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Astron. Astrophys. 342, 87-100 (1999)

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4. Photoionization models

Several photoionization models for the Circinus galaxy have been discussed in the literature. These used line intensities and ratios measured from the central regions of the galaxy and were mostly directed to constraining the intrinsic shape of AGN photoionizing continuum. Quite different conclusions were drawn by M96, who found evidence for a prominent UV bump centered at [FORMULA]70 eV, and Binette et al. (1997, hereafter B97) who showed that equally good (or bad) results could be obtained using a combination of radiation and density bounded clouds photoionized by a pure power-law spectrum. In all cases the metal abundances were assumed to be solar and no attempt was made to constrain metallicities.

Here we mainly concentrate on knot C, an extranuclear cloud whose rich emission line spectrum and simple geometry (a plane parallel region) are better suited for deriving physical parameters from photoionization modelling. We first analyze the observational evidence against shock excitation and then describe in some detail the new modelling procedure which is primarily aimed at determining the gas metal abundances, (cf. Sects. 4.2 and 5.1). We also analyze the problems to reproduce the observed [FeVII]/[FeII] and [NII]/[NI] ratios (Sects. 4.5, 4.6), discuss the role of dust and reanalyze several crucial aspects of the line emission from the brightest regions closest to the nucleus.

4.1. Arguments against shock excitation

Strong evidence against shock excitation comes from the very low strength of [FeII] which indicates that iron is strongly underabundant, i.e. hidden in grains, within the partially ionized region (cf. Figs. 10, 11). Shocks are very effective in destroying dust grains, and velocities as low as 100 km s-1 are enough to return most of the iron to the gas phase (e.g. Draine & McKee 1993). This is confirmed by observations of nearby Herbig-Haro objects (e.g. Beck-Winchatz et al. 1994) and supernova remnants whose near IR spectra are dominated by prominent [FeII] IR lines (e.g. Oliva et al. 1989). Although the low Fe+ gas phase abundance could, in principle, be compatible with a very slow shock ([FORMULA]50 km s-1), this falls short by orders of magnitude in producing high excitation species.

Another argument comes from the HeII/H[FORMULA] and HeII/HeI ratios which are a factor [FORMULA]2 larger than those predicted by shocks models with velocities [FORMULA] km s-1 (Dopita & Sutherland 1995). It should be noted that, although stronger HeII could probably be obtained by increasing the shock speed to [FORMULA]1000 km s-1, these velocities are incompatible with the observed line profiles. More generally, the observed line widths ([FORMULA]150 km s-1, O94) are difficult to reconcile with the fact that only shocks faster than 300 km s-1 can produce prominent high excitation lines such as [OIII] (Dopita & Sutherland 1996). This argument becomes even stronger when interpreting the nuclear spectra where the highest excitation lines, [FeX,XI], do not show any evidence of large scale motions at velocities [FORMULA]200 km s-1. (cf. O94and work in preparation).

Finally, it is worth mentioning that detailed shock + photoionization composite models recently developed by Contini et al. (1998) suggest that shock excited gas does not contribute significantly to any of the optical/IR lines from Circinus.

4.2. Details of the photoionization models

4.2.1. Single component, radiation bounded clouds

We constructed a grid of models covering a wide range of ionization parameters ([FORMULA]), densities ([FORMULA]), metallicities ([FORMULA], [FORMULA]) and shape of the ionizing continuum which we parameterized as a combination of a power law extending from 1 eV to 10 keV with index [FORMULA] and a black-body 2with [FORMULA], the relative fraction of the two components being another free parameter. All the parameters were varied randomly and about 27,000 models were produced using Cloudy (Ferland 1993) which we slightly modified to include the possibility of varying the N-H charge exchange rate. The line intensities were also computed using the temperature and ionization structure from Cloudy and an in-house data base of atomic parameters. The agreement with the Cloudy output was good for all the "standard" species while large discrepancies were only found for coronal species (e.g. [FeX]) whose collision strengths are still very uncertain and much debated.

