For the first time we present a new data set of emission line widths for 118 star-forming regions in H II galaxies (HIIGs). This homogeneous set is used to investigate the L-σ relation in conjunction with optical spectrophotometric observations. We were able to classify their nebular emission line profiles due to our high-resolution spectra. Peculiarities in the line profiles such as sharp lines, wings, asymmetries, and in some cases more than one component in emission were verified. From a new independent homogeneous set of spectrophotometric data, we derived physical condition parameters and performed statistical principal component analysis. We have investigated the potential role of metallicity (O/H), Hβ equivalent width (WHβ), and ionization ratio [O III]/[O II] to account for the observational scatter of the L-σ relation. Our results indicate that the L-σ relation for HIIGs is more sensitive to the evolution of the current starburst event (short-term evolution) and dated by WHβ or even the [O III]/[O II] ratio. The long-term evolution measured by O/H also plays a potential role in determining the luminosity of the current burst for a given velocity dispersion and age as previously suggested. Additionally, galaxies showing Gaussian line profiles present tighter correlations indicating that they are the best targets for the application of the parametric relations as an extragalactic cosmological distance indicator. Best fits for a restricted homogeneous sample of 45 HIIGs provide us with a set of new extragalactic distance indicators with an rms scatter compatible with observational errors of δlog L Hα= 0.2 dex or 0.5 mag. Improvements may still come from future optimized observational programs to reduce the observational uncertainties on the predicted luminosities of HIIGs in order to achieve the precision required for the application of these relations as tests of cosmological models.
distance scale - galaxies: dwarf - galaxies: kinematics and dynamics - galaxies: starburst - H II regions