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Astron. Astrophys. 344, 857-867 (1999)

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3. Spectral analysis

3.1. The PDS high-energy spectrum

A simple power-law fit (with [FORMULA] [FORMULA] 1.61 [FORMULA] 0.05; where NE [FORMULA] [FORMULA]) over the entire energy range ([FORMULA] 13-200 keV) of the PDS data, is clearly unacceptable because below [FORMULA] 20 keV the data are systematically lower than the model, yielding a poor fit with a [FORMULA] = 47 for 28 d.o.f. ([FORMULA]=1.68, rejected at 99.8% level in terms of [FORMULA] statistics). With absorption added to the model, the fit becomes acceptable with: [FORMULA] [FORMULA] 1.79 [FORMULA] 0.12, [FORMULA] [FORMULA] (1.54 [FORMULA] 0.70) [FORMULA] 1024 cm-2 and [FORMULA] = 32.28 for 27 d.o.f. ([FORMULA]=1.19). Here and below, errors are at 90% confidence for one interesting parameter unless otherwise stated. Best-fit spectrum, residuals and [FORMULA] contour plots in the parameter space [FORMULA]-[FORMULA] are shown in Fig. 1. If a 10% systematic error is added to the data below 20 keV to account for residual calibration uncertainties at those energies (Dal Fiume 1998, private communication), we find somewhat larger ([FORMULA] 20%) errors on [FORMULA] and [FORMULA] but the derived best-fit values remain unchanged. The observed (absorbed) 13-150 keV flux is about 1.47 [FORMULA] 10- 10 ergs cm-2 s-1, which makes Mkn 3 one of the brightest known AGNs in the hard X-ray energy range, as bright as 3C 273 (Haardt et al. 1998) and the buried Seyfert 2 galaxy NGC 4945 (Done et al. 1996). Comparison with the OSSE observations (Sect. 1) indicates that the source varied by at least a factor 3 in the 50-150 keV energy range.

[FIGURE] Fig. 1. Background subtracted PDS (13-150 keV) spectrum and residuals. Note that each data point has a S/N [FORMULA] 3. Inserted figures shows the [FORMULA] contour plots in the [FORMULA]-[FORMULA] parameter space with solid line contours indicating the 68%, 90% and 99% confidence limits.

3.2. The 0.6-150 keV broad-band spectrum: baseline model

Given the source spectral complexity (in particular below 10 keV), we addressed separately, in Appendix A, the study of the data below 10 keV alone . This allows us to compare BeppoSAX results to the ones previously reported in the literature, and to illustrate the ambiguities encountered in interpreting the spectrum of Mkn 3 over such a limited energy range. In the following, the results obtained for the overall broad-band spectrum are presented.

The data sets from LECS (0.6-4.5 keV), MECS (2.5-10 keV) and PDS (13-150 keV) detectors were fitted simultaneously. To allow for differences in the absolute flux calibration of the individual detectors, the normalization of different instruments was allowed to vary within 20% of the fiducial values of [FORMULA]/[FORMULA] = 0.65 and [FORMULA]/[FORMULA] = 0.85 (e.g., Haardt et al. 1998). Unless differently stated, the ratios obtained from the fits were all within [FORMULA] 5% of these fiducial values. A column density [FORMULA] = 8.46 [FORMULA] 1020 cm-2 due to absorption by the Galaxy (Dickey & Lockman 1990), was included in all models used in the following.

In Fig. 2, we show the residuals obtained between 0.6 and 150 keV for a fit with a power-law model plus Galactic absorption. The fit (where [FORMULA] [FORMULA] 0.4) clearly illustrates the complex spectral structure below 10 keV (see also Appendix A) and the strong and sharp "rise and fall" of the spectrum above 10 keV.

[FIGURE] Fig. 2. Residuals (in units of standard deviation) of the LECS, MECS and PDS broad-band spectrum for a model consisting of a single power-law with [FORMULA] [FORMULA] 0.45. This figure illustrates the soft excess below [FORMULA] 3 keV, the strong Fe [FORMULA] line at [FORMULA] 6.4 keV and the sharp rise and fall of the spectrum at [FORMULA] 10 keV.

