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3. Results

3.1. Fit with simple power law and comparison with Ginga spectral index

In Table  2 (click here) we present the results of the fit with a simple power law with tex2html_wrap_inline1837 and tex2html_wrap_inline1839 as free parameters. 7 sources have tex2html_wrap_inline18411.25. From the tex2html_wrap_inline1843 statistics (with tex2html_wrap_inline1845) we would expect to have only 2 with values of tex2html_wrap_inline1843 greater than 1.25, were the model statistically acceptable. We therefore conclude that the simple power law model is not an adequate representation of the spectral shape of the sample in the ROSAT bandpass.

Furthermore, as can be seen in Fig. 1 (click here) and Table  2 (click here), the power law indices are usually greater than those of Ginga. The average values are respectively tex2html_wrap_inline1849, tex2html_wrap_inline1851. Only for one object, 3C 390.3, the spectrum in the ROSAT  range is well described by a simple power law with a photon index consistent with that observed by Ginga. This result agrees with the Walter & Fink (1993) finding of about 90% of the sources having a soft excess.

  figure332
Figure 1: Distribution of spectral index from ROSAT simple power law fits vs. Ginga. Note as the ROSAT slopes are sistematically greater than the Ginga slopes

  figure338
Figure 2: Distribution of tex2html_wrap_inline1853 for the 14 objects in the sample

The column densities agree in general very well with the Galactic ones, after taking into account the typical error of about tex2html_wrap_inline1855 on the determination on tex2html_wrap_inline1857. In Fig. 2 (click here) we present the distribution of tex2html_wrap_inline1853. The average value is tex2html_wrap_inline1861 (1 tex2html_wrap_inline1863 error) with a standard deviation of tex2html_wrap_inline1865. Only 3C 390.3 shows a marginal evidence of an intrinsic absorption of the order of tex2html_wrap_inline1867.

3.2. Modeling the soft X-ray excess

Once established the common presence of a soft excess, we attempted, for the 13 out of 14 sources which have a ROSAT power law index different from the Ginga index or an unacceptable simple power law model, to fit the data with a two components model, i.e. consisting of a hard power law (with the spectral index now fixed to the Ginga value) plus a further component describing the soft excess.

Three spectral models, representing the most common physical interpretation of the soft excess, have been investigated:

The results of the analysis are presented in Table  3 (click here), Table  4 (click here) and Table  5 (click here) for the black body, edge and reflection models, respectively.

The parameterization adopted for the three physical models can appear rather simplistic (especially for the warm absorber and reflection models, for which line emission could also be expected), but it is possibly adequate for the energy resolution of the PSPC. In any case, we have checked it by adding a narrow gaussian line to the edge or reflection models for all sources for which these models do not give acceptable results. As described in Sect. 4.5, the addition of the line does not in general make the fit acceptable.

   

Obj.tex2html_wrap_inline1689            tex2html_wrap_inline1691             tex2html_wrap_inline1883              kT4               tex2html_wrap_inline1887
Mkn 335 6.06tex2html_wrap_inline16530.15 3.55tex2html_wrap_inline16530.24 3.51tex2html_wrap_inline16530.68 74.6tex2html_wrap_inline16533.9 1.13
Fairall-99.58tex2html_wrap_inline16530.27 2.11tex2html_wrap_inline16530.15 1.81tex2html_wrap_inline16530.25 105.0tex2html_wrap_inline16537.8 1.26
NGC 3783 8.73tex2html_wrap_inline16530.19 15.90tex2html_wrap_inline16530.70 33.4tex2html_wrap_inline1653 63.4tex2html_wrap_inline16531.9 5.84
NGC 4051 1.67tex2html_wrap_inline16530.08 0.83tex2html_wrap_inline16530.13 1.01tex2html_wrap_inline16530.10 92.7tex2html_wrap_inline16533.8 0.97
MCG 6-30-15      9.18tex2html_wrap_inline16530.29 10.03tex2html_wrap_inline16530.98 25tex2html_wrap_inline165312 55.3tex2html_wrap_inline16533.6 1.38
Mkn 841 5.25tex2html_wrap_inline16530.10 2.75tex2html_wrap_inline16530.26 1.25tex2html_wrap_inline16530.52 58.8tex2html_wrap_inline16537.3 1.02
NGC 7469 7.67tex2html_wrap_inline16530.19 5.21tex2html_wrap_inline16530.24 0.87tex2html_wrap_inline16530.22 107tex2html_wrap_inline165311 0.91
Akn 120 6.69tex2html_wrap_inline16530.25 8.05tex2html_wrap_inline16530.26 1.08tex2html_wrap_inline16530.11 140tex2html_wrap_inline165310 0.89
NGC 5548 4.51tex2html_wrap_inline16530.08 1.92tex2html_wrap_inline16530.21 0.76tex2html_wrap_inline16530.24 59.3tex2html_wrap_inline16537.3 1.29
Mkn 509 13.79tex2html_wrap_inline16530.632.67tex2html_wrap_inline16530.29 4.21tex2html_wrap_inline16530.79 103.2tex2html_wrap_inline16538.7 1.08
NGC 3516 15.70tex2html_wrap_inline16530.264.79tex2html_wrap_inline16530.16 9.4tex2html_wrap_inline16532.9 60.9tex2html_wrap_inline16533.3 2.07
MCG 2-58-22 3.03tex2html_wrap_inline16530.12 2.64tex2html_wrap_inline16530.25 0.36tex2html_wrap_inline16530.08 120tex2html_wrap_inline165316 1.01
NGC 7213 15.9tex2html_wrap_inline16530.3 3.23tex2html_wrap_inline16530.26 5.8tex2html_wrap_inline16532.3 51.6tex2html_wrap_inline16534.9 1.08
Table 3: Fit with black body

