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Astron. Astrophys. 356, 23-32 (2000)

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3. A simple model for the ionized gas in emission and absorption

Our initial hypothesis is that the absorption gas is a subcomponent of the emission gas, sharing the same excitation mechanism and metallicity. We discuss the physical conditions of such gas and proceed to calculate an observable quantity, [FORMULA], against which to compare the information provided by the Ly[FORMULA] and C IV lines in 0943-242.

3.1. Relation between the ionized absorption and emission components

The C IV and Ly[FORMULA] lines are both resonant lines and therefore prone to be seen in absorption against a strong underlying source. This property has consequences for the emission gas as well. In effect, for a geometry consisting of many condensations for which the cumulative covering factor approaches unity, the resonant line photons must scatter many times in between the condensations before they can escape. In this case, the emerging flux of any resonant line from a non uniform distribution of gas will not in general be an isotropic quantity but will depend on geometrical factors and on the relative orientation of the observer, a point which we now develop further.

We propose that some kind of asymmetry within the emission gas distribution can explain how a fraction of the ionized gas can be seen in absorption against other nearby components in emission. Let us suppose that the emission region is composed of low filling factor ionized gas condensations which are denser (therefore brighter) towards the nuclear ionizing source. In this picture, the Ly[FORMULA] or C IV photons are generated within and escape from such condensations, after which they start scattering on the surface of neighboring condensations until final escape from the galaxy (we assume that the cumulative covering factor is unity). Let us now suppose an asymmetry 3 in the global distribution of the outer condensations respective to the plane of the sky. In this case, the total number of scatterings on neighboring condensations before final escape will differ depending on the perspective of the absorber. Since for an observer situated on the side with an excess of condensations many of the resonant photons would have been `reflected' away, we expect that the reduced flux would appear as an absorption line at the same velocity as that of the condensations responsible for reflecting away the resonant photons. The outer condensations (responsible for the absorption) must necessarily be of lower density in order to be of negligible emissivity respective to the inner (denser and therefore brighter) emission gas, otherwise the outer gas would out-shine in emission!

We should point out that for a density of the absorption gas as high as 100cm-3 as argued for in vO97, such a gas cannot be photoionized by the metagalactic background radiation which would be much too feeble to produce C IV . The ionization to such a degree of the absorption gas is in itself puzzling. We adopt as working hypothesis that it is -similarly to the emission gas- photoionized by the AGN or by the hard radiation from photoionizing shocks.

Finally, the fact that both the absorption and emission gas contain a significant amount of C+3 argues in favor of a common geometry and excitation mechanism for the gas, the underlying hypothesis behind the calculations developed below.

3.2. The observable quantity [FORMULA]

The quantities determined from observation of 0943-242 are the following: the emission line ratio measured by Röttgering et al. (1997) is [FORMULA]. We adopt the value of 0.17 following estimation of the missing flux due to the absorption troughs. As for the absorption gas, the H I and C IV column densities are [FORMULA] and [FORMULA], respectively, as discussed in Sect. 2. These four quantities carry information on the three ionization species H0, H+ and C+3. We define the ratio [FORMULA] as the following product of the emission and absorption ratios:


where [FORMULA] is the ratio of the measured absorption columns. If, as postulated above, the gas responsible for absorption is simply a subset of the line emitting gas, the ratio [FORMULA] does not explicitly depend on the abundance of carbon as shown below.

3.3. The simplest case of an homogeneous one-zone slab

To compute [FORMULA], in a first stage let us consider an homogeneous slab of thickness L of uniform gas density, temperature and ionization state to represent both the gas in emission and in absorption. Ignoring any peculiar scattering effects, the emission line ratio [FORMULA] is given by the ratio of the local emissivities [FORMULA] since the slab is homogeneous. For the emissivity of the C IV line, we have


(Osterbrock 1989) where T is the temperature, [FORMULA] the collision strength of the combined doublet, [FORMULA] the statistical weight of the ground state and [FORMULA] the mean energy of the C IV excited level. For the Ly[FORMULA] emissivity, we have


where [FORMULA] is the effective recombination coefficient rate to level [FORMULA] of H (Osterbrock 1989). By putting the temperature dependence and all the atomic constants in the function [FORMULA], the emission line ratio becomes:


where [FORMULA] is the total hydrogen density, [FORMULA] the carbon abundance relative to H of the emission gas, [FORMULA] the fraction of triply ionized C and [FORMULA] the ionization fraction of H.

The ratio of column densities [FORMULA] can be written as:


where [FORMULA] is the neutral fraction of H inside our homogeneous slab and [FORMULA] the carbon abundance of the absorption gas. As we are testing the case which equates the absorption gas with the emission gas, then [FORMULA]. We denote as [FORMULA] the product of the two calculated ratios:


We note that [FORMULA] is not directly dependent on either the abundance of C or on its ionization state. It is, however, dependent on the temperature and on the ionization state of H through the ratio 4 [FORMULA]. To compute this ratio, it is necessary to postulate an excitation mechanism. For this purpose, we have used the code MAPPINGS I c (Binette, Dopita & Tuohy 1985; Ferruit et al 1997) to compute [FORMULA] under the assumption of either collisional ionization or photoionization. Here are the results.

  1. Photoionization. Putting in the atomic constants and calculating the equilibrium temperature and [FORMULA] in the case of photoionization by a power law of index [FORMULA] ([FORMULA]) of either -0.5 or -1, we find that the calculated [FORMULA] always lies within the range 0.8-12. The explored range in ionization parameter 5 U covered all the values which produce significant C IV in emission ([FORMULA]%), that is [FORMULA].