Because of the presence of the very strong Fe [FORMULA] line, we first attempted to fit the overall broad-band spectrum with a pure reflection model 1 plus a steep soft power-law continuum that accounts for the low-energy emission below [FORMULA] 3 keV. Such a model is however ruled out ([FORMULA]) since it falls short of the data between 8-20 keV for any value of photon index, cutoff, inclination and ionization state of the reflecting material. This clearly indicates that the sharp rise and fall observed above [FORMULA] 10 keV cannot be explained only by the presence of an unabsorbed reflection component but requires, instead, the presence of a direct, strongly absorbed power-law component as modeled in Sect. 3.1.

In Appendix A, we show that a model consisting of a soft power-law continuum, an iron line plus a strongly absorbed hard power-law continuum (as initially proposed by I94) gives an acceptable description of the data below 10 keV. In the broad-band spectrum, however, we find that such model is ruled out ([FORMULA] [FORMULA] 1.4, Table 1) since it falls short of the data by a factor of about 2 in the PDS energy range. The continuum below the line (from about 3 to 8 keV) is extremely flat, thus a simple transmission model from cold matter (even with [FORMULA] [FORMULA] 7-10 [FORMULA] 1023 cm-2) cannot simultaneously fit the low and high energy bands. Similar results are obtained if one considers an ionized absorber instead of a neutral one.


Table 1. Fits of the broad band spectrum.
a) See text for descriptions.
b) in units of 1022 cm-2.
c) Line energy in the source rest-frame, in units of keV.
d) Line width, in units of keV.
e) Observed line intensity in units of 10-5 photons cm-2 s-1.
Note: Intervals are at 90% confidence for 2 interesting parameters.

A better solution is found, instead, with a basic description (called "baseline" model in the following) as first proposed by Turner et al. (1997b) that includes a soft power-law component, a strongly absorbed power-law component and an iron line plus an unabsorbed reflection1 component. Photon index and normalization of the primary power-law were assumed to be those of the hard, absorbed, power-law component. In this simplest form, this model adds only 1 free parameter (R), namely the relative amount of reflection compared to the directly-viewed primary power-law. The case R=1 corresponds to a 2[FORMULA] coverage as viewed from the X-ray source. The best-fit parameters obtained from this baseline model are given in line 2 of Table 1. The unfolded spectrum and data-model ratios are given in Fig. 3.

[FIGURE] Fig. 3. Unfolded broad-band spectrum and baseline model obtained by fitting the LECS, MECS and PDS data. For clarity, only the MECS and PDS data are shown here.

The cutoff energy ([FORMULA]) of the primary power-law continuum was then allowed to vary to search for a high-energy cutoff in the data. The fit gives a lower limit of [FORMULA] [FORMULA] 200 keV at 90% confidence (see Fig. 4). However, given the 10% systematic uncertainty between the MECS and PDS normalizations (Cusumano et al. 1998), we estimated an additional [FORMULA] 50 keV systematic error on this limit. It is stressed that it is difficult to obtain a very stringent limit on [FORMULA] in this source because its intrinsic spectrum only emerges at E[FORMULA]20 keV, where with the present data it is difficult to statistically sort out the parameters R, [FORMULA], [FORMULA], and [FORMULA]. However, looking at Fig. 3, we underline the clear absence of any cutoff at high energies up to about 150 keV. In conclusion, if a cutoff does exist, it occurs at energies above [FORMULA] 150 keV.

[FIGURE] Fig. 4. [FORMULA] contour plots in the [FORMULA]-[FORMULA] parameter space. Solid line contours represent the 68%, 90% and 99% confidence limits.

