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Astron. Astrophys. 354, 823-835 (2000)

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6. Physical properties

We calculated the emission measure, Em, via the standard theoretical formula relating this to the H[FORMULA] surface brightness (Spitzer 1978), assuming that the recombination lines are formed under case B conditions (Osterbrock 1974). We used a standard temperature of 104 K in this calculation. This computation was performed for 21 regions, covering the full range of observed radii, and chosen to be isolated from other HII regions, so that the uncertainties in calculating their parameters due to possible overlap with other regions were less than 10%. The results are plotted in Fig 11. Values are given in Table 2 where the luminosity, radius, and emission measure are given, as well as the electron density derived from Em, for all the selected regions. In Fig 12 we plot the rms electron densities against HII region radius, while in Fig 13 we have plotted these rms electron densities against H[FORMULA] luminosity.

[FIGURE] Fig. 11. Emission measure v. radius for a set of HII regions in NGC 3359, selected for minimum geometrical overlap with other HII regions.

[FIGURE] Fig. 12. rms electron density v. radius for the HII regions selected in Fig. 11.

[FIGURE] Fig. 13. rms electron density v. [FORMULA] for the HII regions selected in Fig 11.


[TABLE]

Table 2. Catalogue number of the HII regions, radii, luminosities, emission measures, rms electron densities, filling factors, masses of ionized gas, log of the number of Lyman-[FORMULA] photons s-1 necessary to ionize this gas and equivalent number of O5V stars for each selected HII region.


The general ranges and trends of Em and [FORMULA] for NGC 3359 fit broadly into the pattern found by Kennicutt (1984), and by ourselves (Rozas et al. 1996b, Rozas et al. 1999a) for extragalactic HII regions. Observational selection causes these to be more luminous and larger than the average Galactic HII region. Kennicutt first showed that the electron densities in the largest HII regions are of the order of a few cm-3, which is comparable with that of the diffuse interstellar medium in general. This is plausible, since the OB associations in their centres can ionize very large volumes whose mean matter density is not very high. The measured values of [FORMULA] vary within a range of a factor 2 over the full luminosity range of some two orders of magnitude for the set of regions selected. The scatter is high within this range, but there is a trend to somewhat higher values of [FORMULA] at the highest luminosities. This increase is consistent with models in which there is a change of regime from ionization bounding to density bounding at luminosities higher than [FORMULA] erg s-1, hypothesized in Rozas et al. 1996b, Beckman et al. 2000, and Rozas et al. 1998. The values of [FORMULA], differ from the values found for the central densities of HII regions (Rozas et al. 1998) by two orders of magnitude, but if we assume gaussian internal density distributions and weighting the densities as shown in Table 2 of Rozas et al. (1998), by volume, using the diameters determined here, we find mean electron densities within 20[FORMULA] of the values found here.

To infer the uncertainties in the values of Em and [FORMULA] we estimate the effects of the errors in the determination of the radius and flux of an HII region. Although most of the HII regions in the catalogue are not good projected circles, and it is not too easy in general, to determine the uncertainty in the determination of the radius, this is not the case for the regions selected in the sample, which have nearly circular perimeters, and are certainly close to spherical in form. The error in the determination of the radius is 0.5 pixel, and the uncertainty in the flux determination is of the order of the flux in the outermost ring of the region, with width 0.5 pixel and the radius of the region. These yield relative uncertainties in Em of up to 50% for the smallest, faintest regions ([FORMULA] in erg s-1), below the completeness limit of the LF, and up to 10% in the more luminous HII regions. For [FORMULA] the resulting uncertainty is between 40% and 50% for faint regions, and decreases to well below 10% as the luminosity reaches values typical of brighter HII regions.

In order to calculate the filling factor we need, as well as the rms electron density, [FORMULA], values of the in situ electron density [FORMULA] for any HII region. We have not measured these values in NGC 3359, but used a "canonical" mean value of 135 cm-3 obtained by Zaritsky et al. (1994) for 42 HII regions in a large sample of galaxies, using the intensity ratio of the forbidden S II doublet [FORMULA]6717, 6731Å. 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 [FORMULA], the filling factor, of the total volume. The rest is filled with low density gas which makes a negligible contribution to the observed emission line strengths. The filling factors, computed using [FORMULA] range from 2.7[FORMULA] to 1.47[FORMULA], a range which coincides with those found for 5 galaxies in Rozas et al. 1996b. The electron density values can also be used to estimate the mass of ionized gas within an HII region by integrating over the measured volume of the region, and multiplying by the mass of the hydrogen atom, using the formula:

[EQUATION]

The results are given in Table 2 for our selected HII regions; the masses range from some 300 [FORMULA] to 1.6[FORMULA] [FORMULA]. In Table 2 we also give the rate of emission of Lyman continuum photons required to maintain the HII regions ionized, assuming a Case B regime. We should point out here that the Lyman continuum luminosity of these most luminous HII regions, which are density limited, will in fact be considerably higher than that estimated directly via their H[FORMULA] fluxes. For HII regions with [FORMULA] (erg s-1) the escaping flux is in fact greater than the flux trapped within the region, and observed via the H[FORMULA] emission. Finally we have used the estimates of Vacca, Garmany & Shull (1996) of the Lyc luminosity of stars as a function of their spectra type, to compute the equivalent number of O5V stars (emitting Lyc at a rate of 5[FORMULA] photons s-1) required to supply the luminosities of the HII regions listed in Table 2.

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© European Southern Observatory (ESO) 2000

Online publication: February 25, 2000
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