parallaxes from The Hipparcos and Tycho Catalogues (ESA 1997) the absolute magnitudes are calculated (Table 6), and the stars are plotted in the [FORMULA] -[FORMULA] diagram (Fig. 8). The mass tracks shown are from the new, [FORMULA]-element enhanced, evolutionary models of VandenBerg et al. (1999). Interpolation between the mass tracks (taking into account their dependence on [Fe/H]) leads to the masses given in Table 6, and from the corresponding isochrones the stellar ages given are obtained.

[FIGURE] Fig. 8. Position of the stars in the [FORMULA] -[FORMULA] diagram compared with mass tracks from VandenBerg et al. (1999). Masses are given in units of the solar mass. The full drawn lines refer to [FORMULA] (equal to the metallicity of HD 68284 and HD 130551) and the dotted lines to [FORMULA] (approximately equal to [Fe/H] of the other stars). Both sets of tracks have [[FORMULA]/Fe] = 0.3. The error bars in the x-direction correspond to [FORMULA] ([FORMULA]) = [FORMULA] K and those in the y-direction to the errors of the Hipparcos parallaxes


Table 6. Absolute magnitudes computed from [FORMULA] and Hipparcos parallaxes and masses and ages derived from stellar evolutionary tracks and isochrones of VandenBerg et al. (1999)

The errors of the masses and ages given in Table 6 are standard errors corresponding to the adopted errors of [FORMULA] and [FORMULA]. Additional errors may be present due to inadequate stellar models and uncertainties in the calibration of [FORMULA] and the bolometric correction. Such errors are, however, more systematic and are expected to affect all stars with about the same amount. Hence, we conclude from Table 6 that the two stars for which 6Li has been detected (HD 68284 and HD 130551) have significantly higher masses than the three stars with no 6Li present in their atmospheres. This makes sense, because the depth of the convection zone of a star on the main sequence decreases rapidly as a function of increasing mass. Hence, according to standard stellar models without mixing, the depletion of 6Li is less severe in the more massive stars. In this connection we note that although HD 68284 is already on the subgiant branch and the coolest of the stars, it has spent most of its life as a main sequence star at [FORMULA] [FORMULA] 6300 K.

5.2. Galactic evolution and stellar depletion of 6Li

Interpretation of the novel result of this paper - the detection and quantitative measurement of the 6Li abundance in two old metal-poor disk stars - is contingent on two factors: (i) the expected evolution of the interstellar 6Li abundance with metallicity, and (ii) the depletion of the stellar 6Li abundance by the convective mixing that occurs in the pre-main sequence phase, and the additional depletion occurring on the main sequence.

As is all too well known, prediction of Li depletion by main sequence stars and subgiants is an imprecise art. Standard models by Pinsonneault et al. (1992) predict loss of lithium in the pre-main sequence phase and no subsequent loss for stars of the mass of our quintet. Depletions for masses of up to 0.85[FORMULA] and metallicities corresponding to [Fe/H] = -2.6 and -1.6 are computed by Pinsonneault et al. For their 0.85[FORMULA] model, the predicted 7Li-depletions are negligible and the 6Li-depletions are 0.3 dex at [Fe/H] = -1.6 and by extrapolation less than 0.05 dex at [Fe/H] = -2.6. Extrapolation to [Fe/H] [FORMULA] -0.7 is uncertain but these depletions decrease with increasing mass such that our stars might be anticipated to have lost little, if any, 6Li. Cayrel et al. (1999b) report calculations that essentially confirm the above pre-main sequence depletions but predict a substantial continuing depletion of 6Li on the main sequence. At [FORMULA] and [Fe/H] = -1.5, a total 6Li depletion of about 0.7 dex is predicted in contrast to the 0.3 dex expected by Pinsonneault et al. Consideration of non-standard physics, especially rotationally-induced mixing will result in likely larger and as yet more uncertain depletions - see, for example, the state of the art calculations by Pinsonneault et al. In summary, depletion of 6Li is to be expected but, at present, the magnitude of this depletion is uncertain with even standard calculations unavailable for the mass and metallicity of our old disk stars.

