We demonstrate how the metallicities of red supergiant ( RSG ) stars can be measured from quantitative spectroscopy down to resolutions of \approx 3000 in the J–band .
We have obtained high resolution spectra on a sample of the RSG population of h and \chi Persei , a double cluster in the solar neighborhood .
We show that careful application of the marcs model atmospheres returns measurements of Z consistent with solar metallicity .
Using two grids of synthetic spectra - one in pure LTE and one with NLTE calculations for the most important diagnostic lines - we measure Z = + 0.04 \pm 0.10 ( LTE ) and Z = - 0.04 \pm 0.08 ( NLTE ) for the sample of eleven RSGs in the cluster .
We degrade the spectral resolution of our observations and find that those values remain consistent down to resolutions of less than \lambda / \delta \lambda of 3000 .
Using measurements of effective temperatures we compare our results with stellar evolution theory and find good agreement .
We construct a synthetic cluster spectrum and find that analyzing this composite spectrum with single-star RSG models returns an accurate metallicity .
We conclude that the RSGs make ideal targets in the near infrared for measuring the metallicities of star forming galaxies out to 7-10 Mpc and up to ten times farther by observing the integrated light of unresolved super star clusters .