  Using the OSIRIS tunable narrow band imager on the 10.4m GTC (La Palma) we
have mapped the SAB(rs)cd galaxy NGC 6946 over a 7.3x7.5 square arcminutes
field in the emission lines of the [SII]\lambda\lambda, 6717, 6731 doublet, and
in H\alpha. From these maps we have produced catalogs of the H\alpha
luminosities and effective radii of 557 HII regions across the disk, and
derived the [SII] emission line ratios of 370 of these. The H\alpha
observations were used to derive the mean luminosity-weighted electron
densities for the regions of the sample, while the [SII] line ratios allowed us
to derive values of the in situ electron densities in the denser zones from
which the major fraction of the radiation in these lines is emitted, for 58 of
the regions. This is by far the largest data set of its kind for a single
galaxy. A classical two phase model is used to derive the filling factors of
the regions. We find that although the mean electron density decreases with the
square root of the radius of the regions, the in situ density is essentially
independent of this radius. Thus the filling factor falls systematically, as
the radius and the luminosity of the regions increases, with a power law of
exponent -2.23 between filling factor and radius. These measurements should
enhance the perspectives for more refined physical models of HII regions.