Encouraged by recent observations of 6Li, Be, and B several predictions about the galactic chemical evolution of Li, Be, and B have appeared. Behind such predictions are assumptions about the nucleosynthetic processes of Li, Be, and B manufacture that demand assumptions about the early Galaxy, especially about the cosmic rays that permeated the halo and then the disk. Qualitatively, the key nucleosynthetic processes are known: (i) the Big Bang provided only the 7Li (in addition to H, 2H, 3He, and 4He) that is widely considered to account for the observed Li abundance of the warm halo stars, the so-called Spite plateau; (ii) interactions between standard GCR and ISM and/or interactions between fast C,N,O nuclei from superbubbles with H or He in the ISM provide Li, Be, and B by spallation processes (e.g., O + p [FORMULA] Be) and Li through the fusion process [FORMULA]Li and 7Li; (iii) neutrino-induced spallation processes in Type II supernovae that may provide 7Li and 11B.

A key facet of this suite of processes is that beryllium with 9Be as the single stable isotope is produced solely by spallation of C,N,O in flight or at rest. Hence, observed beryllium abundances may be used to calibrate the yields of cosmic ray spallation. This is especially useful now that there are extensive measurements of the Be abundance in disk and halo dwarf stars. The relative yields of light nuclides, for example 6Li to 9Be, are essentially independent of the cosmic ray spectrum unless there is a large excess of low energy cosmic rays ([FORMULA] MeV nucleon-1) with respect to higher energy particles. This happy circumstance arises because above the similar threshold energies for the different processes (e.g., 9Be from p + O and 10B also from p + O), the spallation cross-sections are almost energy independent. That ratios of yields are independent of the form of the (high) energy spectrum was well illustrated by Ramaty et al. (1996). At energies around the threshold energies for the various processes, the relative yields are energy and composition dependent. Moreover, Li production occurs also through [FORMULA] fusion reactions that do not synthesize Be and B.

The B/Be ratio of halo stars is consistent within measurement uncertainty with production by spallation: Duncan et al. (1997) estimated B/Be = 15 [FORMULA] 3 and García López et al. (1998) from a similar dataset of HST spectra found B/Be = 17 [FORMULA] 10. Relativistic cosmic rays and the suite of (p,[FORMULA]) on (C,N,O) processes are predicted to give B/Be [FORMULA] - see Ramaty et al. (1996) for predicted B/Be ratios as a function of cosmic ray energy and composition. It has long been known that spallation by relativistic cosmic rays is inadequate to account for the solar system's 11B/10B ratio which at 4.05 exceeds the prediction of about 2.5. Low energy spallation or a contribution from Type II supernovae are needed to resolve this discrepancy.

These uncertainties aside, the Be observations are a reasonably firm basis from which to predict the 6Li abundances provided by spallation. Smith et al. (1998) discussed the prediction of 6Li abundances from observed Be abundances - see the long-dashed line in Fig. 9, where beryllium abundances are taken from Gilmore et al. (1992) and Boesgaard et al. (1999b). Predicted 6Li abundances are about a factor of 10 less than the observed 6Li abundances in the halo stars HD 84937 and BD +26o3578 but exceed the 6Li abundances reported here for the disk stars HD 68284 and HD 130551 by about a factor of 3. Since 6Li has almost certainly been depleted during pre-main sequence evolution and possibly during residence on the main sequence, the initial or interstellar 6Li abundance for the halo stars was higher than now observed. The required additional 6Li is probably primarily a product of cosmic ray [FORMULA] fusion production.

[FIGURE] Fig. 9. Abundances of lithium and beryllium as a function of [Fe/H] for 9 halo stars from Smith et al. (1998) and 5 disk stars from the present paper. Open circles indicate the total Li abundance and filled circles the 6Li abundance or an upper limit. Open squares refer to the Be abundance adopted from Gilmore et al. (1992) and Boesgaard et al. (1999b). The big symbols indicate meteoritic abundances from Anders & Grevesse (1989). The upper full drawn line is a fit to the `Spite plateau' of lithium abundances for [FORMULA] and to the upper envelope of the Li abundance distribution for disk stars (see Fig. 7 of Lambert et al. 1991). The lower full drawn line is a linear fit to the beryllium abundances with a slope of one, and the long-dashed line shows the corresponding relation for 6Li if 6Li /Be = 5.8 as found in meteorites and as predicted from spallation of CNO nuclei by high energy cosmic rays. The dotted line represents the evolution of 6Li in the model of Fields & Olive (1999a,b), the dashed-dotted line the model of Vangioni-Flam et al. (1999) and the short-dashed lines refer to the model of Yoshii et al. (1997) for the halo and the disk, respectively

