The Carina dwarf spheroidal (dSph) galaxy is the only galaxy of this type that shows clearly episodic star formation separated by long pauses. Here we present metallicities for 437 radial velocity members of this Galactic satellite. We obtained medium-resolution spectroscopy with the multi-object spectrograph FLAMES at the ESO VLT. Our target red giants cover the entire projected surface area of Carina. Our spectra are centered at the near-infrared Ca triplet, which is a well-established metallicity indicator for old and intermediate-age red giants. The resulting data sample provides the largest collection of spectroscopically derived metallicities for a Local Group dSph to date. Four of our likely radial velocity members of Carina lie outside of this galaxys nominal tidal radius, supporting earlier claims of the possible existence of such stars beyond the main body of Carina. We find a mean metallicity of [Fe/H]=-1.7 dex. The formal full width at half maximum of the metallicity distribution is 0.92 dex, while the full range of metallicities spans ~-3.0<[Fe/H]<0.0 dex. The metallicity distribution might be indicative of several subpopulations. There appears to be a mild radial gradient such that more metal-rich populations are more centrally concentrated, matching a similar trend for an increasing fraction of intermediate-age stars. This as well as the photometric colors of the more metal-rich red giants suggest that Carina exhibits an age-metallicity relation. Indeed the age-metallicity degeneracy seems to conspire to form a narrow red giant branch despite the considerable spread in metallicity and wide range of ages. The metallicity distribution is not well-matched by a simple closed-box model of chemical evolution, but requires models that take into account also infall and outflows. (Abridged)
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