The adopted baseline model (admittedly rather complex) is, however, too simple to describe correctly the overall complexity of the spectrum of Mkn 3. In the following section, we discuss point by point the several "deviations" from the baseline model that are required by the data. For completeness, more complex models, alternative to the proposed baseline model, are presented in Appendix B. Statistically, they represent viable alternative descriptions of the broad-band spectra. However, they were discarded on the basis of physical arguments and lack of simplicity (Occam's razor).

3.3. "Optimizations" of the baseline model

First of all, in constructing the baseline model the absorption model used only considers photo-electric absorption and neglects Compton scattering which, however, becomes relevant for [FORMULA] [FORMULA] 1024 cm-2 (Ghisellini et al. 1994, Yaqoob 1997). To take this effect into account, we used plcabs in XSPEC which describes the X-ray transmission through a uniform, spherical distribution of matter, correctly taking into account Compton scattering (Yaqoob 1997). As expected, this model gives a column density of [FORMULA] 1.1 [FORMULA] 1024 cm-2, slightly lower (though still consistent within the errors) than [FORMULA] 1.3 [FORMULA] 1024 cm-2 obtained with our baseline model. At equal column density, the model that includes Compton scattering is more effective (by [FORMULA] 20-30% between 6 and 30 keV) in reducing the transmitted spectrum. The fit with plcabs is statistically slightly worse than the one obtained with our baseline model ([FORMULA] [FORMULA] 6). A slightly steeper ([FORMULA] [FORMULA] 1.83) high-energy power-law is obtained which, however, does not significantly change the other best-fit parameters (including the line parameters). The main consequences of this correction are thus in the calculations of the source luminosity that strongly depends on the [FORMULA] and [FORMULA] values used. With the plcabs model, the 0.1-150 keV luminosity is reduced to about 2.3 [FORMULA] 1044 ergs s-1, compared to the value of 2.6[FORMULA] 1044 ergs s-1 obtained with the baseline model.

Secondly, there are still residuals at energies between [FORMULA] 2 and 4 keV (Fig. 3), namely a broad absorption structure at [FORMULA] 3 keV and some excess emission at [FORMULA] 4 keV. Such excess counts indicate that the low-energy spectrum is probably more complex than a single power-law continuum, in agreement with ASCA results (Iwasawa 1995 (I95 hereinafter), G98). As suggested by these authors, thermal emission and/or absorption plus emission from a hot photo-ionized medium could be relevant in Mkn 3. Unfortunately, compared to the ASCA results, the poorer statistics of the LECS+MECS spectrum below [FORMULA] 4 keV does not allow a detailed modeling of these features. Alternatively, we note that such features could be due to fluorescence of elements lighter than iron expected from the reflection component (and not included in our model) as calculated by Reynolds et al. (1994). For example, the feature at [FORMULA] 4 keV could possibly be identified as a Calcium K[FORMULA] fluorescence line emission (3.69 keV). In any case, the baseline best-fit parameters only weakly depend on the exact modeling of the soft component because variations by [FORMULA] 50% in the soft power-law slope affect [FORMULA], [FORMULA] and [FORMULA] by less than 10%, i.e. less than the statistical errors reported in Table 1.

Thirdly, the power-law continuum of our baseline model represents only a phenomenological model. We thus tested a more physical and self-consistent model: the Comptonization model ([FORMULA] in XSPEC) calculated by Hua & Titarchuck (1995), that also includes reflection from optically thick gas. This model basically replaces the underlying power-law continuum with an exponential cutoff of our baseline model by a thermal Comptonization spectrum with reflection (Magdziarz & Zdziarski, 1995). The fundamental parameters of the model are the thermal gas optical depth ([FORMULA]) and its temperature (kT). We find that the data can be reasonably well modeled ([FORMULA] = 0.99) by an intrinsic spectrum due to thermal Comptonization with [FORMULA] and [FORMULA] keV (at the 90% confidence level for two interesting parameters).

Fourthly, the baseline model requires a broad iron line whose modeling is addressed in detail in the following section.

