Stellar models have been computed for stars having [ Fe/H ] = 0.0 and -2.0 to determine the effects , primarily on the predicted { T _ { eff } } scale , of using boundary conditions derived from the latest MARCS model atmospheres .
The latter have been fitted to the interior models at both the photosphere and at \tau = 100 , and , at least for the 0.8 – 1.0 { \cal M _ { \odot } } stars considered here , the resultant evolutionary tracks on the H-R diagram were found to be nearly independent of the chosen fitting point .
Particular care was taken to treat the entire star as consistently as possible ; i.e. , both the stellar structure and atmosphere codes assumed the same abundances of helium and the heavy elements , as well as the same treatment of convection ( the mixing-length theory , with the free parameter { \alpha _ { MLT } } chosen to satisfy the solar constraint ) .
Tracks were also computed in which the photospheric pressure was obtained by integrating the hydrostatic equation together with either the classical gray T ( \tau, T _ { eff } ) relation or that derived by Krishna Swamy ( 1966 ) from an empirical solar atmosphere .
Due to the compensating effects of differences in the calibrated values of { \alpha _ { MLT } } , the evolutionary sequences that assumed gray atmospheric structures were in fortuitously close agreement with those using MARCS atmospheres as boundary conditions , independently of the assumed metallicity .
( The structures of gray atmospheres are quite different from those predicted by MARCS models . )
On the other hand , the models based on the Krishna Swamy T ( \tau, T _ { eff } ) relationship implied a much hotter giant branch ( by \sim 150 K ) at solar abundances , which happens to be in good agreement with the inferred temperatures of giants in the open cluster M 67 from the latest ( V - K ) – { T _ { eff } } relations , though they were similar to the other cases at [ Fe/H ] = -2.0 .
Most of the computations assumed Z = 0.0125 for the Sun , as derived by M. Asplund and colleagues , though a few models were calculated for Z = 0.0165 , assuming the Grevesse & Sauval ( 1998 ) metals mix , to determine the dependence of the evolutionary tracks on Z _ { \odot } .
Grids of “ scaled solar , differentially corrected ” ( SDC ) atmospheres were also computed , to try to improve upon theoretical MARCS models .
When they were used to describe the surface layers of stellar models , the resultant tracks were in remarkably good agreement with those that employed a standard scaled-solar ( e.g. , Krishna Swamy ) T ( \tau, T _ { eff } ) relation to derive the boundary pressures , independently of the assumed metal abundance .
To within current distance and metallicity uncertainties , it was possible to obtain a good match of isochrones for [ Fe/H ] = -2.0 to the C-M diagram of the globular cluster M 68 .
Until these uncertainties and those associated with the atmospheric boundary conditions are reduced significantly , it can not be claimed with any confidence that { \alpha _ { MLT } } does or does not vary with [ Fe/H ] .
While our consideration of M 67 giants suggests that this parameter is independent of { T _ { eff } } and \log g , some ( small ) variation with stellar parameters can not be ruled out .