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 multifiber spectroscopy with FLAMES as part of a Large Program with the Very Large Telescope at the European Southern Observatory, Chile. The metallicities were determined based on the well-established near-infrared Ca II triplet technique. This allowed us to achieve a mean random error of 0.16 dex on the metallicities, while other systematic effects, such as unknown variations in the dSph's [Ca/Fe] ratio, may introduce a further source of uncertainty of the order of 0.1 dex. The resulting metallicity distribution 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 -1.08 dex. As in other dSph galaxies, no extremely metal-poor red giants were found. We compare Leo II's observed metallicity distribution with model predictions for several other Galactic dSphs from the literature. Leo II clearly exhibits a lack of more metal-poor stars, analogous 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 Sloan Digital Sky Survey photometry of our target stars and derive approximate ages. The resulting age-metallicity distribution covers the full age range from 2 to about 15 Gyr on our adopted isochrone scale. During the first ~7 Gyr relative to the oldest stars, the metallicity of Leo II appears to have remained almost constant, centering on the mean metallicity of this galaxy. 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 preenriched gas. Evidence for enrichment is seen during the recent 2-4 Gyr. Our findings support earlier derived photometric findings of Leo II as a galaxy with a prominent old population and dominant intermediate-age populations. We do not see a significant indication of a radial metallicity gradient or age gradient in our current data.
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