The thin red giant branch (RGB) of the Carina dwarf spheroidal galaxy appears at first sight quite puzzling and seemingly in contrast with the presence of several distinct bursts of star formation. In this Letter, we provide a measurement of the color spread of red giant stars in Carina based on new BVI wide-field observations, and model the width of the RGB by means of synthetic color-magnitude diagrams. The measured color spread, Sigma{V-I}=0.021 +/- 0.005, is quite naturally accounted for by the star-formation history of the galaxy. The thin RGB appears to be essentially related to the limited age range of its dominant stellar populations, with no need for a metallicity dispersion at a given age. This result is relatively robust with respect to changes in the assumed age-metallicity relation, as long as the mean metallicity over the galaxy lifetime matches the observed value ([Fe/H] = -1.91 +/- 0.12 after correction for the age effects). This analysis of photometric data also sets some constraints on the chemical evolution of Carina by indicating that the chemical abundance of the interstellar medium in Carina remained low throughout each episode of star formation even though these episodes occurred over many Gyr.
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