Photoionization models

We have constructed photoionization models of dusty warm absorbers using the photoionization code CLOUDY. Grids of such models were constructed for various values of the column density , ionization parameter and X-ray photon indices . Since we are interested in the behaviour of the outer warm absorber, the distance of the absorber from the primary source was fixed at 1pc. Otherwise, these models are identical to those of Fabian et al. (1994) and Reynolds et al. (1995) except for the inclusion of dust grains. The grain models used are described in HAZY (the manual to CLOUDY) pp. 284. Prompted by the observations of the previous paragraph, we have fixed the gas/dust ratio to Galactic value. Two such grids were computed: one contains a standard (i.e. local) mixture of silicate and graphite grains whereas the other contains only graphite grains.

 
Table 4: Results of fitting dusty warm absorber models to ASCA data.

These models were fitted to the ASCA data. Since we are interested in modeling fine details of the soft ASCA spectrum, only data from the best calibrated solid-state imaging spectrometer (SIS0) were used in the spectral fitting process. Furthermore, only data in the range 0.6-4keV were fitted: below 0.6keV the ASCA calibration becomes uncertain whereas above 4keV spectral complexities due to the Fe K line become relevant. In detail, our spectral model has three components. First, the primary power-law and the outer warm absorber are modeled using CLOUDY as described above. Secondly, the effect of the inner warm absorber was modeled as a OVIII absorption edge with (rest-frame) threshold energy 0.87keV and optical depth at threshold of (Otani et al. 1996). Lastly, Galactic absorption by a cold column of was included. The spectral fitting results are shown in Table 4.

 

Figure: Dusty warm absorber models fitted to 0.6-4keV data from the ASCA SIS0 (plain crosses). SIS1 data are also shown (filled squares) but have not been used in the spectral fitting reported in Table 4. Panel a) shows the model computed with a standard (i.e. Galactic) mixture of graphite and silicate dust grains. Panel b) shows the model computed with only graphite grains.

Table 4 shows that the assumed dust composition has a significant effect on the goodness of fit. The model which assumes graphite grains only is a much better fit than the model with a standard dust mixture ( for the same number of dof). The reason for this difference is illustrated in Fig. 6 which shows the best-fit unfolded model and the 0.6-2keV SIS0 data for each of the two assumed dust compositions. The standard dust model predicts a large photoelectric K-edge due to neutral oxygen (threshold energy ). Such an edge is not observed. The graphite grain model predicts a significantly smaller neutral oxygen edge which is much more consistent with observations. Note that the neutral oxygen edge in the latter model originates purely from the Galactic column and not from the dusty warm absorber. Thus, the graphite grain model seems to be preferred over the standard dust mixture model.

The signatures of dust in a dusty warm absorber only become significant at X-ray energies below the ASCA band. Thus, we must check that the dusty warm absorber model is consistent with the soft X-ray spectrum as determined by the ROSAT PSPC. In detail, we compared the ROSAT PSPC data with a spectral model consisting of a power-law form (photon index ) absorbed by three components:

a) a dusty warm absorber model as computed by CLOUDY (column density and ionization parameter ),

b) an absorption edge at the threshold energy of OVIII to mimic the effect of the dust-free inner warm absorber (optical depth at threshold ),

c) neutral absorption to account for Galactic and intrinsic cold gas absorption (column density ).

This 6 parameter scheme over-models the ROSAT PSPC spectrum (which has independent energy channels). Thus, we do not formally fit the data since any such fit is very poorly constrained - we merely seek to demonstrate consistency with the fit parameters derived from the ASCA data. Both the standard dust and the graphite dust warm absorber models are found to be consistent with the PSPC data for the following parameters: , , , , . These parameters are roughly consistent with those derived from the ASCA data with the exception of and . We will briefly address these in turn.

First, the photon index is inferred to be significantly steeper in the ROSAT observation than the ASCA observation. At least some of this discrepancy ( ) may be due to previously noted errors in the ROSAT-ASCA cross-calibration. However, there may be a true softening of the X-ray spectrum in the ROSAT band due to the onset of a soft excess. It must be noted that the ASCA data do not show any evidence of a soft excess above (Reynolds 1997). Temporal variations of may also explain such a discrepancy (note that the ROSAT and ASCA observations are separated by over 2 years).

Secondly, the OVIII edge depth is inferred to be significantly deeper in the ROSAT observation than in ASCA observation. This can be understood as a real (i.e., physical) change. Otani et al. (1996) and Reynolds (1996) have found a relationship between the instantaneous value of (as measured by ASCA) and the luminosity of this source. From the analysis of Reynolds (1996), this relation takes the form

where is the 2-10keV luminosity of the source. This can be understood physically in terms of a highly-ionized warm absorber in which most of the oxygen atoms are fully stripped of all electrons (i.e. OIX is the dominant state). A drop in ionizing luminosity results in an increased number of OVIII ions due to recombination of the OIX ions. This produces the observed anti-correlation between and .

During the ROSAT observation, the average 2-10keV luminosity is in the range . The large uncertainty in luminosity is due to the uncertainty in the extrapolation from the ROSAT band to the 2-10keV band. The corresponding range of edge depth is . Thus, the value needed to agree with the ROSAT spectrum, , is completely consistent with this relationship.

To summarize these X-ray results, we have shown that a warm absorber containing sufficient dust to explain the optical reddening is also compatible with the ASCA and ROSAT data. In principle, a detailed examination of the neutral K-edges of the various dust-phase metals allows the composition of the dust to be probed. Although it is extremely hard to make definitive statements yet due to the lack of high-quality soft X-ray spectra, there is evidence that the dust grain composition is non-standard in so far as it contains few silicate grains. We note that due to the tentative nature of this conclusion, we have not taken account of any non-standard dust composition when performing the reddening calculations of Section 3. Clearly, this should be the subject of future work.