Note: (1) Power law flux at 1 keV in units of tex2html_wrap_inline1993 (2) Neutral column density in units of tex2html_wrap_inline1687 (3) Normalization of black body component (tex2html_wrap_inline1997) in units of tex2html_wrap_inline1999 (4) Black body temperature (eV).

   

Obj. tex2html_wrap_inline1839               E2              tex2html_wrap_inline2005             tex2html_wrap_inline2007               tex2html_wrap_inline1887
Mkn 335 2.74tex2html_wrap_inline16530.05 0.93tex2html_wrap_inline16530.02 0.98tex2html_wrap_inline16530.09       8.57tex2html_wrap_inline16530.19 1.97
Fairall-9 1.9tex2html_wrap_inline16530.05 1.15tex2html_wrap_inline16530.05 0.72tex2html_wrap_inline16530.8 12.8tex2html_wrap_inline16530.3 1.74
NGC 3783 9.40tex2html_wrap_inline16530.14 0.84tex2html_wrap_inline16530.01 2.34tex2html_wrap_inline16530.11 16.1tex2html_wrap_inline16530.39 2.71
NGC 4051 0.51tex2html_wrap_inline16530.17 0.93tex2html_wrap_inline16530.01 2.5tex2html_wrap_inline16530.08 3.77tex2html_wrap_inline16530.07 4.74
MCG 6-30-15 5.32tex2html_wrap_inline16530.12 0.79tex2html_wrap_inline16530.02 1.23tex2html_wrap_inline16530.13 12.3tex2html_wrap_inline16530.5 0.95
Mkn 841 2.15tex2html_wrap_inline16530.06 0.79tex2html_wrap_inline16530.05 0.33tex2html_wrap_inline16530.10 5.8tex2html_wrap_inline16530.19 1.17
NGC 7469 5.00tex2html_wrap_inline16530.09 1.04tex2html_wrap_inline16530.04 0.45tex2html_wrap_inline16530.07 9.35tex2html_wrap_inline16530.2 1.1
Akn 120 8.06tex2html_wrap_inline16530.16 1.17tex2html_wrap_inline16530.03 0.69tex2html_wrap_inline16530.07 9.70tex2html_wrap_inline16530.20 1.43
NGC 5548 1.32tex2html_wrap_inline16530.05 0.76tex2html_wrap_inline16530.02 0.69tex2html_wrap_inline16530.10 5.50tex2html_wrap_inline16530.15 1.23
Mkn 509 2.19tex2html_wrap_inline16530.08 1.14tex2html_wrap_inline16530.05 1.02tex2html_wrap_inline16530.13 20.6tex2html_wrap_inline16530.7 1.73
NGC 3516 3.07tex2html_wrap_inline16530.05 0.77tex2html_wrap_inline16530.01 0.90tex2html_wrap_inline16530.08 20.1tex2html_wrap_inline16530.04 1.05
MCG 2-58-22         2.44tex2html_wrap_inline16530.08 1.19tex2html_wrap_inline16530.08 0.53tex2html_wrap_inline16530.09 3.84tex2html_wrap_inline16530.11 1.27
NGC 7213 1.75tex2html_wrap_inline16530.04 1.03tex2html_wrap_inline16530.16 0.16tex2html_wrap_inline16530.07 16.3tex2html_wrap_inline16530.37 1.85
Table 4: Fit with absorption edge

Note: (1) Neutral column density in units of tex2html_wrap_inline1687 (2) Edge threshold energy (keV) (3) Absorption depth at threshold (4) Power law flux at 1 keV in units of tex2html_wrap_inline1993.