Out of this large grid we selected about 400 models whose [OIII]/H[FORMULA], [OIII]/[OII]/[OI], [ArV]/[ArIV]/[ArIII], [SIII]/[SII], [OIII][FORMULA]5007/[FORMULA]4363, [OII][FORMULA]3727/[FORMULA]7325, [SII][FORMULA]6731/[FORMULA]6716, [ArIV][FORMULA]4711/[FORMULA]4740 line ratios were reasonably close to those observed in knot C. These were used as the starting point for computing the "good models", with adjusted values of relative metal abundances, which minimized the differences between predicted and observed line ratios. Note that to reproduce both [FeVII] and [FeII] we were in all cases forced to vary the iron gas phase abundance between the fully and partially ionized regions (cf. also Sect. 4.5). The results of the best model are summarized in Table 4 and discussed in Sect. 4.3. Note the large discrepancy for [NI] which is overpredicted by a factor of [FORMULA]5, this problem is discussed in Sect. 4.6.


Table 4. Photoionization models for knot C [FORMULA] 12+log(X/H) where X/H is the absolute abundance by number [FORMULA] Abbreviation used: HeII=[FORMULA]4686, HeI=[FORMULA]5876, [NII]=[FORMULA]6583, [NI]=[FORMULA]5200, [OIII]=[FORMULA]5007, [OII]=[FORMULA]3727, [OI]=[FORMULA]6300, [NeIII]=[FORMULA]3869, [NeV]=[FORMULA]3426, [SiVI]=[FORMULA]19629, [SiVII]=[FORMULA]24827, [SII]=[FORMULA]6731, [SIII]=[FORMULA]9531, [ArIII]=[FORMULA]7136, [ArIV]=[FORMULA]4740, [ArV]=[FORMULA]7006, [FeVII]=[FORMULA]6087, [FeVI]=[FORMULA]5146, [FeII]=[FORMULA]16435 [FORMULA] Gas phase abundance in the partially ionized region [FORMULA] Gas phase abundance in the fully ionized region [FORMULA] UV-bump has [FORMULA] K and [FORMULA]=1.4, cf. Fig. 7 [FORMULA] [FORMULA] [FORMULA] Models 2,3 include density bounded clouds with the same density and U as radiation bounded regions, cf. Sect. 4.6.2 [FORMULA] Flux relative to that produced by a radiation bounded model

The most important results are the abundance histograms shown in Figs. 10, 11 which were constructed by including all the "good" models with [FORMULA]. Although the choice of the cutoff is arbitrary, it should be noticed that variations of this parameter do not alter the mean values, but only influence the shape of the distributions whose widths roughly double if the [FORMULA] cutoff is increased to values as large as 30.

4.2.2. Multi-density components, radiation bounded clouds

The large grid described above was also organized to have at least 4 models with the same photon flux, continuum shape and abundances but different densities, and these were used as starting points to construct multi-density models. We simulated 2-density clouds by coupling all available models with different weights and selected about 300 of them, which were used as starting points to compute the "good models" following the same procedure adopted for the single-density case. We also simulated clouds with [FORMULA]3 density components, but these results are not included here because this complication had virtually no effect on the quality of the fit.

The most important result is that single and multi-density models are equally good (or bad) in reproducing the observed line ratios. Obviously, this does not necessarily imply that knot C is a single-density cloud, but rather indicates that the stratifications which probably exist have little effect on the available density sensitive line ratios.

4.2.3. Mixed models with density and radiation bounded clouds

We constructed a grid of about 10,000 models photoionized by a power law AGN continuum with index [FORMULA], which turns into [FORMULA] beyond 500 eV, and covering the same range of physical parameters as the radiation bounded clouds described above. The column density of the radiation bounded component was always large enough to reach a temperature [FORMULA]3000 K at its outer edge. For each model we also computed line intensities from a density bounded cloud which we defined as a layer with thickness [FORMULA] equal to 5% of the nominal radius of the HII Strömgren sphere, numerically (f= filling factor)


The relative contribution of density and radiation bounded regions was set by imposing HeII[FORMULA]4686/H[FORMULA]=0.6

This approach is somewhat similar to that adopted by B96apart from the following details. The radiation bounded component here is formed by high density gas, a condition required to match the observed [ArIV][FORMULA]4711/[FORMULA]4740, and is concentrated within the projected size of knot C, i.e. [FORMULA]80 pc. In practice, the two components have the same densities and see un-filtered radiation from the AGN.