Predictions of the growth of 6Li in the Galaxy made recently by Fields & Olive (1999a,b), Vangioni-Flam et al. (1999) and Yoshii et al. (1997) are shown in Fig. 9. These call on the same production processes but in different proportions.

Fields & Olive discuss what they term the standard picture of galactic cosmic ray nucleosynthesis in a model galaxy. The key assumptions are that the cosmic rays always had the composition of the ambient interstellar gas (i.e., they were very CNO-poor early in the life of the Galaxy), the energy spectrum of the cosmic rays was that measured for contemporary cosmic rays in the solar neighborhood (i.e., relativistic energies are dominant), and the cosmic ray flux has been proportional to the local supernova rate, and scaled so that solar abundances of 6Li, B, and 10B are reproduced. These assumptions with a simple chemical evolution code (Fields & Olive report results for the canonical closed box) lead to the predicted run of the 6Li abundances with [Fe/H] where iron is a product of stellar nucleosynthesis with yields from Woosley & Weaver (1995) and a standard initial mass function. The key novel ingredient in the otherwise familiar calculation is the incorporation of recent measurements of the oxygen abundance in halo stars that indicate [O/Fe] increasing with decreasing [Fe/H] (Israelian et al. 1998; Boesgaard et al. 1999a). A higher O abundance increases the yields of spallation products. (A `fudge' is needed as the O/Fe from these recent observations is considerably higher than predicted for Type II supernovae). The predicted 6Li vs [Fe/H] relation is shown by the dotted line in Fig. 9. A large part of the increase in the 6Li prediction at low [Fe/H] over the simple expectation from spallation is due to the inclusion of the [FORMULA] fusion reactions but the use of the observed O abundances through the associated contribution from p + O spallation appears necessary to match the observed 6Li abundances of the halo stars. Fields & Olive adjust their model to reproduce the solar 6Li which also accounts well for the Be and B abundances of the sun, disk and halo stars.

Vangioni-Flam et al. (1999) incorporate a different mix of the light element producing processes into their chemical evolution model. In particular, they invoke low energy nuclei that they associate with the acceleration of supernovae ejecta in the superbubbles created collectively by winds from the massive stars in OB associations. (`Low energy' refers to energies close to the threshold energies of the spallation and fusion reactions.) A key point about this component is that the He, C, and O abundances of the ejecta are considered to be much higher than in the halo interstellar medium and, then, the dominant spallation process is between (say) O in the ejecta and protons in the interstellar gas whereas in the standard picture (Fields & Olive 1999a,b) the leading process is between protons in the cosmic rays and (say) O in the interstellar gas. In Fig. 9, we show predictions (dashed-dotted line) from a model adjusted to fit the measured 6Li abundances of the two halo stars. This model predicts a 6Li abundance at [Fe/H] = 0 that exceeds slightly the solar abundance.

The close correspondence between the two predictions is unlikely to be a fair measure of the uncertainties in predicting the 6Li abundance of 1 [FORMULA], [Fe/H] [FORMULA] disk stars starting from either the solar 6Li abundance or the 6Li abundance of halo stars. While the 6Li contribution from spallation by galactic high-energy cosmic rays is rather well constrained by the observed Be abundance, there are no comparable constraints on the contributions of the fusion reactions and of spallation by low energy cosmic rays.