   

Obj. tex2html_wrap_inline2119                 E02                    tex2html_wrap_inline2123                 tex2html_wrap_inline2007             tex2html_wrap_inline1887
Mkn 335 3.17tex2html_wrap_inline16530.06 0.67tex2html_wrap_inline16530.03 12.7tex2html_wrap_inline16531.7 6.17tex2html_wrap_inline16530.13 1.52
Fairall-9 2.07tex2html_wrap_inline16530.07 0.90tex2html_wrap_inline16530.05 12.2tex2html_wrap_inline16530.7 9.58tex2html_wrap_inline16530.26 1.36
NGC 3783 11.3tex2html_wrap_inline16530.33 0.68tex2html_wrap_inline16530.01 47.0tex2html_wrap_inline16533.8 8.11tex2html_wrap_inline16530.13 5.09
NGC 4051 0.94tex2html_wrap_inline16530.06 0.69tex2html_wrap_inline16530.02 9.72tex2html_wrap_inline16530.62 1.83tex2html_wrap_inline16530.05 1.48
MCG 6-30-15        6.26tex2html_wrap_inline16530.32 0.60tex2html_wrap_inline16530.03 25.8tex2html_wrap_inline16535.7 8.52tex2html_wrap_inline16530.18 1.43
Mkn 841 2.70tex2html_wrap_inline16530.20 0.49tex2html_wrap_inline16530.04 7.4tex2html_wrap_inline16531.2 5.80tex2html_wrap_inline16530.50 1.03
NGC 7469 5.21tex2html_wrap_inline16530.12 0.83tex2html_wrap_inline16530.05 6.4tex2html_wrap_inline16531.0 7.81tex2html_wrap_inline16530.14 0.91
Akn 120 8.43tex2html_wrap_inline16530.21 0.97tex2html_wrap_inline16530.04 9.11tex2html_wrap_inline16530.45 7.23tex2html_wrap_inline16530.16 0.99
NGC 5548 1.78tex2html_wrap_inline16530.16 0.49tex2html_wrap_inline16530.03 8.1tex2html_wrap_inline16532.0 4.51tex2html_wrap_inline16530.07 1.31
Mkn 509 2.53tex2html_wrap_inline16530.14 0.84tex2html_wrap_inline16530.06 28.8tex2html_wrap_inline16534.2 14.2tex2html_wrap_inline16530.6 1.31
NGC 3516 3.59tex2html_wrap_inline16530.15 0.58tex2html_wrap_inline16530.02 29.2tex2html_wrap_inline16535.1 15.3tex2html_wrap_inline16530.2 1.93
MCG 2-58-22 2.64tex2html_wrap_inline16530.11 0.90tex2html_wrap_inline16530.07 3.11tex2html_wrap_inline16530.52 3.10tex2html_wrap_inline16530.10 1.08
NGC 7213 3.03tex2html_wrap_inline16530.25 0.45tex2html_wrap_inline16530.03 48.8tex2html_wrap_inline16532.1 15.9tex2html_wrap_inline16530.4 1.07
Table 5: Fit with reflection

Note: (1) Neutral column density in units of tex2html_wrap_inline1687 (2) Cut off energy (keV) (3) Normalization of reflected component in units of tex2html_wrap_inline1993 (4) Power law flux at 1 keV in units of tex2html_wrap_inline1993.

In Table  6 (click here) we summarize the applicability of each model to the sample of spectra; a cross means that the fit is statistically acceptable (we define as statistically "acceptable" any fit for which tex2html_wrap_inline2239. 3C 390.3 is not included in the Table because no model gives a fit significantly better than the simple power law. It is worth noticing that for two sources, NGC 3783 and Fairall 9, all models fail to successfully fit the data. We will come back to this point in the following. A first, very important result is already clear from the Table: none of the models is a good description of the soft excess for all sources. In other words, the soft excess seems to be different in origin from source to source.

Let us now briefly discuss the results obtained for the different models.

