## 3. A simple model for the ionized gas in emission and absorptionOur 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, , against which to compare the information provided by the Ly and C IV lines in 0943-242. ## 3.1. Relation between the ionized absorption and emission componentsThe C IV and Ly 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 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 We should point out that for a density of the absorption gas as
high as 100cm Finally, the fact that both the absorption and emission gas contain
a significant amount of C ## 3.2. The observable quantityThe quantities determined from observation of 0943-242 are the
following: the emission line ratio measured by Röttgering
et al. (1997) is . 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
and
, respectively, as discussed in
Sect. 2. These four quantities carry information on the three
ionization species H where 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 does not explicitly depend on the abundance of carbon as shown below. ## 3.3. The simplest case of an homogeneous one-zone slabTo compute , in a first stage let
us consider an homogeneous slab of thickness (Osterbrock 1989) where where is the effective recombination coefficient rate to level of H (Osterbrock 1989). By putting the temperature dependence and all the atomic constants in the function , the emission line ratio becomes: where is the total hydrogen density, the carbon abundance relative to H of the emission gas, the fraction of triply ionized C and the ionization fraction of H. The ratio of column densities can be written as: where is the neutral fraction of
H inside our homogeneous slab and
the carbon abundance of the We note that 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 -
*Photoionization.*Putting in the atomic constants and calculating the equilibrium temperature and in the case of photoionization by a power law of index () of either -0.5 or -1, we find that the calculated 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 (%), that is . -
*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 remains in the similar low range of 6-13. At the lower temperature end, Ly emission is enhanced considerably by collisional excitation, which contributes in reducing . -
*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 obtained.
We conclude that for the simple one-zone case, consistently remains below the observed value by more than two orders of magnitude. ## 3.4. The ionization stratified slabTo verify whether a stratified slab geometry might alter the above discrepancy in , 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 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 for a slab as a function of (left panel) and (right panel). (One can interpret of Panel b as the mean neutral fraction of the slab: .)
The solid line in Fig. 5 represents a sequence of different
slab models with increasing ionization parameter from left to right
covering the range for a gas of
either solar metallicity () or with
a significantly reduced metallicity of
th solar. The practical constraint
that C IV be a strong emission line implies that
. In all calculations, the thickness
of the slab is set by the observable condition that
. Interestingly, such parameters
result in a slab which in all cases is "marginally" ionization-bounded
with less than 10% of the ionizing photons The monotonic increase of the
column with 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 .
Another way of looking at this discrepancy is to consider separately
the emission ratio or the
column ratio. Forgetting
, just to achieve the observed column
of
(
), one would have to use a gas
metallicity below solar by a factor
(see sequence with ), which cannot
be done without irremediably weakening the C IV
Might the observed 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 . This ratio is also that expected
from photoionization models if a sufficiently high value of 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 ).
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 . (Varying © European Southern Observatory (ESO) 2000 Online publication: March 28, 2000 |