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

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7. The diffuse H[FORMULA] flux

Here we examine whether the rate of escape of ionizing photons from the HII regions in NGC 3359, above all from the density bounded HII regions of high luminosity, is sufficient to account for the ionization of the diffuse interstellar medium (ISM) outside the HII regions which is detected via its H[FORMULA] emission. In this galaxy the flux from the diffuse ionized gas (DIG) is a fairly high fraction of the H[FORMULA] emission, up to 30% of the total emission from the galaxy (as we will see below). The test entails measuring the diffuse H[FORMULA] flux, computing with our model the ionizing flux which escapes from the HII regions, and comparing the two. If the latter is large, we can infer that there is at least a prima facie case for concluding that the diffuse flux is caused by ionization processes due to photons from OB stars leaking from the density-bounded luminous HII regions. If we can go on to show a geometrical correlation between the postulated escaping flux and the measured diffuse flux, we can take this conclusion a step further and consolidate this hypothesis to explain the diffuse flux.

7.1. The total flux, and the diffuse flux: observational

The total H[FORMULA] flux from NGC 3359 was measured by integrating the continuum-subtracted flux-calibrated H[FORMULA] image over an elliptical area, with the inclination and position angles of the galaxy disc, then subtracting off a constant level estimated for the sky background integrated over this elliptical area. The result is [FORMULA](total) = (8.8[FORMULA]0.6)[FORMULA]1040 erg s-1. The principal source of error is the uncertainty in our determination of the sky level, which produces an uncertainty of 12% in [FORMULA](total). The other important source of error is the continuum subtraction, moreover, this error is smaller than the previous one: variations of the continuum subtraction scaling factor by [FORMULA]% (the maximun estimated error in this factor) lead to changes of the total H[FORMULA] luminosity of [FORMULA]%. Both errors are included in the results that we present in this subsection.

To measure the diffuse flux we need to take more than one approach, due to the difficulty of estimating the distribution of the diffuse emitting gas perpendicular to the plane of the galaxy, in particular in the regions surrounding the largest HII regions. In the first method we used the equivalent areas of the HII regions in the catalogue to prepare a masked image in which the H[FORMULA] surface brightness was first set to zero in the zones occupied by the HII regions. Integrating over the resulting image we obtained a measure of the diffuse flux. The implied assumption here is that where we observe an HII region there is much less diffuse gas in the total emitting column above the galaxy disc, so that to a first approximation the diffuse emission here may be set to zero. In the second method, we used the same masked image but then, before integrating over the resulting image to obtain the total diffuse flux, we assigned a constant non-zero level to the masked areas. The idea here is than even above an HII region there is still some diffuse emission. One simple approach is to fill in the blanks to a surface brightness value equivalent to the mean value of the diffuse brightness measured in the field surrounding each HII region. This is technically simple, but while the use of total blanks in the first method must give a lower limit to the diffuse flux, filling the blanks fully at the level of the surrounding flux, as in the second method, will give an upper limit, since the HII regions themselves occupy part of the emitting column, so the diffuse emission from above will be less than that from the surrounding plane. A previous study of diffuse H[FORMULA] in disc galaxies by Ferguson et al. (1996) took the second approach, and their fractional H[FORMULA] fluxes should be taken as upper limits, though clearly not extremely far from true estimates. To obtain the lower limiting diffuse flux we integrated over the masked image (explained above) in which surface brightness was set to zero in the areas occupied by the catalogued HII regions. To estimate the additional flux due to HII regions below the completeness limit, we extrapolated the LF below [FORMULA] erg s-1, normalizing to the number measured in NGC 3359 at this luminosity, and following the curve of Walterbos & Braun (1992), measured for M31 (the only galaxy for which this information is available) at lower luminosities, down to their observational limit of 1035 erg s-1. Any correction below this luminosity would be completely negligible. The difference between the integrated luminosity of the extrapolated LF to lower luminosities and the luminosity due to the catalogued HII regions below the completeness limit was then subtracted from the integration of the masked image. Doing this directly gives us a lower limit to the diffuse flux of:


which can be used to compute a required rate of Lyc photons flowing into the diffuse medium, assuming case B and a temperature of 104 K, yielding [FORMULA].