  2. Collisional ionization. In this sequence of models, we calculated the ionization equilibrium of a plasma whose temperature varied from 30 000 K to 50 000 K. We find that [FORMULA] remains in the similar low range of 6-13. At the lower temperature end, Ly[FORMULA] emission is enhanced considerably by collisional excitation, which contributes in reducing [FORMULA].

  3. Additional heating sources. To cover the case of photoionization at a higher temperature than the equilibrium value (due to additional heating sources such as shocks), we artificially increased the photoionized plasma temperature to 40 000 K or 50 000 K for calculations with the same values of U as above. This did not extend the range of [FORMULA] obtained.

We conclude that for the simple one-zone case, [FORMULA] consistently remains below the observed value by more than two orders of magnitude.

3.4. The ionization stratified slab

To verify whether a stratified slab geometry might alter the above discrepancy in [FORMULA], we have calculated in a similar fashion to Bergeron & Stasiska (1986) and Steidel (1990b) the internal ionization and temperature structure of a slab photoionized by radiation impinging on one-side (i.e. one-dimensional "outward only" radiation transfer) using the code MAPPINGS I c . We adopted a power law of index [FORMULA] as energy distribution. Since the column densities of H and C are useful diagnostics on their own right, we present in Fig. 5 the value of [FORMULA] for a slab as a function of [FORMULA] (left panel) and [FORMULA] (right panel). (One can interpret [FORMULA] of Panel b as the mean neutral fraction of the slab: [FORMULA].)

[FIGURE] Fig. 5. a Calculated and observed [FORMULA] as a function of the column density [FORMULA]. The filled circle represents the observed value for 0943-242. b The same models as a function of the column ratio [FORMULA]. In both panels, the solid line represents a sequence of photoionized slabs with U increasing from left to right, starting at [FORMULA]. The gas total metallicity is either solar ([FORMULA]) or 1/50th solar. The separation between tick marks corresponds to an increment of 0.25 dex in U. All slab calculations were truncated at a depth corresponding to the observed [FORMULA]. The slab total column or [FORMULA] can be inferred from panel b. [If we were to reduce by 100 the abundance of the absorption gas while keeping solar the emission gas ([FORMULA], see Eqs. 4 and 5), this would be equivalent to translating by 2 dex both up and to the left the [FORMULA] sequence of panel a.] The dotted line represents a sequence of slabs of arbitrary uniform temperatures (all with [FORMULA] and [FORMULA]) covering the range 10 000 K to 40 000 K (from left to right) by increments of 0.1 dex in T. The open triangle represents a slab photoionized by a high velocity shock of [FORMULA] = 500 km s-1 from Dopita & Sutherland 1996.

The solid line in Fig. 5 represents a sequence of different slab models with increasing ionization parameter from left to right covering the range [FORMULA] for a gas of either solar metallicity ([FORMULA]) or with a significantly reduced metallicity of [FORMULA]th solar. The practical constraint that C IV be a strong emission line implies that [FORMULA]. In all calculations, the thickness of the slab is set by the observable condition that [FORMULA]. Interestingly, such parameters result in a slab which in all cases is "marginally" ionization-bounded with less than 10% of the ionizing photons not absorbed.

The monotonic increase of the [FORMULA] column with U is in part due to the increasing fraction of C IV but mostly it is the result of the slab getting thicker (larger [FORMULA] at constant [FORMULA]) since [FORMULA] decreases monotonically throughout the slab with increasing U. The slope or curvature of the two solid lines reflect changes in the internal temperature stratification of the slab with increasing U. Because of the dependence of [FORMULA] on T (see Eq. 6), there exists an indirect dependence of [FORMULA] on the total metallicity given that the equilibrium temperature is governed by collisional excitation of metal lines (when [FORMULA]).

The striking result from the slab calculations in Fig. 5 is that the models with solar metallicity are still two order of magnitudes below the observed [FORMULA]. Another way of looking at this discrepancy is to consider separately the [FORMULA] emission ratio or the [FORMULA] column ratio. Forgetting [FORMULA], just to achieve the observed column of [FORMULA] ([FORMULA] [FORMULA]), one would have to use a gas metallicity below solar by a factor [FORMULA] (see sequence with [FORMULA]), which cannot be done without irremediably weakening the C IV emission line to oblivion. Alternatively, reducing U much below [FORMULA] in the solar case can reproduce the [FORMULA] column but again the C IV emission line would be totally negligible.

Might the observed [FORMULA] emission line ratio be anomalous? This is not the case as the observed value in 0943-242 is typical of the value observed in others HZRG without, for instance, any evidence of dust attenuation of Ly[FORMULA] . This ratio is also that expected from photoionization models if a sufficiently high value of U is used (Villar-Martín et al. 1996).

Another possibility to consider is the presence of other heating sources such as shocks which would increase the temperature above the equilibrium temperature given by photoionization alone. Alternatively, small condensations in rapid expansion would result in strong adiabatic cooling and the temperature would be less than given by cooling from line emission alone. To explore such cases, we have calculated various isothermal photoionized slabs of different (but uniform) temperatures (all with [FORMULA]). They cover the range 10 000-40 000 K and are represented by the dotted line in Fig. 5. These models are in no better agreement with respect to [FORMULA]. (Varying U for any of these isothermal temperature slabs would result in an horizontal line). We also computed [FORMULA] for a solar metallicity (precursor) slab submitted to the ionizing flux of a 500 km s-1 photoionizing shock (Dopita & Sutherland 1996). This model which is represented by an open triangle in Fig. 5 does not fare better than the power law photoionization models.

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Online publication: March 28, 2000