8 Number-luminosity-diameter relation

  

Figure 14: Lower: 3-dimensional plot for the HII regions of the disc of NGC 7479 of the number (z-axis) of HII regions as a function of luminosity (y-axis) and diameter (x-axis). Upper: Projection of the lower plot onto the diameter-log luminosity plane

In Fig. 14 we give a three-dimensional plot of the number of HII regions of the disc as a function of two separate parameters: luminosity and diameter. It is of use to present the data this way as it allows us to see any correlation between the variables, which may give a clue to the underlying physical properties of the regions. Above the 3-d plot we have a projection into the luminosity-diameter plane, on a grey scale, in which we can readily see a change in the slope at a specific luminosity, which shows up clearly in spite of the obvious wide scatter of diameters at a given luminosity. This change is the equivalent of a change in the internal surface brightness gradients of the individual regions, and we will examine this quantitatively below. We have attributed this change, found in other disc galaxies, (see Rozas et al. 1996; Beckman et al. 1999) to the "Strömgren'' transition from ionization bounded regions to density bounded regions. The luminosity at which this occurs will be the same as that of the small glitch peak in the luminosity function, but is not as well defined in the luminosity-diameter plot since the peak in the LF is determined uniquely by the luminosity, while the change in slope of the luminosity-diameter plot has to be found amid the scatter of diameters in placental clouds with a range of intrinsic gas densities, giving rise to the spread seen in the grey scale projection.