We present metallicities and ages for 52 red giants in the remote Galactic dwarf spheroidal (dSph) galaxy Leo II. These stars cover the entire surface area of Leo II and are radial velocity members. We obtained medium-resolution multi-fiber spectroscopy with ESO/VLTs FLAMES spectrograph. The metallicities were determined based on the near-infrared Ca II triplet. The resulting metallicity distribution (MD) is asymmetric and peaks at [Fe/H]=-1.74 dex on the Carretta & Gratton scale. The full range in metallicities extends from -2.4 to -1.1 dex. As in other dSphs, no extremely metal-poor red giants were found. We compare Leo IIs observed MD with model predictions for several other Galactic dSphs from the literature. Leo II clearly exhibits a lack of more metal poor stars, in analogy to the classical G-dwarf problem, which may indicate a comparable `K-giant problem. Moreover, its evolution appears to have been affected by galactic winds. We use our inferred metallicities as an input parameter for isochrone fits to SDSS photometry and derive approximate ages. The resulting age-metallicity distribution covers the full age range from 2-15 Gyr on our adopted isochrone scale. During the first 7 Gyr relative to the oldest stars [Fe/H] appears to have remained almost constant. The almost constant metallicity at higher ages and a slight drop by about 0.3 dex thereafter may be indicative of rejuvenation by low metallicity gas. Overall, the age-metallicity relation appears to support the formation of Leo II from pre-enriched gas. Evidence for enrichment is seen during the recent 2-4 Gyr. Our findings support earlier photometric findings of Leo II as a galaxy with a prominent old and a dominant intermediate-age population. We do not find a significant radial metallicity gradient nor age gradient in our data.(Abridged)
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