Astron. Astrophys. 319, 593-606 (1997)

3. Model atmospheres

For the present investigation we used version 9 of the ATLAS code to compute the atmospheric models appropriate for metal-poor stars. This version of the ATLAS code (Kurucz 1993) differs from previous ATLAS versions mostly for the opacity and for the way in which the mixing-length convection is handled. In the ATLAS9 models the opacity distribution functions (ODFs), which account for the line opacity, were computed with a much larger number of atomic lines than in the previous versions and, for cool stars, molecular lines were also added. Continous opacities were implemented by taking into account also the contribution of the OH and CH molecules. Convection is still based on the mixing-length approach, but two modifications have been made in ATLAS9; the first one allows for a horizontally averaged opacity and the second one allows for an approximate overshooting (Castelli 1996).

As far as convection is concerned, Castelli, Gratton and Kurucz (1996) have shown that the first modification of the mixing-length has negligible effects on the results, while the second one alters the whole structure of the models, mostly when   is between 5500 K and 8000 K. Fig. 1 compares the T-log  relations for   = 5750 K, log g=3.5, and [M/H]=-1.0, with and without overshooting. The zone of formation of the Be II lines is around log where the temperature is higher for models with overshooting. While the different convection affects the whole structure, the different chemical composition due to the enhancement of the -elements, mostly affects the structure of the deepest layers, as can be seen from the figure. The discrepancy between models with and without overshooting changes with log g, and metallicity. The Kurucz solar model computed with overshooting fits the observations very well, but for other stars no overshooting models generally yield more consistent   values when different methods are used to derive them, such as methods based on colors, Balmer profiles, and the infrared flux. A test on Procyon has also shown that, for this star, no overshooting models give parameters which are more consistent with the fundamental values, derived from model independent methods.

Fig. 1. Temperature structure for models with =5750, = 3.50 and metallicity [Fe/H]=-1.0: enhanced with (x) and without (squares) overshooting; no enhancement with(+) and without (triangles) overshooting

On the basis of these results and also because the ad hoc inclusion of the overshoot in the ATLAS9 code is not really the physical overshoot (Freytag 1996), we decided to use for this investigation ATLAS9 models with the overshooting option switched off. We kept the same value =1.25 adopted by Kurucz for the mixing-length to pressure height scale ratio, because we found that it well reproduces the solar irradiance also when overshooting is dropped. The choice of the mixing length in the range from 0.5 to 2.0 for the pressure scale height makes negligible differences (less than 0.01 dex) over the whole grid, and the adopted microturbulent velocity does not affect the derived Be abundance for the range of equivalent width under consideration.

We used the -enhanced opacity distribution functions (ODFs) provided by Kurucz (1993a), which are obtained by assuming that all   elements are enhanced by 0.4 dex over iron. This is certainly a more realistic chemical composition for Pop II stars than the usual approach which uses the ODFs with solar-scaled abundances. Furthermore, for these ODFs the solar iron abundances is log ( / )=-4.53 (Hannaford et al 1992), instead of log ( / )=-4.37 (Anders and Grevesse 1989), which was used for all the ODF's for solar and solar-scaled abundances.

We selected the ODFs computed with a microturbulent velocity of 1 to allow for very low microturbulent velocities, as can be found in some Pop II stars, instead of the 2 of the Kurucz (1993a) grid. The grid covers the range from 4750 K to 6250 K in   at steps of 250 K, from 2.50 to 4.75 in   at steps of 0.25 and from -0.5 to -3.00 in [Fe/H]  at steps of 0.5. For all the models of this grid we also computed the emergent flux and the Johnson UBV and the Strömgren uvby colour indices. Colour indices were then used to derive effective temperature and surface gravity for all the stars of our sample, except HD 218502 for which no observed photometric Johnson or Strömgren indices have been found in the literature. Model parameters for the stars of our sample will be discussed in the next section.

