In Table 2 (click here) we present the results of the fit with a simple power law
with and
as free parameters. 7 sources have
1.25. From the
statistics (with
) we would expect to have only 2 with values of
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 ,
.
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.
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
Figure 2: Distribution of
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 on the determination on
. In
Fig. 2 (click here) we present the distribution of
. The average value
is
(1
error) with a
standard deviation of
.
Only 3C 390.3 shows a marginal evidence of an intrinsic
absorption of the order of
.
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. | ![]() | ![]() | ![]() | kT4 | ![]() |
Mkn 335 | 6.06![]() | 3.55![]() | 3.51![]() | 74.6![]() | 1.13 |
Fairall-9 | 9.58![]() | 2.11![]() | 1.81![]() | 105.0![]() | 1.26 |
NGC 3783 | 8.73![]() | 15.90![]() | 33.4![]() | 63.4![]() | 5.84 |
NGC 4051 | 1.67![]() | 0.83![]() | 1.01![]() | 92.7![]() | 0.97 |
MCG 6-30-15 | 9.18![]() | 10.03![]() | 25![]() | 55.3![]() | 1.38 |
Mkn 841 | 5.25![]() | 2.75![]() | 1.25![]() | 58.8![]() | 1.02 |
NGC 7469 | 7.67![]() | 5.21![]() | 0.87![]() | 107![]() | 0.91 |
Akn 120 | 6.69![]() | 8.05![]() | 1.08![]() | 140![]() | 0.89 |
NGC 5548 | 4.51![]() | 1.92![]() | 0.76![]() | 59.3![]() | 1.29 |
Mkn 509 | 13.79![]() | 2.67![]() | 4.21![]() | 103.2![]() | 1.08 |
NGC 3516 | 15.70![]() | 4.79![]() | 9.4![]() | 60.9![]() | 2.07 |
MCG 2-58-22 | 3.03![]() | 2.64![]() | 0.36![]() | 120![]() | 1.01 |
NGC 7213 | 15.9![]() | 3.23![]() | 5.8![]() | 51.6![]() | 1.08 |
Note: (1) Power law flux at 1 keV in units of
(2) Neutral column density in units of
(3) Normalization of black body component (
)
in units of
(4) Black body temperature (eV).
Obj. | ![]() | E2 | ![]() | ![]() | ![]() |
Mkn 335 | 2.74![]() | 0.93![]() | 0.98![]() | 8.57![]() | 1.97 |
Fairall-9 | 1.9![]() | 1.15![]() | 0.72![]() | 12.8![]() | 1.74 |
NGC 3783 | 9.40![]() | 0.84![]() | 2.34![]() | 16.1![]() | 2.71 |
NGC 4051 | 0.51![]() | 0.93![]() | 2.5![]() | 3.77![]() | 4.74 |
MCG 6-30-15 | 5.32![]() | 0.79![]() | 1.23![]() | 12.3![]() | 0.95 |
Mkn 841 | 2.15![]() | 0.79![]() | 0.33![]() | 5.8![]() | 1.17 |
NGC 7469 | 5.00![]() | 1.04![]() | 0.45![]() | 9.35![]() | 1.1 |
Akn 120 | 8.06![]() | 1.17![]() | 0.69![]() | 9.70![]() | 1.43 |
NGC 5548 | 1.32![]() | 0.76![]() | 0.69![]() | 5.50![]() | 1.23 |
Mkn 509 | 2.19![]() | 1.14![]() | 1.02![]() | 20.6![]() | 1.73 |
NGC 3516 | 3.07![]() | 0.77![]() | 0.90![]() | 20.1![]() | 1.05 |
MCG 2-58-22 | 2.44![]() | 1.19![]() | 0.53![]() | 3.84![]() | 1.27 |
NGC 7213 | 1.75![]() | 1.03![]() | 0.16![]() | 16.3![]() | 1.85 |
Note: (1) Neutral column density in units of
(2) Edge threshold energy (keV)
(3) Absorption depth at threshold
(4) Power law flux at 1 keV in units of
.
Obj. | ![]() | E02 | ![]() | ![]() | ![]() |
Mkn 335 | 3.17![]() | 0.67![]() | 12.7![]() | 6.17![]() | 1.52 |
Fairall-9 | 2.07![]() | 0.90![]() | 12.2![]() | 9.58![]() | 1.36 |
NGC 3783 | 11.3![]() | 0.68![]() | 47.0![]() | 8.11![]() | 5.09 |
NGC 4051 | 0.94![]() | 0.69![]() | 9.72![]() | 1.83![]() | 1.48 |
MCG 6-30-15 | 6.26![]() | 0.60![]() | 25.8![]() | 8.52![]() | 1.43 |
Mkn 841 | 2.70![]() | 0.49![]() | 7.4![]() | 5.80![]() | 1.03 |
NGC 7469 | 5.21![]() | 0.83![]() | 6.4![]() | 7.81![]() | 0.91 |
Akn 120 | 8.43![]() | 0.97![]() | 9.11![]() | 7.23![]() | 0.99 |
NGC 5548 | 1.78![]() | 0.49![]() | 8.1![]() | 4.51![]() | 1.31 |
Mkn 509 | 2.53![]() | 0.84![]() | 28.8![]() | 14.2![]() | 1.31 |
NGC 3516 | 3.59![]() | 0.58![]() | 29.2![]() | 15.3![]() | 1.93 |
MCG 2-58-22 | 2.64![]() | 0.90![]() | 3.11![]() | 3.10![]() | 1.08 |
NGC 7213 | 3.03![]() | 0.45![]() | 48.8![]() | 15.9![]() | 1.07 |
Note: (1) Neutral column density in units of (2)
Cut off energy (keV) (3) Normalization of reflected component in units
of
(4) Power law flux at 1 keV
in units of
.
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 . 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 | ![]() | ||
Fairall-9 | |||
NGC 3783 | |||
NGC 4051 | ![]() | ||
MCG 6-30-15 | ![]() | ||
Mkn 841 | ![]() | ![]() | ![]() |
NGC 7469 | ![]() | ![]() | ![]() |
Akn 120 | ![]() | ![]() | |
NGC 5548 | ![]() | ||
Mkn 509 | ![]() | ||
NGC 3516 | ![]() | ||
MCG 2-58-22 | ![]() | ![]() | |
NGC 7213 | ![]() | ![]() | |
Note: A cross indicates that the model in its simplest version gives a satisfactory fit.
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 ).
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
, where
and
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).
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).
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
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).
This model gives a good fit for 5 sources but
it is never the only good model.
The edge energy is , 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 2
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.