We have used extensive libraries of model and empirical galaxy spectra (assembled respectively from the population synthesis code of Bruzual and Charlot and the fourth data release of the Sloan Digital Sky Survey) to interpret some puzzling features seen in the spectra of high redshift star-forming galaxies. We show that a stellar He II 1640 emission line, produced in the expanding atmospheres of Of and Wolf-Rayet stars, should be detectable with an equivalent width of 0.5-1.5AA in the integrated spectra of star-forming galaxies, provided the metallicity is greater than about half solar. Our models reproduce the strength of the He II 1640 line measured in the spectra of Lyman break galaxies for established values of their metallicities. With better empirical calibrations in local galaxies, this spectral feature has the potential of becoming a useful diagnostic of massive star winds at high, as well as low, redshifts. We also uncover a relationship in SDSS galaxies between their location in the [O III]/Hb vs. [N II]/Ha diagnostic diagram (the BPT diagram) and their excess specific star formation rate relative to galaxies of similar mass. We infer that an elevated ionisation parameter U is at the root of this effect, and propose that this is also the cause of the offset of high redshift star-forming galaxies in the BPT diagram compared to local ones. We further speculate that higher electron densities and escape fractions of hydrogen ionising photons may be the factors responsible for the systematically higher values of U in the H II regions of high redshift galaxies. The impact of such differences on abundance determinations from strong nebular lines are considered and found to be relatively minor.
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