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Astron. Astrophys. 338, 386-398 (1998)

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3. Results

The observed spectrum of an AGN within the frame of the OTCM is in general a sum of the primary, a reflected component and an emission from the dark sides of the clouds, with the relative weight of the last two given by the covering factor (see Paper I). We make first a general qualitative discussion without adopting any specific value of this parameter (Sect. 3.1). More detailed discussion, however, clearly involves the covering factor as additional parameter of the model (Sects. 3.2 and 3.3).

3.1. General properties of the primary, reflected and emitted components

3.1.1. The choice of the cloud parameters

The clouds are parameterized by the density, n, and the hydrogen density column, [FORMULA]. The reflected radiation, i.e. the radiation of the bright illuminated sides of the clouds is not very sensitive to the column density as long as the total optical depth of a cloud is high and in this paper we deal with such a clouds. In Fig. 4 we show two examples of the reflected spectra for two values of the column density (for model A). We see that the spectrum is softer in the optical band and slightly harder in the soft X-rays. The column density is important, however, for determination of the emission of the dark sides of the clouds (see Fig. 5). Larger column density leads to almost a black body type of emission although atomic features are clearly visible while lower column density is characterized by very strong atomic features superimposed on the continuum. The comparison with optically thin clouds was already discussed in Paper I.

[FIGURE] Fig. 4. Two examples of the optical/X-ray spectrum coming from the bright sides of clouds calculated for model (A) assuming the cloud column density [FORMULA] cm-2 (continuous line) and [FORMULA] cm-2 (dotted line). Other parameters: ionization parameter [FORMULA], extension of the incident spectrum from 0.1 eV to 280 keV, the slope of the incident spectrum [FORMULA] and cloud density [FORMULA] cm-3.

[FIGURE] Fig. 5. Two examples of the optical/X-ray spectrum coming from the dark sides of clouds calculated for model (A) assuming the cloud column density [FORMULA] cm-2 (continuous line) and [FORMULA] cm-2 (dotted line). Other parameters: ionization parameter [FORMULA], extension of the incident spectrum from 0.1 eV to 280 keV, the slope of the incident spectrum [FORMULA] and cloud density [FORMULA] cm-3.

Examples of the spectra calculated for three values of the ionization parameter [FORMULA] (300, 1000 and 3000) were shown in Paper I.

The dependence on the density of the clouds is weak since we parameterize the incident radiation not by flux but by the ionization parameter [FORMULA]. Clouds with lower density ([FORMULA] cm-3) are characterized by slightly bigger hydrogen and helium edges. Clouds with larger densities ([FORMULA] cm-3) are slightly optically thicker in the optical range thus leading to lower emission in those wavelengths.

3.1.2. The high energy extension and the slope of the primary emission

We tested two values of the high energy extension of the incident spectrum: 100 keV and 280 keV. The effective change of the bolometric luminosity required to preserve the value of the ionization parameter is practically negligible. However, high energy photons penetrate more easily deeper layers of the clouds so the radiation is thermalized more effectively and the UV part of the reflected spectrum as well as the dark sides of clouds are slightly brighter.

More important role for the shape of the reflected spectrum is played by the slope of the incident radiation. In Fig. 6 we show two examples of model A (reflected spectrum) calculated for the energy index [FORMULA] equal to 0.9 and 1.1. Steeper spectrum of the incident radiation results in steeper (i.e. softer) spectrum both in the optical band and in the soft X-rays.

[FIGURE] Fig. 6. Two examples of the optical/X-ray spectrum coming from the bright sides of clouds calculated for model (A) assuming the slope [FORMULA] (dotted line) and 1.1 (continuous line). Other parameters: ionization parameter [FORMULA], extension of the incident spectrum from 0.1 eV to 280 keV, cloud density [FORMULA] cm-3 and the column density [FORMULA] cm-2.

3.1.3. The nature of the primary emission

In order to show the dependence of the OTCM model on the assumption about the primary emission we present examples of solutions in which identical distributions of clouds are exposed to primary emission with the same ionization parameter but different spectral properties. The shapes of the incident spectra were shown in Fig. 3.

In the IR/optical band model (A) is different from the other two. If the covering factor of the source is not close to 1 the primary emission directly contributes to this spectral band and may strongly modify the optical slope of the resulting spectrum (see also Sect. 3.2) making it softer. The visibility of the primary emission in that energy band also affects the variability since in this case a fraction of the optical emission is not expected to be delayed with respect to the X-ray band.