   

Source bb           edge           refl.
Mkn 335 tex2html_wrap_inline2241
Fairall-9
NGC 3783
NGC 4051 tex2html_wrap_inline2241
MCG 6-30-15        tex2html_wrap_inline2241
Mkn 841 tex2html_wrap_inline2241 tex2html_wrap_inline2241 tex2html_wrap_inline2241
NGC 7469 tex2html_wrap_inline2241 tex2html_wrap_inline2241 tex2html_wrap_inline2241
Akn 120 tex2html_wrap_inline2241 tex2html_wrap_inline2241
NGC 5548 tex2html_wrap_inline2241
Mkn 509 tex2html_wrap_inline2241
NGC 3516 tex2html_wrap_inline2241
MCG 2-58-22 tex2html_wrap_inline2241 tex2html_wrap_inline2241
NGC 7213 tex2html_wrap_inline2241 tex2html_wrap_inline2241
Table 6: Summary of model applicability

Note: A cross indicates that the model in its simplest version gives a satisfactory fit.

3.3. Black body

As can be seen in Table  3 (click here), the black body gives a satisfactory fit for 8 out of 13 sources (a ninth source, Fairall 9, is just above the "acceptability threshold" of tex2html_wrap_inline2277). The temperature is comprised between 50 and 140 eV. (Fig. 3 (click here), panel a); the sources identified with a cross are those for which the black body is the only acceptable model, those with an open triangle are the other sources for which the fit is good, while finally the solid circles identify sources which cannot be fitted with the black body). Parametrizing the relative intensity of the soft excess with the quantity tex2html_wrap_inline2279, where tex2html_wrap_inline2281 and tex2html_wrap_inline2283 are the power law and total count rate respectively, we found that such quantity is consistent with a constant, apart from NGC 4051 (Fig. 3 (click here), panel b).

  figure498
Figure 3: Distribution of blackbody temperature (panel a) and intensity of the soft excess (panel b) vs. L(0.1-2.4 keV). The objects for which the blackbody is the only model providing a good fit are identified with a cross; those for which is a good fit, but that are also well fitted by at least another model are identified by an open triangle; the other by a filled circle

A certain correlation between temperature and luminosity is apparent, expecially if NGC 4051, who has a much lower luminosity than the other sources, is excluded. It should be noted, however, that this correlation is largely due to three sources for which the black body is not the only model which provides a good fit. It is therefore possible that this behaviour is an artifact of attributing a temperature to a component which is completely different in origin, like the other two under investigation. In any case, these results argue against a pure standard disc origin for the soft excess, because in this case the temperature would decrease with luminosity (at least assuming a constant accretion rate per unit mass of the black hole).

Finally, it is interesting to note that also for the sources where the black body model is not statistically acceptable, the temperature and the relative normalization of the soft excess are similar to the average values.

An example of a source (Mrk 509) for which a black body model provides a good fit is presented in the upper panel of Fig. 4 (click here).

  figure504
Figure 4: Unfolded spectra and residuals for: a) black body fit to Mrk 509; b) absorption edge fit to NGC 3516; c) reflection model fit to NGC 7469

3.4. Absorption edge

Formally, the absorption edge gives a good fit for 5 objects. For 4 sources the edge energy is around 0.8 keV, corresponding to O VII and/or O VIII absorption. For NGC 7469 the edge would correspond to mildly ionized neon; such an edge is not expected to be present without a (strongest) oxygen edge, and we then consider the result physically meaningless. It is worth noticing that the 3 sources for which the absorption edge is the only successful model (MCG-6-30-15, NGC 5548 and NGC 3516, see Table  6 (click here)) have all the "right" edge energy.

An example of a source (NGC 3516) for which an absorption edge fits well the data can be found in the middle panel of Fig. 4 (click here).

3.5. Reflection

This model gives a good fit for 5 sources but it is never the only good model. The edge energy is tex2html_wrap_inline2291, and then consistent with C VI, for two sources (Mkn 841 and
NGC 7213); around 0.8-0.9, and then consistent with O VIII, for other two sources (NGC 7469 and MCG-2-58-22). For Ark 120 the fit is formally acceptable, but the edge energy (0.97) appears to be too high to be physically meaningful. Finally, in all the 4 sources in which the fit is good and E0 meaningful, the normalizations of the reflection and primary components are of the same order, as expected for a 2tex2html_wrap_inline2297 illuminated matter (much different reflection components could occur only if the primary radiation were anisotropic, or as a result of a delayed response of the reflecting matter to changes in the primary emission).

In the lower panel of Fig. 4 (click here) an example of a source (NGC 7469) for which the reflection model provides a good fit is shown.


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