The "good models" were optimized, and the best abundances derived using the the same procedure depicted above. Worth mentioning is that most of the "good models" have spectral slopes in the range 1.3-1.5 which are in good agreement with those used by B96. The most important result is that these mixed models give similar, though slightly poorer (cf. Sect. 4.3) results than radiation bounded clouds.

4.2.4. The role of dust in extranuclear knots

Dust can modify the ionization and temperature structure because it competes with gas in absorbing the UV photons, and because it hides refractory elements such as iron. Given the low ionization parameters, however, the first effect is negligible, i.e. the ionization structure of the fully ionized region of knot C is not affected by dust although this plays an important role in modifying the heating-cooling balance of the partially ionized region heated by X-rays.

Cooling: the refractory species hidden in the grains cannot contribute to the line cooling and this effect is correctly computed by Cloudy. For example, depleting Fe on grains produces higher gas temperature and stronger [OI], [SII] etc. lines, because it suppresses the near IR lines of [FeII] which are among the major coolants for quasi-solar Fe/O gas phase abundances.

Heating: the metals hidden in the dust still contribute to the heating of the gas because the X-rays have energies much larger than the binding energy of the grains, and cannot therefore recognize metals in dust from those in the gas phase.

The major problem is that Cloudy (and probably other photoionization models) does not include the X-ray heating from the grain metals and therefore underestimates the temperature of the partially ionized region and hence may predict weaker fluxes of [OI], [SII] and other low excitation lines. Therefore, the models for knot C, having most of iron depleted on grains, are not fully self-consistent and most probably require a too high flux of X-rays to reproduce e.g. [OI]/[OIII]. This may imply that the "true" models should have somewhat softer spectra than those of Fig. 7.

[FIGURE] Fig. 7. The AGN ionizing continua used to compute the best models (Table 4) are plotted together with the observed X and IR continua. The solid line refers to a single density, radiation bounded component which provides a good fit for all lines but [NI]. The broken curves are for combinations of density and radiation bounded clouds, but these models cannot simultaneously reproduce the [OII]/[OIII] and [ArV]/[ArIII] ratios. The dashed curve provides the best fit for high excitations lines while the dotted curve best reproduces the OI/OII/OIII ionization balance (see Sect. 4.3 for details). Note that the curves show the spectra seen by knot C, and should be scaled by a coefficient which takes into account the "intrinisic beaming" of the AGN ionizing radiation (a factor of 2 for an optically thick disk) before being compared with the observed points. See Sect. 4.4 for a discussion of the AGN energy budget.

4.3. Best photoionization models of knot C: the shape of the AGN continuum and the role of density bounded clouds

Table 4 lists the results of the best photoionization models, selected from the several hundred which provided a reasonable fit to the spectrum of knot C. Note that the results of multi-density clouds (Sect. 4.2.2) are not included because they are virtually indistinguishable from those of single-density models.

Fig. 7 shows the AGN continuum adopted for the "best models" of Table 4. Radiation bounded models require a prominent UV bump centered (in [FORMULA]) at about 100 eV. This is slightly bluer than that found by M96and somewhat harder than model spectra of more luminous accretion disks (cf. e.g. Laor 1990), but in qualitative agreement with the predicted dependence of spectral shape with AGN luminosity, i.e. that lower luminosity accretion disks should have harder spectra (Netzer et al. 1992).

The amplitude of the UV bump could be significantly decreased by relaxing the assumption on the gas density distribution and, with a properly tuned combination of density and radiation bounded clouds, one may probably get a similarly good fit with a power law. It is nevertheless instructive to analyze why our mixed models provide a worse fit to the data and, in particular, are unable to simultaneously reproduce the OII/OIII balance and the [ArV]/[ArIII] and [FeVII]/[FeVI] ratios (cf. last two columns of Table 4). Model #2 has a high ionization parameter and correctly predicts high excitation lines but underestimates all [OII] lines while model #3, with a lower value of U, correctly reproduces the [OII]/[OIII] ratio but predicts very faint high excitation lines. The main reason for the above difference is that, for a given gas density, the [OII]/[OIII] ratio is a measure of the flux of soft ionizing photons ([FORMULA]=13-54 eV), while [ArV]/[ArIII] and [FeVII]/[FeVI] depend on the flux of harder radiation ([FORMULA] 80 eV). The spectrum of knot C is characterized by a quite large [OII]/[OIII] ratio, which points towards low fluxes of soft photons, and strong high excitation lines, which require large fluxes of hard photons. These somewhat contradictory requirements can be easily satisfied by a spectrum which steeply rises beyond the Lyman edge, and peaks at [FORMULA]100 eV, i.e. a spectrum similar to that of Model #1.

