The validity of the emission line luminosity vs. ionised gas velocity dispersion ( L - \sigma ) correlation for HII galaxies ( HIIGx ) , and its potential as an accurate distance estimator are assessed .

For a sample of 128 local ( 0.02 \lesssim z \lesssim 0.2 ) compact HIIGx with high equivalent widths of their Balmer emission lines we obtained ionized gas velocity dispersion from high S/N high-dispersion spectroscopy ( Subaru-HDS and ESO VLT-UVES ) and integrated H \beta fluxes from low dispersion wide aperture spectrophotometry .

We find that the L ( \mathrm { H } \beta ) - \sigma relation is strong and stable against restrictions in the sample ( mostly based on the emission line profiles ) .
The ‘ gaussianity ’ of the profile is important for reducing the rms uncertainty of the distance indicator , but at the expense of substantially reducing the sample .

By fitting other physical parameters into the correlation we are able to significantly decrease the scatter without reducing the sample .
The size of the starforming region is an important second parameter , while adding the emission line equivalent width or the continuum colour and metallicity , produces the solution with the smallest rms scatter= \delta \log L ( \mathrm { H } \beta ) = 0.233 .

The derived coefficients in the best L ( \mathrm { H } \beta ) - \sigma relation are very close to what is expected from virialized ionizing clusters , while the derived sum of the stellar and ionised gas masses are similar to the dynamical mass estimated using the HST corrected Petrosian radius .
These results are compatible with gravity being the main mechanism causing the broadening of the emission lines in these very young and massive clusters .
The derived masses range from about 2 \times 10 ^ { 6 } M _ { \odot } to 10 ^ { 9 } M _ { \odot } and their ‘ corrected ’ Petrosian radius , from a few tens to a few hundred parsecs .