3.4. On the iron K line complex

It is interesting to note that if the shape of the continuum below the line (in the energy interval [FORMULA] 3-10 keV) is parameterized by a single power-law model (with [FORMULA] = -0.5), the line residuals (Fig. 5) suggest a complex profile. It comprises a red-shifted wing down to about 5 keV, a narrow and strong component peaking at [FORMULA] 6.4 keV plus a clear wing on the high-energy side of the line which drops at [FORMULA] 7 keV. A continuum [FORMULA] = -0.5 model is clearly unphysical and should rise doubts on the interpretation of the line profile obtained in this way. However, such multi-peaked structure may suggest a physical origin in an accretion disk (for the red and blue wings) plus a superposition of a narrow line at [FORMULA] 6.4 keV produced far from the black hole. Such conditions have been found in other Seyfert 2 galaxies often grouped under the name of Narrow Emission Line Galaxies (Weaver et al. 1997, Weaver & Reynolds 1998). However, contrary to what found by these authors in the sources they analyzed, in Sects. 3.1 and 3.2 we have shown that Mkn 3 certainly has a large absorption column which strongly affects the modeling of the underlying continuum between 3-10 keV. Indeed if we parameterize the continuum as given by our baseline model, we obtain the residuals shown in Fig. 6. Clearly, the red wing can be almost entirely explained by the combination of the reflection continuum and strong absorption. This illustrates the complexities of spectral modeling of emission lines when the underlying continuum is not well defined. The intrinsic power of broad band spectroscopy in sorting out these complexities and the advantage of using BeppoSAX in this case are clearly evidenced.

[FIGURE] Fig. 5. Iron line feature obtained from fitting the LECS + MECS spectrum between 3-5 keV and 7-10 keV with a single power-law model ([FORMULA]).

[FIGURE] Fig. 6. Data to model ratios obtained from fitting the LECS + MECS + PDS spectrum between 0.8-5 keV and 7-100 keV with the baseline model (Table 1, line 4).

However, Fig. 6 shows that "even" with our baseline model, the line appears complex with a significant excess emission at energies between 6.4-7 keV. Fitting the data with two narrow ([FORMULA] = 0 eV) Gaussian lines yields a significantly better fit ([FORMULA] = 6, for one more free parameter). The fit gives E1 = 6.43[FORMULA] keV, I1 = 3.5[FORMULA] [FORMULA] 10-5 photons cm-2 s-1 (observed) for the neutral fluorescence iron line and E2 = 7.00[FORMULA] keV, I2 = 1.3[FORMULA] [FORMULA] 10-5 photons cm-2 s-1 (observed) for the line at higher energies, respectively. These values are similar to the results previously found with ASCA (I94, G98, Netzer et al. 1998). The observed intensity of the neutral line corresponds to an equivalent width of [FORMULA] 645 [FORMULA] 180 eV with respect to the reflection component and [FORMULA] 650 [FORMULA] 182 eV with respect to the absorbed power-law continuum. The observed intensity of the line at higher energies corresponds to an equivalent width of [FORMULA] 235 [FORMULA] 160 eV, [FORMULA] 164 [FORMULA] 113 eV and [FORMULA] 6.2 [FORMULA] 4.3 keV with respect to the reflection component, the absorbed power-law continuum and the (soft) scattered continuum, respectively.

From Fig. 6, there is also an indication of a weak red-wing of the 6.4 keV iron line that could be attributed to Compton down-scattering in optically thick, cold matter as found in the Seyfert 2 galaxy NGC 1068 by Iwasawa et al. (1997). Theoretical models predict that this Compton shoulder should contribute with an intensity about one tenth that of the line core (Matt et al. 1991). Unfortunately, we cannot reach any firm conclusion about this because the feature is not statistically significant in the data.

3.5. Long-term X-ray history of Mkn 3

The observed 2-10 keV flux (calculated with our baseline model) is 6.5 [FORMULA] 10- 12 ergs cm-2 s-1 which places Mkn 3 in an intermediate state between its brighter state observed by Ginga in 1989 ([FORMULA] [FORMULA] 6-10 [FORMULA] 10- 12 ergs cm-2 s-1, depending on the adopted model: Awaki & Koyama 1993, I95, G98) and the fainter state measured by ASCA in 1993 ([FORMULA] [FORMULA] 1.3-1.9 [FORMULA] 10- 12 ergs cm-2 s-1, depending on the adopted model: I94, G98, Turner et al. 1997a).