Independently on the detailed results of the models, the following arguments indicate that density bounded clouds may indeed play an important role.

  • Ionizing spectra with pronounced UV-bumps tend to produce too high [OIII] temperatures and model #1 is indeed quite hot, though still compatible (within 1.5[FORMULA]) with the somewhat noisy measurement of [OIII][FORMULA]4363 (cf. Fig. 3 and Table 4). Curiously, though, the result of Model #1 is the opposite of that obtained by most previous models in the literature which failed to produce hot enough [OIII]. Therefore, the classical "[OIII] temperature problem" may just reflect the fact that past models were mostly biased toward high metallicities and rather flat (i.e. without strong bumps) continua.

  • The H[FORMULA] flux from knot C is only [FORMULA]5% of that expected if the gas absorbed all the ionizing photon impinging on the [FORMULA] (40[FORMULA]40 pc2) geometrical cross-section of the cloud. Such a small "effective covering factor" could, in principle, be obtained by assuming a suitable distribution of radiation bounded, geometrically thin clouds or filaments. However, density bounded clouds seem to provide a more self-consistent interpretation because the measured value is remarkably close to the 6% predicted by models #2 and #3 (cf. note f of Table 4).

  • The variation of line ratios between the different knots cannot be explained by radiation bounded clouds illuminated by the same ionizing continuum, but require e.g. intrinsic beaming of the AGN continuum and/or filtering by matter bounded clouds closer to the nucleus. Mixed models could give a more natural explanation to the spatial variation of line ratios (see also B96).

4.4. Energy budget of the AGN

The ionizing photon flux seen by knot C is constrained by the U-sensitive and density sensitive line ratios which yield


This can be translated into [FORMULA], the total number rate of ionizing photons from the AGN, once the angular distribution of the UV ionizing radiation is known. Assuming that it arises from a geometrically thin, optically thick accretion disk, one finds [FORMULA] (e.g. Laor & Netzer 1989) and


where [FORMULA] is the projected distance of knot C i.e. [FORMULA] or d=300/[FORMULA] pc from the nucleus, i being the inclination angle of the cone relative to the plane of the sky. Detailed kinematical studies indicate [FORMULA] (Elmouttie et al. 1998).

The AGN luminosity in the ionizing continuum is therefore


where [FORMULA] is the average photon energy which is here assumed to be [FORMULA]50 eV. The ionizing luminosity is therefore very large but compatible, within the errors, with the observed FIR luminosity [FORMULA][FORMULA] [FORMULA] (Siebenmorgen et al. 1997). This implies that the AGN emits most of its energy in the ionizing continuum or, equivalently, that the AGN intrinsic spectrum has a prominent peak or bump in the ionizing UV, and much weaker emission at lower energies. This is in good agreement with computed models of accretion disks which also predict that low luminosity AGNs, such as Circinus, should be characterized by a quite hard ionizing continuum (cf. Laor 1990, Netzer et al. 1992).

The global properties of the AGN are summarized in Table 5 which also includes a comparison between [FORMULA] and the observed recombination rate, based on ISO observations of the Br[FORMULA] H-recombination line at 4.05 µm (cf. M96). The difference is remarkably large, with only [FORMULA]1% of the AGN ionizing photons being accounted for by emission from "normal" ionized gas. This indicates that the bulk of the Lyman continuum radiation either goes into ionizing regions which are obscured even at 4 µm (i.e. [FORMULA] mag), or is directly absorbed by grains in dusty clouds lying very close to the AGN.


