Determination of robust metallicities for metal-rich red giant branch
  stars
  The study of the Milky Way relies on our ability to interpret the light from
stars correctly. This calls for a reinvestigation of how reliably we can
determine, e.g., iron abundances in such stars and how well they reproduce
those of dwarf stars. Here we explore robust ways to determine the iron content
of metal-rich giant stars. We aim to understand what biases and shortcomings
widely applied methods suffer from. In this study we are mainly concerned with
standard methods to analyse stellar spectra. This includes the analysis of
individual lines to determine stellar parameters, analysis of the broad wings
of certain lines (e.g., H$\alpha$ and calcium lines) to determine effective
temperature and surface gravity for the stars. For NGC 6528 we find that [Fe/H]
= $+0.04$ dex with a scatter of $\sigma=0.07$ dex, which gives an error in the
derived mean abundance of 0.02 dex. Our work has two important conclusions for
analysis of metal-rich red giant branch stars. 1) For spectra with S/N below
about 35 per reduced pixel [Fe/H] become too high, 2) Determination of $T_{\rm
eff}$ using the wings of the H$\alpha$ line results in [Fe/H] values about 0.1
dex higher than if excitational equilibrium is used. The last conclusion is
perhaps not surprising as we expect NLTE effect to become more prominent in
cooler stars and we can not use the the wings of the H$\alpha$ line to
determine $T_{\rm eff}$ for the cool stars in our sample. We therefore
recommend that in studies of metal-rich red giant stars care needs to be taken
to obtain sufficient calibration data in order to be able to also use the
cooler stars.
