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Formation and evolution of late-type dwarf galaxies. I. NGC 1705 and NGC 1569

(Abridged.) We present one-zone chemical evolution models for two dwarf starburst galaxies, NGC 1705 and NGC 1569. Using information about the past star formation history and initial mass function of the systems previously obtained from Hubble Space Telescope colour-magnitude diagrams, we identify possible scenarios of chemical enrichment and development of galactic winds. In order not to overestimate the current metallicity of the interstellar gas inferred from H II region spectroscopy, we suggest that the winds efficiently remove from the galaxies the metal-rich ejecta of dying stars. Conversely, requiring the final mass of neutral gas to match the value inferred from 21-cm observations implies a relatively low efficiency of interstellar medium entrainment in the outflow, thus confirming previous findings that the winds driving the evolution of typical starbursts are differential. These conclusions could be different only if the galaxies accrete huge fractions of unprocessed gas at late times. By assuming standard stellar yields we obtain a good fit to the observed nitrogen to oxygen ratio of NGC 1569, while the mean N/O ratio in NGC 1705 is overestimated by the models. Reducing the extent of hot bottom burning in low-metallicity intermediate-mass stars does not suffice to solve the problem. Localized self-pollution from stars more massive than 60 MSun in NGC 1705 and/or funneling of larger fractions of nitrogen through its winds are then left to explain the discrepancy between model predictions and observations. Inspection of the log(N/O) vs. log(O/H)+12 diagram for a sample of dwarf irregular and blue compact dwarf galaxies in the literature favours the latter hypothesis.