In the EUV/X-ray band model (C) is significantly different from the other two models. Power law models are featureless while the Comptonization of the radiation emitted by the clouds preserves traces of atomic features if the optical depth of the hot medium is lower than [FORMULA]. Therefore in synchrotron models all line emission (in particular, Fe [FORMULA] line) has to be delayed with respect to the power law while in the last case the clear division of the X-ray emission into primary and reflected component is difficult and a fraction of the line flux does not have to be delayed with respect to power law.

The extension of the primary emission into gamma band simply reflects the adopted assumptions.

The spectra reflected by the clouds are shown in Fig. 7. The emission lines are included; they are plotted adopting a spectral resolution [FORMULA] equal to 30. The properties of the three spectra are influenced by the choice of the primary emission mechanism.

[FIGURE] Fig. 7. Three examples of the IR-Xray spectrum reflected from OTCM clouds calculated under assumptions of three primary emission models described in Sect. 2.2: model (A) - dotted line, model (B) - dashed line, model (C) - continuous line. In all cases the ionization parameter of the clouds is equal to 1000, cloud density is [FORMULA] cm-3 and the column density is [FORMULA] cm-2.

The model (A) presented here differs with respect to the model given in Fig. 9a of Paper I mostly because of the change in the shape of the incident radiation (slope of 0.9 instead of 1.0, and the high energy cutoff (280 keV instead of 100 keV). The new spectrum is generally harder because the incident radiation is harder and elastically scattered photons constitute a significant fraction of the reflected spectrum. The improvement of the physical input into the code resulted in slightly stronger emission lines and a more shallow Lyman edge.

The optical/UV slope of the reflected component is significantly flatter in the case of model (A) than in the other two. However, the traces of a Balmer edge and of a significant Lyman edge can be seen in all these spectra.

The soft X-ray part of the reflected spectrum looks similar in all three models as it is mostly determined by the adopted value of the ionization parameter. There is considerable emission below 2 keV with an approximate photon index 2.5 between 0.2 and 2 keV. The strong Fe [FORMULA] line is also characteristic for all three spectra, but the [FORMULA] edge is the weakest for model (A) and the most profound for model (C).

The broad band spectral index [FORMULA], measured customary between 2500 Å  and 2 keV, for the reflected component itself is equal to 1.09 for model (A), 0.94 for model (B) and 1.14 for model (C).

The high frequency part of the spectrum is again similar in all three cases which is due to the fact that the shape of the reflection component at high frequencies is simply determined by the Klein-Nishina cross-section for scattering.

An example of radiation spectra emitted by the dark sides of the clouds is shown in Fig. 8. The figure shows case (C) but the other two spectra are also characterized by an extremely large Lyman discontinuity in emission unless an extra heating of the dark sides of the clouds is allowed (dotted line).

[FIGURE] Fig. 8. The emission of the dark sides of OTCM clouds calculated under assumptions of model (C) described in Sect. 2.2.1 (continuous line). Dotted line shows a case (A) spectrum but with the temperature of the dark side of the cloud equal to [FORMULA] K, higher than results from pure radiative heating. The ionization parameter of the clouds is equal to 1000, cloud density is [FORMULA] cm-3 and the column density is [FORMULA] cm-2.

For these spectra the [FORMULA] index is high in all cases since the contribution of the dark side of the clouds to the spectrum at 2 keV is negligible. Therefore any contribution of the dark sides of the clouds to the resulting spectra would give steeper [FORMULA] than pure reflection spectra. Any contribution from primary emission would work in the opposite direction, and additionally it would modify the soft X-ray slope.

3.2. Optical/UV slope

We show an expanded fragment of the spectrum calculated from model (A) in Fig. 9. We consider two extreme cases interesting from the observational point of view. The lower curve shows a pure reflection component, i.e. corresponds to the case when the primary emission is not seen directly because it comes from a compact source and is shadowed by one of the clouds. The upper curve was obtained assuming that half of the primary source emission reaches the observer.

[FIGURE] Fig. 9. Optical/UV spectrum of OTCM clouds calculated under assumptions of emission model (A) described in Sect. 2.2.1. The lower curve shows the reflected spectrum and the upper curve shows a case of an equal contribution from the reflected and primary emission. The ionization parameter of the clouds is equal to 1000, cloud density is [FORMULA] cm-3 and the column density is [FORMULA] cm-2 The dashed line shows the mean spectrum of radio quiet quasars from Laor et al. (1997) and the dotted line shows the mean quasar spectrum of Francis et al. (1991).

