3 Variation of input parameters

3.1 Stellar mass loss

The mass loss of stars, especially for low mass stars, is still not understood very well. A formulae often used to describe mass loss is Reimers' law:

$$\dot{M} = 1.27 \ 10^{-5} \cdot \eta M^{-1} L^{1.5} T_{\rm eff}^{-2},$$ (5)

where the parameter $\eta$ is not known a priori and is probably a function of metallicity.

On the horizontal branch, stars tend to be hotter the lower their mass, thus a larger value of $\eta$ makes the HB population bluer .

In this work we adopt for $\eta$ a value of 0.35 independent of metallicity for lack of better knowledge. For a careful study of the effects of changing $\eta$ e.g. on the HB morphology see Buzzoni et al. (1989). Covino et al. (1994) present an extensive study of the effect of different HB morphologies of theoretical isochrones on the integrated colours.

We found that there is no signifcant effect of the HB morphology of observed Galactic globular clusters on the optical colours.

3.2 Non-solar abundance ratios

There are many observations showing that the $\alpha$ - element-to-iron ratio is larger than solar for stars with low metallicities in the Milky Way (e.g. Furmann et al. 1995). Nevertheless, most stellar evolutionary track calculations for sub-solar metallicities use solar abundance ratios. Salaris et al. (1993) show that the effect of different $\alpha$-to-Fe element ratios on the stellar evolution can be accounted for by appropriately changing the conversion of global metallicity Z to ${\rm [Fe/H]}$. Despite the observed $\alpha$-enhancement for metal poor stars in the MW, no correction is applied since we checked that a correction did not give better fits to the observations. In this paper, $\log(\frac{Z}{Z_\odot}) (=: [M/H])$ was assumed to be equal to ${\rm [Fe/H]}$.

For absorption indices, any correction for $\alpha$ - enhancement would be inappropriate for our models since we are using the index calibrations from Worthey, which depend only on the metallicity and not explicitily on ${\rm [\alpha/Fe]}$ - element ratios. Since Worthey's index calibrations are determined from Galactic stars, the dependence of $\alpha$ - enhancement on metallicity is so implicitly included.

Somewhat surprisingly we found no previous study that has examined the effect of ${\rm [\alpha/Fe]}$ on the colours at fixed temperature. An analysis by Kurth (1998) shows that at least for solar type stars, the colour is only dependent on ${\rm [Fe/H]}$ and not on ${\rm [Mg/Fe]}$.

There may still be an effect of non-solar abundance ratios on the morphology of the horizontal branch, but since our models agree with the observations no further investigation in this direction is attempted at the present stage.