Ten eclipsing binaries in the Small Magellanic Cloud: fundamental parameters and SMC distance

We present the first results of an observational programme to measure the fundamental parameters of over 100 eclipsing binaries in the Small Magellanic Cloud (SMC). The spectroscopic data were obtained by using the 2dF multi-object spectrograph on the 3.9-m Anglo-Australian Telescope, and are used in conjunction with photometry from the OGLE database of SMC eclipsing binaries. Ten systems are discussed in this first paper. Three are detached early-B binaries, six are in a semi-detached configuration, and one is in a marginal contact state. We conclude that the semi-detached systems are undergoing the slow mass-transfer phase of case-A binary evolution, in which the mass donor has reached its Roche lobe while still on the main sequence. Each system provides a primary distance indicator. By constructing a new calibration between spectral type and temperature for O and early B stars, we find a mean distance modulus to the SMC of 18.89 +- 0.04 (statistical) +- 0.10 (systematic). This value represents one of the most precise determinations to date of the distance to the SMC.