Electron densities and filling factors of extragalactic HII regions: NGC 2403 and NGC 628
Measurements of the electron density of populations of extragalactic HII regions in nearby galaxies remain limited, despite the relevance of this quantity for characterizing the porosity of the interstellar medium and the escape of the ionizing radiation. We initiated a project aimed at analyzing the root-mean-square electron density ne_rms, the in-situ density ne and the volume filling factor (phi) of extragalactic HII regions, investigating the dependence of these attributes on nebular and host galaxy properties. We present an image-segmentation methodology for constructing homogeneous HII region catalogues, and apply it to two pilot galaxies: NGC 2403 and NGC 628. We derive ne_rms from their Halpha luminosities and equivalent radii (R_eq), and obtain ne and phi for spectroscopic subsamples. While ne is below 300 cm$^{-3}$, ne_rms is typically one to two orders of magnitude lower, implying that phi is in the range ~$10^{-4}$ to $10^{-1}$. The two galaxies exhibit a similar size-density relation, which breaks for R_eq >~ 50 pc, show at most a weak dependence of ne_rms on galactocentric radius for NGC 2403, and no clear dependence of ne or phi on these parameters. Combining these results with published data, ne_rms presents tentative scaling relations with the median HII region size, the fraction of large regions in the parent galaxy, and the star formation rate surface density. These trends, if confirmed, would provide new constraints for massive cluster formation models and important clues for interpreting dependencies observed at high redshift, underscoring the necessity of consistently extending this analysis to larger samples.