In order to appreciate the differences with the Kurucz (1993a) grid we computed models for = 5250, 5750, 6250 K, = 3.0, 3.5, 4.0 and metallicity [Fe/H]= -1.0, -1.5, -2.5 with the enhanced ODFs and the overshooting option, and other models with the same parameters, but using the ODFs without enhancement and overshooting.

For all these models, as well as for those from our grid and from the Kurucz(1993a) grid, we computed the curves of growth  for the Be II 313.1065 nm line. Fig. 2 shows the different curves of growth for Be II 313.1065 nm corresponding to the same model parameters   = 5750 K, log g=3.5, and [M/H]=-1.0 and to the different T-log  relations displayed in Fig. 1.

Fig. 2. Curves of growth for the BeII 313.1065 nm line for models with =5750, log g = 3.50 and metallicity [Fe/H]=-1.0: enhanced with (x) and without (squares) overshooting; no enhancement with(+) and without (triangles) overshooting

In the very low metallicity domain, i.e. [Fe/H]  -2.0, the effect of   element enhancement is very small, of the order of 0.01 dex at most, with the   enhanced models yielding higher abundances. On the other hand, the effect of overshooting is not negligible and the models with overshooting yield abundances which are higher by as much as 0.08 dex. This difference is almost constant at all temperatures.

In the low metallicity domain (i.e. [Fe/H]  between -2.0 and -1.0) the effect of overshooting is of the same order of magnitude as in the very low metallicity regime, but the effect of   enhancement begins to be notable in particular for the cool models. Models with enhanced -elements yield higher abundances of the order of 0.08 dex at = 5250 K , but of only 0.03 dex at = 6000 K and less than 0.01 dex at =6250 K. No overshooting in the models implies lower abundances, while   enhancement implies higher abundances so that there is some compensation between the two effects. The result of these opposite behaviours is that while our models yield abundances larger than those of the Kurucz 1993a grid at low-temperatures, the reverse is true at the high temperature end.

For solar metallicities there is little or no difference in the Be abundances with respect to the implementation of overshooting in the models. This is because metal-poor models have convective zones which start at much shallower depths (D'Antona and Mazzitelli 1984).

Our models yield abundances which are identical within few hundredths of a dex to those obtained using Kurucz 1979 models and are therefore directly comparable with the Be literature values which are obtained mostly using those models. This also implies that the much larger number of lines included in the computations of the ODFs implemented in version 9 of the ATLAS code has relatively small effects on the temperature structure of the models. We stress that our choice of switching off overshooting makes the present analysis consistent with the older grids of models which make use of either Gustafsson-Bell or old (i.e. computed with version 8 or earlier ones of the ATLAS code) Kurucz models.

In conclusion, the differences in Be abundances found at low metallicities when using the Kurucz 1993a models, with respect to the Kurucz 1979 ones, are due to the presence of overshooting. The low effect on the metal-poor stars of the increased blanketing in the new models is explained by the small importance of the new lines in the metal poor stars. In fact, the large number of atomic lines added for computing the new ODFs arise from high-excited states and are therefore weak lines in solar metallicity stars. The effect of the molecular lines has still to be investigated. The abundances derived from lines whose depth of formation is close to the top of the convection zone, as for Be II and also for LiI, are quite sensitive to the assumptions made on overshooting (Molaro et al 1995b, c).

This extensive theoretical grid allowed us to perform an efficient comparison between observed and computed quantities (spectra and colours) and also to experiment the effects of small changes in the atmospheric parameters on the derived abundances. In addition to the models of the grid, more models were computed with atmospheric parameters appropriate for our program stars (see next section), including a small number of models with [Fe/H]  = -0.5 for which we used ODFs with solar-scaled abundances rather than with   enhanced, the other assumptions being the same as the more metal-weak models.

Non-LTE effects have been shown to be negligible in the sun by Chmielewski et al (1975). For metal-poor stars absolute NLTE corrections to the Be abundances have been shown to be lower than 0.1 dex by Garcia Lopez et al (1995) and Kiselman & Carlsson (1995).

© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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