In both cases we see the characteristic atomic features: noticeable Balmer edge, Lyman edge and weak [FORMULA] line. Equally profound spectral features are seen in models (B) and (C) since the spectral shape of the incident radiation has little effect. The Comptonization within the clouds is not expected to remove these features for the clouds of the adopted properties and [FORMULA] (Paper I).

The clear difference between model (A) and models (B) and (C) is in the slope of this part of the spectrum. We compare the models with the mean spectrum for radio quiet quasars derived recently by Laor et al. (1997). Our case (A) nicely coincides with the data in the optical part (if primary and the dark sides of the clouds are not seen) but is far too bright in the UV which means that the temperature of the clouds is too high. In the case of model (B) and (C) the reflection spectra are definitely too hard in the optical band and any contribution from the primary emission does not change that.

The comparison with the mean quasar spectrum obtained by Francis et al. (1991) is more favorable for model (A) and in that case a minor contribution from the primary emission would even be allowed. However, models (B) and (C) are still too hard to match observations for the ionization parameter [FORMULA].

Any contribution from the emitted spectra would give still harder spectra, in contradiction with the data.

The choice of lower value of the ionization parameter [FORMULA] results in a lower value for the cloud temperature which in principle helps to reconcile the models (B) and (C) with the data. We computed the spectra assuming [FORMULA]. However, in that case the spectral features (Balmer edge in absorption and Lyman edge in emission) are strong, giving a change in the continuum by 50 % and 100 %, respectively, in the case of a reflection component and even more (100 % and 500 % respectively) in the case of emission from the dark sides of the clouds.

3.3. Soft X-ray emission

Since the spectrum emitted by the dark sides does not contribute to the soft X-rays we can restrict our study of that band to the reflected component and the contribution from the primary emission.

We show an expanded version of model (A) in Fig. 10, in two versions: pure reflection spectrum and reflection plus half of the primary emission. We assumed [FORMULA].

[FIGURE] Fig. 10. Soft X-ray spectrum of OTCM clouds calculated under assumptions of emission model (A) described in Sect. 2.2.1. The lower curve shows the reflected spectrum and the upper curve shows the observed spectrum for the weight from primary 0.5. The ionization parameter of the clouds is equal to 1000, cloud density is [FORMULA] cm-3 and the column density is [FORMULA] cm-2. The dashed line shows the mean spectrum of radio quiet quasars from Laor et al. (1997).

The overall shape of the spectrum looks like a power law. When pure reflection is considered the slope of this power law is similar to the mean spectrum of radio quiet quasars (Laor et al. 1997). If a significant contribution from the primary is allowed the slope is too flat. Models (B) and (C) are generally similar in this spectral band so they are also an adequate description of the data.

Precise values of the slope between 0.2 keV and 2 keV for the reflected component in the three models are equal to 1.48, 1.35 and 1.57, respectively. The slope in the Laor et al. (1997) sample is 1.6 so model (C) is the best representation of the data. Even in the last model there is no place for a significant contribution from the direct primary emission since the slope would be too flat.

We see a number of quite strong emission lines, with OVIII at 0.653 keV being the most prominent. Complex spectral features are observed in a number of sources both in absorption and in emission, and they are usually explained by warm absorbers, i.e. optically thin clouds with a column density [FORMULA] and located at a distance of several light weeks (e.g. Otani et al. 1996). The same features are seen in models (B) and (C). Neither the mean quasar spectrum of Laor et al. (1997) nor observations of sigle quasars (e.g. Leach et al. 1995 for 3C 273) indicate the presence of such features.

A higher value of the ionization parameter would give too flat slopes for all three models.

Lower values of the ionization parameter give systematically steeper slopes. Model (A) calculated for [FORMULA] requires a contribution of the primary emission with a weight of 0.2 in order to reproduce the observed slope. For model (C) the allowed contribution of the primary is always slightly higher for a given value of the ionization parameter, and for [FORMULA] the required weight of the primary is [FORMULA]. The line emission is much stronger in that case.

In any case, the OTCM model for quasars explains the soft X-ray emission as a reflection from a partially ionized gas. The same mechanism was suggested to produce weak soft X-ray excesses in a number of Seyfert 1 galaxies (Czerny & Zycki 1994). However, in their case there were some problems to achieve the required ionization state of the gas within the frame of the adopted model. No such problems are encountered here.

