7 Physical properties

Using a distance to NGC 7479 of 31.92 Mpc (derived assuming H₀=75  km s^-1 km s^-1 Mpc^-1) we employed the standard theoretical formula relating the surface brightness of an HII region with its emission measure Em (Spitzer 1978), assuming that the recombination lines are formed under the conditions of case B (Osterbrock 1974), to calculate Em for each HII region. A standard temperature of 10⁴ K was taken for the calculation. We performed this for a total of 39 regions (22 in the disc and the rest in the bar), covering the full range of observed radii. They were chosen as isolated, so that the uncertainties in calculating their luminosities due to the overlapping of other regions are never as high as 10%. The results are plotted in Fig. 11. Values are given in Table 2 where the luminosity, radius, and emission measure are shown, as well as the electron density, computed from Em; the rms electron densities, derived from the emission measures, are plotted against radius of the HII region, in Fig. 12.

 

Table 2: Measured physical properties of individual HII regions selected for their isolation and projected circularity: catalogue number, radius, luminosity, emission measure, rms electron density, filling factor, mass of ionized gas, log of the number of Lyman-$\alpha$ photons s^-1 necessary to ionize this gas, equivalent number of O5V stars and an indication of the position (bar or disc) for each selected HII region

  

Figure 11: Emission measure versus radius for the selected HII regions in NGC 7479

  

Figure 12: rms electron density versus radius for the selected HII regions

  

Figure 13: rms electron density for the selected HII regions versus log L

In Fig. 13 we show the rms electron densities $<N_{\rm e}\gt _{\rm rms}$ for the same regions, plotted against luminosity. The general ranges and behaviour of Em and $<N_{\rm e}\gt _{\rm rms}$ for NGC 7479 agree well with those found by Kennicutt (1984) and by ourselves (Rozas et al. 1996b) for extragalactic HII regions. Due to observational selection, these tend to be more luminous and larger than Galactic regions.

Kennicutt (1984) first showed that the electron densities in the largest HII regions are of order 1 cm^-3, which is comparable with that of the general diffuse interstellar medium. This is not unexpected, as the powerful central sources can ionize very large volumes of space, whose average matter density is not high. The measured values of $<N_{\rm e}\gt _{\rm rms}$ vary by a factor two for the whole set of regions measured in NGC 7479; although the scatter within this range is high, there is a clear trend for $<N_{\rm e}\gt _{\rm rms}$ to increase with L for high luminosities. This density increase is consistent with the increase in surface brightness found for regions with L>10^38.6 erg s^-1, associated with the change of regime from ionization bounding to density bounding hypothesised in Rozas et al. (1996b), in Beckman et al. (1999), and in Rozas et al. (1998).

To infer the uncertainties in the calculation of the Em and $<N_{\rm e}\gt _{\rm rms}$, we have estimated the propagation of the error in the determination of the radius and in the flux of the regions. Although most of the regions in the catalogue are not perfect spheres and, in general, it is not easy to estimate the uncertainties in the determination of the radius, this is not the case for the regions selected in the sample; they are nearly spherical since they have been chosen for their circularity in projection. Errors in the determination of the radius are $\sim$0.5 pix, and the uncertainty in the determination of the flux is of the order of the flux in an external ring of the region with width 0.5 pix and radius equal to that of the region.

In this way, the relative uncertainty in the calculation of the Em is of the order of 50% for smallest HII regions (log L < 38, below the completeness limit of the LF) and $\sim$10% in more luminous regions. For $<N_{\rm e}\gt _{\rm rms}$ the resulting uncertainty is between $40-50\%$ for faint regions and decreases to well below 10% as the luminosity reaches values typical of brighter regions. In order to calculate the filling factor we need to know, as well as the value of the rms electron density $<N_{\rm e}\gt _{\rm rms}$ values of the in situ electron density $N_{\rm e}$ for each region. We have not measured these values for NGC 7479, but have used a "canonical'' mean value of 135 cm^-3 obtained by Zaritzky et al. (1994) for 42 HII regions in a large sample of galaxies, via the intensity ratio of the forbidden SII doublet $\lambda\lambda$6717, 6731 Å. The value of $N_{\rm e}$ might well differ from bar to disc and it would certainly be worth making direct spectroscopic comparison in NGC 7479. However for the present we cannot improve on the use of a constant value for all HII regions.

The implicit model is that an HII region is internally clumpy, so that the observed flux comes from a high density component, which occupies a fraction $\delta$ (filling factor) of the total volume; the rest of the volume is filled with low density gas which makes a negligible contribution to the observed emission line strengths. The filling factors, computed from $(<N_{\rm e}\gt _{\rm rms}/N_{\rm e})^2$ for the regions range from $4.3\ 10^{-4}$ to $1.5\ 10^{-3}$, a range which coincides well with those found for 5 galaxies in Rozas et al. (1996b). Values of $<N_{\rm e}\gt _{\rm rms}$ can also be used to estimate the mass of ionized gas, by integrating over the measured volume of the region, and multiplying by the mass of a hydrogen atom, using the formula:

$$M({\rm H}^+)=\int\delta^{1/2} <N_{\rm e}\gt _{\rm rms} m(p) {\rm d}V.$$ (2)

Results are given in Table 2 for the selection of regions; the masses range from some 3000 $M_\odot$ to 1.5$\ 10^6$ $M_\odot$. In Table 3 we also give the rate of emission of Lyman continuum photons required to maintain the regions ionized, assuming a case B regime. It is important to note here that the Lyman continuum luminosity of those most luminous regions which are density limited will in fact be considerably higher than that estimated directly via their HH$\alpha$ fluxes. For regions with log $L_{\rm H\alpha}\geq$ 39, the escaping flux is in fact greater than the flux trapped within the region and observed via HH$\alpha$.Finally we have used the estimates of Vacca et al. (1996) of the Lyc luminosity of stars as a function of their spectral type, to compute the equivalent number of O5V stars (emitting Lyc at a rate of 5$\ 10^{49}$ photons/s) required to supply the luminosities of the regions listed in Table 3.