Table 5. Global properties of the AGN ionizing continuum[FORMULA] [FORMULA] Assuming a distance of 4 Mpc [FORMULA] Required to reproduce the U-sensitive and density sensitive line ratios measured in Knot C (cf. Sects. 4.3, 4.4) [FORMULA] Ratio between the covering factor and the [FORMULA] pc2 geometric cross section of the knot [FORMULA] Total number rate of AGN ionizing photons, assuming emission from an optically thick disk (cf. Sect. 4.4) [FORMULA] From L(Br[FORMULA])=[FORMULA] [FORMULA] (M96) [FORMULA] Assuming that half of the observed Br[FORMULA] emission is produced by the starburst ring [FORMULA] Assuming an average photon energy of 50 eV [FORMULA] From Siebenmorgen et al. (1997)

4.5. Iron depletion and the [FeVII]/[FeII] problem

The observed [FeVII][FORMULA]6087/[FeII][FORMULA]16435[FORMULA]1 ratio cannot be explained using the same iron gas phase abundance in the HeIII Strömgren sphere, where FeVII is formed, and in the partially ionized region, where iron is predominantly FeII due to the rapid charge exchange recombination reactions with neutral hydrogen. It should be noted that this is a fundamental problem unrelated to the details of the photoionization models and primarily reflects the fact that the [FeVII] line has a very small collision strength ([FORMULA]) which is factor of about 10 lower than the [FeII] transition. A Fe+6/Fe[FORMULA] integrated relative abundance is thus required to reproduce the observed line ratio. This number is incompatible with the relative sizes of the HeIII and partially ionized regions which are constrained by e.g. the HeII and [OI] lines. It is also interesting to note that this problem is even exacerbated if the shock models of Dopita & Sutherland (1996) are adopted because these predict Fe+6/Fe+ ratios much smaller than the photoionization models described above.

A possible solution could be to advocate that the [FeVII] collision strengths are underestimated by a factor of [FORMULA]10 which would reconcile the observed [FeVII] and [FeII] intensities with a low (2% of solar) iron abundance (cf. Figs. 10, 11). However, although the collision strengths of coronal Fe lines are known to be very uncertain, and vary by factors [FORMULA]10 depending on whether resonances are included in the computation (cf. Sect. 5 of Oliva 1997), the available collision strengths for [FeVII] increase by only 20% between the old DW computations of Nussbaumer & Storey (1982) and the newer R-MAT (i.e. including resonances) values of Keenan & Norrington (1991). More detailed modelling of the [FeVII] lines and spectroscopic studies of nearby astrophysical laboratories (e.g. high excitation planetary nebulae) are required to clarify this issue.

The alternative possibility is to assume that the iron depletion is much larger in the partially than in the fully ionized region, as already suggested by Netzer & Laor (1993) and Ferguson et al. (1997). However, we could not find any simple explanation for such a stratification in knot C which lies far from the AGN and receives a relatively modest flux of hard UV photons. Therefore, Fe-bearing dust cannot be photo-evaporated and the only mechanism to destroy grains is sputtering. The slow shock produced by the ionization front which propagated outward when the AGN turned on was too slow ([FORMULA]40 km s-1) to effectively return Fe to the gas phase (e.g. Draine & McKee 1993). Faster shocks ([FORMULA]100 km s-1) are a natural and efficient source of sputtering but cannot explain the observations because they are expected, and observed, to emit prominent [FeII] lines from the dust-free recombining gas. A possibility to overcome this problem is a combination of shocks and photoionization where e.g. the dust-free gas processed by the shock is kept fully ionized by the AGN radiation. However, this situation is short lived because, after a few thousand years, the gas piled up behind the shock will eventually reach a column density high enough to become radiation bounded, and shield the recombining gas which will therefore show up in [FeII].

