We present the results of spectrophotometry and V,R,I, Halpha CCD photometry of the blue compact dwarf (BCD) galaxy SBS 0940+544. Broad-band images taken with the 2.1m KPNO and 1.23m Calar Alto telescopes reveal a compact high-surface-brightness H II region with ongoing star formation, located at the northwestern tip of the elongated low surface brightness (LSB) main body of the BCD. High signal-to-noise 4.5m Multiple Mirror Telescope (MMT) and 10m Keck II telescope long-slit spectroscopy of SBS 0940+544 is used to derive element abundances of the ionized gas in the brightest H II region and to study the stellar population in the host galaxy. The oxygen abundance in the brightest region with strong emission lines is 12+log(O/H) = 7.46-7.50, or 1/29-1/26 solar, in agreement with earlier determinations and among the lowest for BCDs. Hbeta and Halpha emission lines and Hdelta and Hgamma absorption lines are detected in a large part of the main body. Three methods are used to put constraints on the age of the stellar population at different positions along the major axis. They are based on (a) the equivalent widths of the emission lines, (b) the equivalent widths of the absorption lines and (c) the spectral energy distributions (SED). Several scenarios of star formation have been considered. The observed properties in the main body can be reproduced by a continuous star formation process which started not earlier than 100 Myr ago, if a small extinction is assumed. However, the observations can be reproduced equally well by a stellar population forming continuously since 10 Gyr ago, if the star formation rate has increased during the last 100 Myr in the main body of SBS 0940+544 by at least a factor of five. In summary, we find no compelling evidence which favors either a young or an old age of SBS 0940+544.
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