9 The diffuse HH$\alpha$ flux

In this section we examine, using our data on NGC 7479, whether the rate of escape of ionizing photons from HII regions, notably from the high luminosity regions which are density bounded, is sufficient to account for the ionization of the diffuse interstellar medium (ISM) outside the regions, detected via its HH$\alpha$ emission. In NGC 7479 the flux from the diffuse ionized gas (DIG) is a rather high fraction of the HH$\alpha$ emission, between 35% and 60% of the total. In order to make the test we needed to measure the diffuse HH$\alpha$ flux, compute the escaping ionizing flux from the HII regions, and compare the two. If the second is the larger, we can conclude that the diffuse flux does not necessarily have an origin in processes other than ionization by the photons leaking out of HII regions. If we can show a geometrical correlation between the computed escaping flux and the measured diffuse flux then we can take our conclusions a step further, and attribute the latter to the effects of the former.

9.1 The total luminosity, and the diffuse luminosity:
Observational

To estimate the total luminosity emitted in HH$\alpha$ by NGC 7479 we first integrated the continuum-subtracted flux-calibrated HH$\alpha$ image over an elliptical area with the appropriate inclination and position angles, then subtracted off a constant level estimated for the background sky, integrated over this ellipse. The result is $L_{\rm H\alpha}$(total) = (1.3 $\pm$ 0.2)$\$10⁴² erg s^-1, corresponding to (9.5 $\pm$ 1.5)$\$10⁵³ Lyc photons s^-1. The chief source of error here is that due to the uncertainty in our determination of the sky level. Comparing this luminosity with the major sample of spirals in Devereux & Young (1991), we find that it is just above the upper limit of the full range of this sample, i.e. NGC 7479 has a very high total H$\alpha$ luminosity for a normal galaxy. To then estimate the diffuse flux we took more than one approach, due to a degree of geometrical uncertainty associated with the distribution of the diffuse emitting gas in the direction perpendicular to the plane of the galaxy. In the first method we used our catalogue of HII region fluxes, integrated over the whole set, and subtracted this from $L_{\rm H\alpha}$(total). The implied scenario here is that above an HII region there is much less diffuse gas in the total emitting column above the galaxy disc, so that to a first approximation this diffuse emission may be set to zero. In the second method, we used the equivalent areas of the HII regions in the catalogue to prepare a masked image, in which the HH$\alpha$ surface brightness was first set to zero in the areas occupied by all the regions. Then before integrating over the resulting image to obtain the total diffuse flux, we could assign a constant, non-zero level to the masked areas, with the idea that even above an HII region there is still some diffuse emission. One simple approach is to fill in the blanks to a surface brightness level equivalent to the mean value of the diffuse brightness measured in the field surrounding each region. This has the merit of being simple, but just as the use of blanks in the first method must give a lower limit to the total diffuse flux, filling these blanks fully at the level of the surrounding flux as in the second method will give an upper limit. The previous study by Ferguson et al. (1996) took the second approach, and the fractional HH$\alpha$ fluxes in the galaxies measured by these authors should be taken as upper limits, though not extremely far from true estimates. An intermediate approach is to fill the blanks with flux at a level which is the average for the diffuse flux over the whole galaxy. This again has the virtue of simplicity, and will give a value for the flux between the two limits, but is not guaranteed to give a precise value as a final result. To obtain the lower limiting diffuse flux we first obtained, from the full HII region catalogue, the fluxes and positions of all the regions with fluxes above the completeness limit, and integrated the flux of all these regions. To estimate the total due to weaker regions, we extrapolated the LF below $L_{\rm H\alpha}= 10^{38}$ erg s^-1, normalizing to the number in NGC 7479 at this luminosity, and following the curve measured by Walterbos & Braun (1992) for M 31 at lower luminosities, down to their measurement limit of 10³⁵ erg s^-1. We were forced to this approach since M 31 is the only external galaxy for which complete measurements significantly below 10³⁷ erg s^-1 have been taken. The sum of the integrated flux due to these weaker regions, and that of the stronger regions was then subtracted from the total estimated for the galaxy. Then making a minor correction (< 2% of the total) for foreground stellar images and removing the sky level, we can find the diffuse flux (lower limit) by subtracting the HII region total from the galaxy total. The result found here was

$$L_{\rm H\alpha}{\rm (DIG)}_1 = (4.6\pm1.5)\ 10^{41} \,{\rm \,erg \,s}^{-1}.$$ (3)

This can be used to compute an estimated requirement for the rate of Lyc photons flowing into the diffuse medium, which we did assuming case B, and a mean temperature in an HII region of 10⁴ K, yielding

$${L}_{{\rm Lyc}_1} = (3.4\pm1.1)\ 10^{53} \,{\rm \,Lyc\, photons\, s}^{-1}.$$ (4)

In Fig. 15, we show the resulting aspect of the emission in HH$\alpha$ of the galaxy after subtracting off the catalogued HII regions.

The upper limiting case was obtained by removing the HII regions and filling the spaces at a level computed by taking a 4-pixel-wide ring around each region, and averaging the counts per pixel in this ring. Then, we integrated the masked image over the elliptical area we described in the determination of the total flux. After, we took off the difference between the luminosity from the HII regions with log L < 38 using the M 31 luminosity function as described above, and the luminosity due to those regions with L less than 10³⁸ erg s^-1 which had been catalogued individually in our full HII region catalogue. This was done in order not to subtract any region twice.