3.4. Matching soft X-ray emission with UV

So far we discussed the comparison of the models with the mean quasar spectrum in the optical/UV band and in the soft X-ray band separately, i.e. with an arbitrary normalization in both bands. The comparison of the data with the model in the entire optical/UV/soft X-ray band is shown in Fig. 11 (model C, pure reflection). If the normalization is adjusted to soft X-rays we notice that the observed flattening towards high X-rays (at [FORMULA] keV) is reproduced by the models.

[FIGURE] Fig. 11. Optical/UV/soft X-ray spectrum of OTCM clouds for pure reflection calculated under assumptions of emission model (C) described in Sect. 2.2.1 (continuous line). The ionization parameter of the clouds is equal to 1000, cloud density is [FORMULA] cm-3 and the column density is [FORMULA] cm-2. The dashed line shows the mean spectrum of radio quiet quasars from Laor et al. (1997).

The [FORMULA] index of the mean quasar spectrum of Laor et al. (1997) is equal to 1.46 while in the reflected spectra shown in Fig. 7 it is equal to 1.09, 0.94 and 1.14, respectively. However, a contribution of the emission of the dark sides of the clouds helps to fill the gap.

Since the temperature of the dark side of a cloud depends significantly on the value of the ionization parameter [FORMULA] we can adjust its value to model the UV/EUV spectrum (apart from the spectral features present in the model and absent in the data).

In the case of model (A) the best value of the ionization parameter is [FORMULA] and an example of the resulting spectrum is shown in Fig. 12. Even the slight bend below [FORMULA]0.2 keV is reproduced by the models. The contribution of the dark sides of the clouds required to provide the flux in the optical band is rather moderate and the entire spectrum is mostly dominated by reflection. In the case of model (C) the best value of the ionization parameter is slightly higher, [FORMULA] (see Fig. 13). However, there is a large deficit of emission in the optical band which shows that a number of additional, cooler clouds should be included in the model, i.e. a single cloud population located at a given distance (i.e. parametrized by a single value of ionization parameter) is not an adequate description of the data in the case model (C).

[FIGURE] Fig. 12. Optical/UV/soft X-ray spectrum of OTCM clouds calculated under assumptions of emission model (A) described in Sect. 2.2.1 (continuous line) and assuming the weight of the reflected radiation equal to 1.0, of the dark sides emission 1.2, and of the primary 0.15. The ionization parameter of the clouds is equal to 300, cloud density is [FORMULA] cm-3 and the column density is [FORMULA] cm-2. The dashed line shows the mean spectrum of radio quiet quasars from Laor et al. (1997).

[FIGURE] Fig. 13. Optical/UV/soft X-ray spectrum of OTCM clouds calculated under assumptions of emission model (C) described in Sect. 2.2.1 (continuous line) and assuming the weight of the reflected radiation equal to 1.0, of the dark sides emission 5.0, and of the primary 0.15. The ionization parameter of the clouds is equal to 500, cloud density is [FORMULA] cm-3 and the column density is [FORMULA] cm-2. The dashed line shows the mean spectrum of radio quiet quasars from Laor et al. (1997).

3.5. High energy tail and the level of primary emission

The high energy cut-off of the spectrum is not well constrained observationally in the case of radio quiet quasars. Therefore, it is difficult to formulate any preferences for any of the discussed models on the basis of this spectral band.

The intensity of the iron [FORMULA] line given by the model is clearly large, in contradiction with observations of quasars, since a significant contribution from the primary emission is not allowed. For [FORMULA] the EW is [FORMULA] eV if the direct primary emission is not seen (lower curve in Fig. 14) but it is reduced to [FORMULA] eV if the contribution with a weight 0.5 would be allowed (upper curve in Fig. 14). For lower [FORMULA] it is still larger, and equals [FORMULA] keV and [FORMULA] eV, respectively. This is not surprising if the reflected spectrum dominates since the line intensity expected in such case is large (e.g. Zycki & Czerny 1994).

[FIGURE] Fig. 14. The spectrum of OTCM clouds calculated under assumptions of emission model (A) described in Sect. 2.2.1 (continuous line). Dotted line shows a case (A) spectrum with the contribution from the primary with the weight 0.5. The ionization parameter of the clouds is equal to 1000, cloud density is [FORMULA] cm-3 and the column density is [FORMULA] cm-2.

Observations of moderately bright quasars (Nandra et al. 1997b) give the equivalent width of the iron [FORMULA] line not higher than 300 eV, with a clear trend for a decrease of this value with an increase of a quasar luminosity.

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© European Southern Observatory (ESO) 1998

Online publication: September 14, 1998
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