The galaxy-wide distributions of mean electron density in the HII
  regions of M51 and NGC 4449
  Using ACS-HST images to yield continuum subtracted photometric maps in
H\alpha of the Sbc galaxy M51 and the dwarf irregular galaxy NGC 4449, we
produced extensive (over 2000 regions for M51, over 200 regions for NGC4449)
catalogues of parameters of their HII regions: their H\alpha luminosities,
equivalent radii and coordinates with respect to the galaxy centers. From these
data we derived, for each region, its mean luminosity weighted electron
density, <n_e>, determined from the H\alpha luminosity and the radius, R, of
the region. Plotting these densities against the radii of the regions we find
excellent fits for <n_e> varying as R^{-1/2}. This relatively simple relation
has not, as far as we know, been predicted from models of HII region structure,
and should be useful in constraining future models. Plotting the densities
against the galactocentric radii, r, of the regions we find good exponential
fits, with scale lengths of close to 10 kpc for both galaxies. These values are
comparable to the scale lengths of the HI column densities for both galaxies,
although their optical structures, related to their stellar components are very
different. This result indicates that to a first approximation the HII regions
can be considered in pressure equilibrium with their surroundings. We also plot
the electron density of the HII regions across the spiral arms of M51, showing
an envelope which peaks along the ridge lines of the arms.