An upper limiting value was found by removing the HII regions, and refilling the spaces at a level computed by taking a 4 pixel-wide ring round each HII region, and filling with the averaged counts in this ring. From the total integration over this new image we then subtracted the integrated luminosity from faint HII regions (using the M31 LF) and the sky contribution. The upper limit thus obtained for the diffuse emission was


which converts to [FORMULA] Lyc photons s-1.

We should emphasize that to take this upper limit as a correct value is significantly to overestimate the diffuse component, because it is based on a totally plane geometry, in which the volume of the HII regions is not taken into account. For the largest most luminous regions this assumption is particularly poor, as they occupy the major part of the column density above the plane, leaving relatively less for the diffuse component. The intermediate case, which can be taken as the best estimate for the DIG emission was obtained via a similar procedure to the upper limit, but instead of refilling the blanks left by the HII regions with the flux averaged around each, they were filled in with the mean background averaged over the full disc. This will be a better approximation than the limiting cases, and gives a value of


which is produced by [FORMULA] Lyc photons s-1.

As we can see from these results (Eqs. 3 to 5), the H[FORMULA] emision of the diffuse ionized gas is between 20%-30% of the total H[FORMULA] luminosity of the galaxy.

7.2. The ionizing flux escaping from the HII regions

We can obtain an observational estimate of the ionizing flux which must be escaping from the HII regions based on the hypothesis that above the observed luminosity [FORMULA] (erg s-1), the Strömgren luminosity, [FORMULA], the HII regions are density bounded. This is necessarily a slight simplification, because there will be some leak-out of photons from less luminous regions, and some fluctuations due to inhomogeneities in the degree of escape from the more luminous, but it allow us to make a first order estimate, within the theoretical framework given in Beckman et al. (2000). We can, on this assumption, extrapolate the LF for NGC 3359, using its measured slope in the range below LStr, to give the predicted LF if all the Lyc photons produced within the HII regions had been converted to H[FORMULA] inside them. By then subtracting off the measured LF for the HII regions observed with L[FORMULA]LStr, and integrating this difference, using [FORMULA] erg s-1 as our upper limit, we obtain an estimate of the escaping flux, [FORMULA]. The result for NGC 3359 is:


which corresponds to a Lyman continuum flux of photons of 5.2[FORMULA] 1052 Lyc photons s-1. The fact that this initial estimate is bigger than the maximum estimate of the flux required to ionize the diffuse medium suggests that in NGC 3359 there are strong prima facie grounds for our hypothesis to be supported. The Lyc photon flux leaking from the density bounded HII regions is more than enough to ionize the diffuse medium. The geometrical correlation between the positions of the density bounded HII regions, and the observed diffuse H[FORMULA] has been studied in Zurita, Rozas & Beckman (2000) pointing strongly to a causal link. Similar use of this type of evidence made by Ferguson et al. (1996), and by Hoopes, Walterbos & Greenawalt (1996), but without reference to specific density bounded HII regions. To test the scenario in more depth, we will need to make detailed models in which the degree of clumping in the diffuse medium can be simulated, to see whether the mean free path can be long enough for the photons coming out of HII regions can cause the geometrical distribution observed in the diffuse H[FORMULA]. This should also be accompanied by geometrical analysis of a number of discs, to compare the predictions of a model with a Strömgren transition (Zurita, Rozas & Beckman 2000) to those of models in which the clumpiness of all the regions gives rise to a more or less constant leak factor across the whole range of HII region luminosities.

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© European Southern Observatory (ESO) 2000

Online publication: February 25, 2000