4.6. The [NII]/[NI] dilemma

The photoionization models of knot C systematically overestimate by large factors ([FORMULA]6) the strength of [NI] relative to [NII] (cf. Table 4 and Fig. 10). Although [NI][FORMULA]5200 has a quite low critical density ([FORMULA]1500 cm-3), this error cannot be attributed to the presence of higher density clouds because these would also effect the [SII] density sensitive ratio. In other words, multi-density models which correctly reproduce the high [NII]/[NI] ratio inevitably predict too large [SII][FORMULA]6731/[FORMULA]6716 ratios. Also, we can exclude observational errors because, in knot C, the [NI] doublet has an equivalent width of about 2.5 Å and is only marginally affected by blending with neighbouruing stellar absorption lines.

A possible solution is to argue that the rate coefficients for N-H charge exchange are overestimated, as already suggested by e.g. Ferland & Netzer (1983). In the partially ionized region, NII is mostly neutralized via charge exchanges with H0 and adopting lower charge exchange efficiencies yield larger [NII]/[NI] ratios. This is evident in Fig. 8 where this ratio is plotted as a function of the assumed value of [FORMULA](N), the charge exchange rate coefficient. Assuming a N-H charge exchange a factor of [FORMULA]30 lower than presently adopted yields the correct [NII]/[NI] ratio.

[FIGURE] Fig. 8. Effect of varying [FORMULA](N), the rate coefficient of N-H charge exchange, on the [NII]/[NI] and [NI]/H[FORMULA] ratios predicted by the photionization models discussed in Sect. 4.3. The solid line refers to model #1 while the dashed curve is for model #2 (cf. Table 4), and the dashed area show the value (with errors) measured in knot C. The parameter [FORMULA](N) is the standard rate coefficient used by Cloudy.

Noticeably, the problem we find here is exactly the opposite of what was reported by Stasinska (1984) whose models systematically underpredicted the [NI]/[NII] ratio in objects with low [OI]/[OII].

4.7. Modelling the nuclear spectrum: dusty, dust-free and diffuse components

A puzzling aspect of the line emission from regions very close to the nucleus is the simultaneous presence of high (e.g. [FeXI]) and low (e.g. [SII], [OI]) ionization species. More specifically, the images of M94clearly show that [SII] peaks at a distance of only [FORMULA] or 10 pc from the nucleus (cf. Fig. 9 of M94). This result is incompatible with the standard idea according to which low excitation lines are produced in clouds with low ionization parameters. Numerically, combining the ionizing continuum inferred from the spectrum of knot C with n=1.2[FORMULA] cm-3, the highest density compatible with the FIR [NeV] doublet (Table 3.3), yields [FORMULA] at r=10 pc from the AGN, an ionization parameter far too large for the production of low excitation species. Not surprisingly therefore, all the models so far developed for the high excitation lines (O94, M96, B97) predict that [SII] should peak much farther out and have a much lower surface brightness than that observed.

A simple and indeed natural solution is to assume that the low excitation lines are formed in dusty clouds. At these large ionization parameters dust dominates the absorption of UV ionizing photons and, therefore, quenches the HeIII and HII Strömgren spheres. Consequently, the X-ray dominated partially ionized region starts at much smaller radii, and is also slightly hotter than in the dust free model (cf. Fig. 9). Therefore, dusty clouds have a [SII] peak much closer to the nucleus and a [FORMULA]10 times higher surface brightness than dust-free clouds. It should be noted, however, that the total luminosity of low excitation optical lines is similar in the two cases, fundamentally because the available luminosity of soft X-rays is the same.

[FIGURE] Fig. 9. Ionization structure and spatial variation of the line emission from two nuclear clouds exposed to the AGN continuum of "Model #1" (cf. Fig. 7) and with identical physical parameters ([FORMULA] cm-3 and filling factor f=0.025) except for dust. The model without dust emits most of the coronal lines, while the dusty cloud accounts for the prominent low excitation lines observed close to the nucleus. However, both models fail to produce enough [OIV] and other intermediate ionization lines which therefore require a third, more diffuse component. See Sect. 4.7 for details.

