The L-sigma Relation of Local HII Galaxies
  We present for the first time a new data set of emission line widths for 118
star-forming regions in HII galaxies (HIIGs). This homogeneous set is used to
investigate the L-sigma relation in conjunction with optical spectrophotometric
observations. 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 the statistical principal
component analysis. We have investigated the potential role of metallicity
(O/H), Hbeta equivalent width (WHbeta) and ionization ratio [OIII]/[OII] to
account for the observational scatter of L-sigma relation. Our results indicate
that the L-sigma relation for HIIGs is more sensitive to the evolution of the
current starburst event (short-term evolution) and dated by WHbeta or even the
[OIII]/[OII] 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 more tight correlations indicating that
they are 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 a set of new extragalactic distance
indicators with an RMS scatter compatible with observational errors of
Delta_log(LHalpha) = 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.
