We present a technique that applies spectral synthesis to medium resolution spectroscopy ( MRS , R \sim 6000 ) in the red ( 6300 ~ { } \mathrm { \AA } < \lambda < 9100 Å ) to measure [ Fe/H ] and [ \alpha /Fe ] of individual red giant stars over a wide metallicity range .
We apply our technique to 264 red giant stars in seven Galactic globular clusters and demonstrate that it reproduces the metallicities and \alpha enhancements derived from high resolution spectroscopy ( HRS ) .
The MRS technique excludes the three Ca ii triplet lines and instead relies on a plethora of weaker lines .
Unlike empirical metallicity estimators , such as the equivalent width of the Ca ii triplet , the synthetic method presented here is applicable over an arbitrarily wide metallicity range and is independent of assumptions about the \alpha enhancement .
Estimates of cluster mean [ Fe/H ] from different HRS studies show typical scatter of \sim 0.1 dex but can be larger than 0.2 dex for metal-rich clusters .
The scatter in HRS abundance estimates among individual stars in a given cluster is also comparable to 0.1 dex .
By comparison , the scatter among MRS [ Fe/H ] estimates of individual stars in a given cluster is \sim 0.1 dex for most clusters but 0.17 dex for the most metal-rich cluster , ( catalog M71 ) ( \langle \mathrm { [ Fe / H ] } \rangle = -0.8 ) .
A star-by-star comparison of HRS vs. MRS [ \alpha /Fe ] estimates indicates that the precision in \mathrm { [ \alpha / Fe ] } _ { \mathrm { MRS } } is 0.05 dex .
The errors in \mathrm { [ Fe / H ] } _ { \mathrm { MRS } } and \mathrm { [ \alpha / Fe ] } _ { \mathrm { MRS } } increase beyond 0.25 dex only below signal-to-noise ratios of 20 ~ { } \mathrm { \AA } ^ { -1 } , which is typical for existing MRS of the red giant stars in UGC 5470 ( catalog Leo~I ) , one of the most distant Milky Way satellites ( 250 kpc ) .