Although the combined emission of dusty and dust-free clouds can account for the observed emission of low ionization and coronal species, it falls short by large factors in producing [OIV] and other relatively low ionization species which form within the HeIII sphere. This is an intrinsic limitation of "compact models" such as those of Fig. 9, and can be understood as follows. Compact models are characterized by large "ionization parameters" (cf. Sect. 3 of Oliva 1997 for a critical discussion on this parameter) and therefore have large fluxes of OIV ionizing photons which keep oxygen in higher ionization stages (mostly OVI and OVII) at all radii inside the HeIII Strömgren sphere. Outside the HeIII region, on the contrary, oxygen cannot be ionized above OIII because most of the OIII ionizing photons have already been absorbed by HeII. Therefore, OIV can only exist in a very narrow range of radii, just at the edge of the HeIII sphere, and its relative abundance is therefore very low.

In practice, we found it impossible to construct a single model which simultaneously produces a compact coronal line region, such as that observed in [FeXI] (O94), and which comes anywhere close to the [OIV][FORMULA]25.9/[OIII][FORMULA]5007[FORMULA]0.3 observed ratio. We did indeed construct many thousands of randomly generated dusty and dust-free models, and attempted an approach similar to that used for knot C (Sect. 4.2) but, in no case, could we find a model which satisfies these contradictory constraints. It should also be noted that B97independently come to a similar conclusion.

The main conclusion therefore is that, regardless of the details of the models, the nuclear spectrum and line spatial distribution can only be modeled by adding a third "diffuse" component (e.g. with a lower filling factor) to the dusty and dust-free clouds discussed above and depicted in Fig. 9. Given the large number of free parameters, we abandoned the idea of using photoionization models to constrain abundances and other physical properties of the gas, We made some attempt to verify that a mixture of clouds exposed to the same continuum, and with the same abundances as Model #1 of knot C (Table 4 and Fig. 7) could reasonably well reproduce the observed properties of the nuclear spectrum. However, the results are not too encouraging and, apart from the much improved [SII] surface brightness and [OIV]/[OIII] ratio, the solutions are not significantly better than those already discussed by M96and B97, and are not therefore discussed here.

4.8. Modelling other extra-nuclear knots

An analysis similar to that used for knot C was also applied to the other extra-nuclear knots using the more limited number of lines available in their spectra. The results can be summarized as follows.

The abundances derived in the Seyfert-type knots A, B, D, G, F (cf. Fig. 6) are similar those found in knot C but affected by much larger errors because of the more limited numbers of lines available for the analysis. In particular, the density sensitive [ArIV] doublet and the U-sensitive [ArV] line is not detected in any of these knots, and the reddening correction for [OII][FORMULA]3727 could be very uncertain in the high extinction regions (cf. note b of Table 2).

We also attempted to verify if the observed line ratios in these knots could be explained as photoionization by the same AGN continuum seen by knot C but could not find any satisfactory solution using radiation bounded clouds exposed to the same continuum. Adding matter bounded clouds alleviates the problem (as already stressed by B96) but requires an ad hoc choice of their photoelectric opacities, i.e. the radius at which the ionization structure is cut. In particular, explaining the drop of low excitation lines between the adjacent knots C and D (cf. Sect. 3.2) requires matter bounded clouds cut at about 1.2[FORMULA] the HII Strömgren radius, the exact position of the cut depending on the assumed shape of the AGN continuum. Another parameter affecting the ratio of low-to-high excitation lines (e.g. [OI]/[OIII]) is the iron gas phase abundance which influences the cooling of the partially ionized region (cf. Sect. 4.2.4). If iron is more abundant in knot D, as indicated by its stronger [FeVII] line emission (cf. Table 2 and Sect. 3.2), than [OI], [SII], [NII] could be depressed by the increased [FeII] cooling.

The abundances derived for the LINER-like knots (H, I) are very uncertain ([FORMULA]1.3 dex at least). Their spectra are not compatible with illumination from the same continuum seen by knot C but require a harder (i.e. more X rays relative to 13-80 eV photons) spectrum which could be in principle obtained by filtering the AGN continuum through an absorber with a carefully tuned photoelectric opacity. Alternatively, the weak (in surface brightness) spectrum of these low excitation knots could be explained by shock excitation, in which case one expects [FeII][FORMULA]16435/H[FORMULA][FORMULA]1 and a factor [FORMULA]10 larger than in the case of pure photoionization.

Finally, the oxygen lines in the highly reddened HII-like knots (E, L) are too weak to allow any reliable abundance analysis.

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Online publication: December 22, 1998