That the range of permissible predictions is wider than perhaps suggested by the above two recent papers is suggested by an earlier discussion by Yoshii et al. (1997). The prediction shown in Fig. 9 is from their Fig. 2 1 for a model that considers high-energy cosmic rays with cosmic ray protons and alphas spallating interstellar C,N, and O nuclei as well as [FORMULA] reactions. The cosmic ray flux was assumed to increase with decreasing metallicity. Different models are adopted for the halo and disk. This model predicts a rather shallow decline of the 6Li abundance in the halo, and a steeper increase in the disk. Almost all of the 6Li in the halo is the product of the [FORMULA] reactions. The prediction fails by about 0.4 dex to account for the solar 6Li abundance, so that the discrepancy between prediction and observation for our disk stars might be larger for a revised model that did reproduce the solar 6Li abundance.

Our old disk stars with detectable 6Li have Li abundances slightly in excess of the Spite plateau. If, as standard models of pre-main sequence and main sequence evolution predict, the depletion of 7Li has been extremely slight, we may use the observed abundance and the prediction that cosmic ray production of the Li isotopes gives an isotopic ratio 7Li/6Li [FORMULA] to estimate the contribution of 6Li from cosmic rays. Consider HD 68284 with a Li abundance log[FORMULA](Li) = 2.35. This is higher than the Spite plateau of log[FORMULA](Li) = 2.21 (Smith et al. 1998). On the assumption that plateau stars have not depleted Li, the increase of Li in HD 68284 corresponds to Li [FORMULA] on the scale H =1012. If cosmic rays were entirely responsible for this increase, a division 7Li [FORMULA] 36 and 6Li [FORMULA] 24 is appropriate for a production ratio 7Li/6Li [FORMULA]. The Be abundance implies 6Li [FORMULA] 30 so that at this metallicity spallation rather than fusion reactions may be dominant. The observed 6Li abundance is 6Li [FORMULA] 10. (HD 130551 provides similar figures.) Given that 6Li has assuredly been depleted to at least a modest extent, this elementary dissection of the observed Li abundance reveals no obvious difficulty with a cosmic ray contribution to the Li isotopes.

Recently, Ryan et al. (1999) have argued on the basis of lithium abundances of Spite plateau stars in the range [FORMULA] [Fe/H] [FORMULA] that the plateau has a metallicity dependence due to the manufacture of the Li isotopes by cosmic rays. They consider the primordial abundance to be log[FORMULA](Li) [FORMULA] 2.00 at [Fe/H] = -3.5. If Smith et al.'s [FORMULA] -scale is adopted, this abundance is raised to be about 2.12 according to 4 stars common to both analyses. This and Ryan et al.'s metallicity dependence predict HD 68284 to have a Li abundance of 2.44 which is similar to the observed value of 2.35. Relative to a plateau of 2.12, the observed abundance implies cosmic rays have added Li in the proportion 7Li = 54 and 6Li = 36 which are consistent with our observations provided that 6Li has been depleted by about 0.6 dex. At some point in the evolution of the Galaxy, sources (presumably stellar) contributed 7Li with little or no 6Li in order to raise the 7Li/6Li ratio to the solar ratio of 12.5. Inclusion of such a contribution in the above argument reduces the 6Li inferred from the increase in Li abundance over the plateau's value.

The preceding argument may be inverted: the predicted growth of 6Li with [Fe/H] may be used to infer the 7Li abundance. For example, the models proposed by Fields & Olive, and Vangioni-Flam et al. predict a 6Li abundance in the ISM at the birth of HD 68284 and HD 130551 of about 120, a factor of 12 greater than observed. Assuming again a production ratio of 6Li/7Li = 1.5 the attendant 7Li abundance is 180. Added to the primordial 7Li abundance of 160 this implies a total 7Li abundance of 340 (log[FORMULA](7Li) = 2.53), a value considerably greater than the observed value of about 200. The obvious implications are that either the predicted 6Li abundance is greatly overestimated or 7Li has been depleted by about 0.2 dex. In sharp contrast, Yoshii et al.'s prediction is a 6Li abundance of about 30 providing a total 7Li abundance of 205 or log[FORMULA](Li) = 2.31, in excellent agreement with the observed 7Li abundances of HD 68284 and HD 130551. This model fails, however, to account for the meteoritic 6Li abundance by a large amount.

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© European Southern Observatory (ESO) 1999

Online publication: July 16, 1999