Removing the sky level within the DIG area i.e. integration ellipse of the disc minus the HII regions area, we found a value of

$$L_{\rm H\alpha}{\rm (DIG)}_2 = (8\pm2)\ 10^{41}\,{\rm \,erg\, s}^{-1},$$ (5)

which converts to

$${L}_{{\rm Lyc}_2} = (5.7\pm1.2)\ 10^{53} \,{\rm \,Lyc\, photons\, s}^{-1},$$ (6)

for the upper limit. The intermediate case, which can be taken as the best estimate for the DIG component, was obtained by filling the HII region blanks with the mean background taken over the whole disk. This is certainly a better approximation than either of the limiting cases, and yielded a value of

$${L}_{\rm H\alpha}{\rm (DIG)}_3 = (6\pm2)\ 10^{41} \,{\rm \,erg\, s}^{-1},$$ (7)

which is produced by

$${L}_{{\rm Lyc}_3} = (4.5\pm1.2)\ 10^{53} \,{\rm \,Lyc \,photons\, s}^{-1}.$$ (8)

9.2 The ionizing flux escaping from the HII regions

We can obtain an estimate of the escaping flux from regions of the disc on the basis of the assumption that the luminosity log $L_{\rm H\alpha} = 38.6$ erg s^-1 (i.e. the Strömgren luminosity, $L_{\rm Str}$) marks the boundary between the population of ionization bounded and density bounded HII regions. This is a simplifying assumption, because there will be some leak-out of photons from the less luminous regions, and some fluctuation in the degree of escape from the more luminous, but it allows us to make a first order estimate, within the theoretical framework given in Beckman et al. (1999). Using this, we can extrapolate the LF for NGC 7479, with its measured slope for the range below $L=L_{\rm Str}$, to give the predicted LF if all the Lyc photons produced with the HII regions had been down-converted to HH$\alpha$ inside them. By then subtracting off the measured LF for the regions observed with $L \gt L_{\rm Str}$, and integrating this difference using the maximum observed luminosity of a region as our upper limit, we obtain an estimate of the escaping flux. The first simple test to apply is whether this luminosity is as big as the observed HH$\alpha$ luminosity in the diffuse emission (or at least of the same order, since we are taking into account only the disc HII regions). If not, our basic hypothesis has been shown to be inadequate, but if there are sufficient escaping photons then we have at least shown that escaping photons from the density bounded regions could be the originators of the diffuse emission. This would be a sufficient though not a necessary condition that the ionization of the diffuse medium is caused by these escaping photons.

  

Figure 15: Diffuse emission in HH$\alpha$ found after subtracting off the catalogued HII regions (these appear as uniform regular filled grey circles). The close geometrical association of the diffuse HH$\alpha$ with above all, the most luminous HII regions is evident

The result of this estimate of the escaping flux, $L_{\rm esc}$, for NGC 7479, using the LF in Fig. 5 is

$${L}_{\rm esc(disc)} = 2.2\ 10^{42} \,{\rm \, erg\, s}^{-1}\ {\rm in\,} \relax \ifmmode {\rm H}\alpha\else H$\alpha$\fi\ ,$$ (9)

which corresponds to 1.6 10⁵⁴ Lyc photons s^-1.

We may consider this value as a lower limit to the escaping flux that is, in principle, available to ionize the diffuse gas, since there must be a considerable photon flux escaping from the regions of the bar. The problem is that due to the irregularity of the LF of the bar we cannot apply the above method, based on the linearity of the LF, to estimate escaping flux from the density bounded regions of the bar. However, the escaping flux in the disc alone is sufficient to ionize the diffuse medium of NGC 7479 (neglecting in this first approximation the necessity of analyzing carefully the geometrical problem of the DIG and the location of the ionizing photon sources) since the escaping disc flux is higher than the Lyc photon flux required to ionize the total DIG of the galaxy.

One rough approximation to calculate the escaping flux from the bar regions is to consider that the escaping flux in a density bounded region of the bar is a determined fraction of its luminosity in HH$\alpha$. For the HII regions of the disc, using the method described above, this escaping flux, for a region with observed flux $L_{\rm H\alpha}$, varies between $1.5~L_{\rm H\alpha}$ and 10.0 $L_{\rm H\alpha}$, with a mean value of 3.5 $L_{\rm H\alpha}$. Extrapolating this result to the regions of the bar with log L > 38.6 we found that

$${L}{\rm (bar)} = 6.0\ 10^{41} {\rm \, erg\, s}^{-1} = 4.4\ 10^{53}~ {\rm Lyc \, photons\, s}^{-1}$$ (10)

so for the whole galaxy

$${L}_{\rm esc} \simeq 2.8\ 10^{42} {\rm \, erg\, s}^{-1} = 2.0\ 10^{54}~{\rm Lyc \, photons\, s}^{-1}.$$ (11)

Even if we are overestimating this escaping flux, the fact that our initial estimate is bigger by a factor of over 4 than the flux needed to ionize the diffuse medium suggests strongly that in NGC 7479 there are prima facie grounds for our hypothesis to be supported.

The geometrical correlation between the positions of the density bounded regions and the observed diffuse H$\alpha$ is clear in Fig. 15, showing that evidence for a causal link is present. This evidence was pointed out by Ferguson et al. (1996) in the galaxies they studied but without distinguishing between density and ionization bounded HII regions.

In order to proceed further with tests for the scenario, it will be necessary to make detailed models in which the degree of clumping in the diffuse medium can be realistically simulated, to see whether the mean free path can be long enough for the photons from the HII regions to cause the geometrical distribution of HH$\alpha$ observed. We would also need to examine more carefully the details of this distribution as observed in a number of discs, to be able to model its dependence on the positions of the density bounded HII regions as the suspected principal sources of its ionization (Zurita et al. 1999, in preparation).

By subtracting from the total hypothetical flux escaping from the HII regions the value of the measured diffuse flux, we obtain an estimate of the Lyc flux which escapes completely from NGC 7479. This value is $\geq$ 1.4 10⁵⁴ photons s^-1.