Giant H II regions as distance indicators - I. Relations between global parameters for the local calibrators

The correlations among integrated parameters of giant H II regions, Hβ luminosity, L(Hβ), emission-line width, σ, core radius, R_c, and oxygen abundance O/H, are studied on the basis of a new homogeneous sample of data for 22 giant nebulae in 10 galaxies with known distances. We confirm the existence of significant correlations between these parameters. Using appropriate statistical techniques to account for the observational errors in all parameters, we find correlations of the form $$R_{c} \propto \sigma ^{2.5}, L \propto \sigma ^{5} \,\text{and} \,L(H\beta)/R_{c}\sigma ^{2} = f\text{(O/H)}.$$ These correlations provide a powerful distance indicator for galaxies with giant H II regions. The various mechanisms that may generate supersonic gas motions are discussed. We find that the ‘virial-turbulence’ model proposed by Terlevich & Melnick explains best, although not completely, the existence of supersonic motions in the ionized gas and the observed correlations. We show that the observations are not consistent with a Kolmogoroff-like turbulence and that energy is fed at all spatial frequencies into the turbulent motions.