Given the spectral complexity of Mkn 3, it is not straightforward to compare the present BeppoSAX results with previous X-ray observations because any residual feature (in particular the iron line intensity and continuum flux) is a strong function of the model adopted for the underlying continuum (see Appendix A) and also depends inevitably on the instrumental sensitivity and resolution. In order to provide a fair comparison, we thus re-analyzed the archival ASCA GIS and Ginga (upper-layer) data and compared it directly to the BeppoSAX MECS data. To reduce as much as possible the model-dependency in this comparison, we fitted each dataset only between 3-10 keV using a single power-law model with [FORMULA] fixed to -0.25 (the average value obtained from the 3 instruments) and free normalization. A direct comparison between the three unfolded spectra is shown in Fig. 7. Inspection of the figure reveals that i) the continuum above the line (E [FORMULA] 6.5 keV) decreased by about a factor of 4 between Ginga and ASCA and increased by about a factor 2 between ASCA and BeppoSAX, ii) the [FORMULA] 5-6 keV continuum and Fe [FORMULA] line intensity varied significantly less, by a factor of about 2 between Ginga and ASCA, and by less than 50% between ASCA and BeppoSAX and iii) the 3-5 keV continuum did not vary at all. The slow responses of the Fe [FORMULA] line and 3-6 keV continuum to the flux variations clearly indicate that such variations cannot be due to pure transmission but need dilution by a constant component. The argument, in turn, is giving support to the results of our spectral analysis (Sect. 3.2) which require inclusion of a Compton reflection component. As a matter of fact, all observations are consistent with a variable direct component and associated (variable) transmitted Fe [FORMULA] line plus a constant reflection component and associated (constant) reprocessed Fe [FORMULA] line. The non-varying (reprocessed) Fe [FORMULA] line indicates that it did not respond to continuum variations occured 7 years apart and places a rough lower limit of [FORMULA] 2 pc from the central source on the location of the Fe [FORMULA] line emitter. It should also be noted that the implication that the direct component of Mkn 3 varies with time is also supported by the observed increase (by a factor of [FORMULA] 3) between the OSSE and BeppoSAX high energy fluxes (see Sect. 3.1).

[FIGURE] Fig. 7. Overplot of the BeppoSAX (MECS), ASCA (GIS) and Ginga (top-layer) unfolded spectra. See text for details. 3-10 keV data fitted with a single (inverted) power-law with [FORMULA]=-0.25.

In the soft (E[FORMULA] 3 keV) X-ray band, the BeppoSAX flux of [FORMULA] 7.6 [FORMULA] 10- 13 ergs cm-2 s-1 between 0.6-3 keV (corresponding to a luminosity of [FORMULA] 6 [FORMULA] 1041 ergs s-1) is comparable to previous measurements with the Einstein IPC (Kruper et al. 1990), BBXRT (Marshall et al. 1992), ROSAT PSPC (Turner et al. 1993) and ASCA (I95). Therefore, as previously pointed out by I95, the lack of variability of the soft X-rays suggests that they originate from an extended region and immediately rules out a partial covering of the X-ray continuum which predicts that both hard and soft X-rays should vary simultaneously. Mkn 3 does not show evidence for starburst contamination (Pogge & De Robertis 1993) and Turner et al. (1997b) estimated a thermal emission in the 0.5-4.5 keV band lower than [FORMULA] 6 [FORMULA] 1040 ergs s-1 on the basis of its far infra-red luminosity. Therefore the most probable explanation for the lack of variations is that the soft X-rays are dominated by scattering of the intrinsic continuum (see also G98 and Netzer et al. 1998).

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Online publication: March 29, 1999