AGB stars in the Magellanic Clouds. III. The rate of star formation across the Small Magellanic Cloud

Aims.This article compares the K s magnitude distribution of Small Magellanic Cloud asymptotic giant branch stars obtained from the DENIS and 2MASS data with theoretical distributions.Methods.Theoretical K s magnitude distributions have been constructed using up-to-date stellar evolution calculations for low-and intermediate-mass stars, and in particular for thermally pulsing asymptotic giant branch stars.Separate fits of the magnitude distributions of carbon-and oxygen-rich stars allowed us to constrain the metallicity distribution across the galaxy and its star formation rate.Results.The Small Magellanic Cloud stellar population is found to be on average 7-9 Gyr old but older stars are present at its periphery and younger stars are present in the direction of the companion galaxy the Large Magellanic Cloud.The metallicity distribution traces a ring-like structure that is more metal rich than the inner region of the galaxy.Conclusions.The C/M ratio discussed in Paper I is a tracer of the metallicity distribution only if the underlying stellar population is of intermediate-age.