Mean Hα line velocity dispersion, σ_mean (in km s^-1), versus total Hα luminosity (in erg s^-1) for different samples of local and high redshift galaxies. Local galaxies (green triangles) are taken from Green et al. (2010) and the model results for our sample are represented by red and blue stars. The blue stars show the results where we assign to each pixel in a galaxy an Hα surface brightness based on the model relationship,  km s^-1 and use the observed local Hα velocity dispersion. We then estimate the total Hα luminosity by summing up the predicted pixel-by-pixel surface brightnesses, and estimate σ_mean by weighting the pixel-by-pixel velocity dispersion measurements by the Hα surface brightnesses derived from the model.