5 Determination of the lithium abundances

The analysis was performed by comparing our observations with a grid of synthetic spectra with different temperatures and lithium abundances.

The synthetic spectra were calculated with the Turbospectrum program (Alvarez & Plez 1998), using MARCS model atmospheres (Gustafsson et al. 1975; Plez et al. 1992; Asplund et al. 1997; Gustafsson et al. 2003). The models and the spectra are spherically symmetric, at LTE, and include up-to-date continuous and line opacities for a large number of atoms and molecules. Some details are provided in Hill et al. (2002). The line lists for VO, ZrO, CN and TiO (Plez 1998), and atomic lines (VALD, Kupka et al. 1999) were used. The spectra were initially computed at a resolution of 0.01 Å, and then degraded to match the resolution of the observations.

The stellar parameters needed for synthetic spectra computation ( $T_{\rm eff}$, $\log g$) were initially derived from the photometry. The K band bolometric correction BC_K was obtained by using the BC_K versus V-K relation by (Bessell et al. 1998, BCP98) for the nine stars of NGC 1866 that have V-K colors. The same stars were used to derive a BC_K versus J-K relation that was needed to derive the bolometric correction for the stars of the other clusters, for which V-K is not available.

  

Table 2: Observed and derived target properties.

The bolometric magnitudes were computed assuming a distance modulus for the LMC of m-M=18.6. The $T_{\rm eff}$ values were obtained by means of the $T_{\rm eff}$ versus J-K and $T_{\rm eff}$ vs. V-K relations by BCP98, and these, together with $M_{\rm bol}$ and an assumed mass of 4.5 $M_\odot$  finally yield the gravity values. A small grid of synthetic spectra with various lithium abundances was generated for the derived parameters. We found that the photometric $T_{\rm eff}$ did not allow a good fit of the spectra of the cooler stars. Therefore, in order to derive the abundances, new values of $T_{\rm eff}$ were set by looking at the best overall fit over the 6350-7100 Å region. AGB-tip stars are known to be long-period variables, thus we expect differences between the $T_{\rm eff}$ derived from photometry and the $T_{\rm eff}$ used for spectroscopy (photometric and spectroscopic observations were not simultaneous).

Moreover, we do not expect the above mentioned transformations to be very accurate for AGB-TP stars. Therefore, in the following discussion, we will stick to the spectroscopic $T_{\rm eff}$ values. We will use, for instance, the $M_{\rm bol}$ values that can be derived using backwards the spectroscopic $T_{\rm eff}$ and the above-mentioned calibrations. The results are listed in Table 2.