3.1. Timing analysis
In Fig. 1 the satellite orbit-averaged (i.e.: binning time 5700 s) light curves in the 0.1-3 keV (LECS) and 3-10 keV (MECS) energy ranges are shown (the energy boundaries have been chosen to sample different spectral components, see Sect. 3.2). Peak-to-peak variability by factors of 80% and 130% is evident in the 0.1-3 keV and 3-10 keV bands, respectively. The 3-10 keV/0.1-3 keV hardness ratio (HR) exhibits a much smaller () dynamical range. Fig. 2 shows HR plotted against intensity (CR) and shows that the HR tends to increase with increasing intensity up to and then "saturates" to a constant level. If the data points in Fig. 2 are fit with a broken linear relation, s-1.
This pattern of variability is typical of the quiescent X-ray state of Mkn 421 (Giommi et al. 1990; Sambruna et al. 1994). Indeed, simultaneous optical and TeV -ray observations of the source confirm the lack of any significant activity at the time (McEnery & Weekes, private communication). The state of quiescence is further substantiated by the BATSE light curve covering the the three days of the BeppoSAX observations (see Fig. 3). The BATSE daily monitoring sensitivity is 100 mCrab, implying that sensitivities of the order of few mCrab could be achieved by integrating the data over a period of few years. Over the 100 days covering the BeppoSAX observation, the 2 upper limit on the 20-100 keV flux was erg s-1 cm-2.
3.2. Spectral analysis
Spectra from the three observations were combined, in order to maximize the signal statistics. However, given the spectral variations revealed by the timing analysis, spectral analysis was performed separately on three different data sets (a) the total time-averaged spectrum ("Phase T" hereafter); (b) a spectrum integrated over the time intervals when the 5700 s binned 3-10 keV MECS light curve has a count rate ("Phase A" hereafter); (c) the complement of Phase A ("Phase B" hereafter). Spectra from the three MECS units were summed together after gain equalization and fit together with the data from the other instruments. Data were selected between 0.1-4.0 keV, 1.8-10 keV and 13-30 keV for the LECS, MECS and PDS, respectively. Factors were included in the spectral fitting to account for known normalization uncertainties between the instruments and the PDS to MECS factor was fixed to 0.75. This value is a factor lower than reported by Cusumano et al. (1998) for the Crab Nebula observation, to account for the effects of the RT screening algorithm. The following results are not affected by a residual uncertainty on the exact value of this parameter. The spectral results are summarized in Table 2.
Table 2. Best-fit spectral parameters fixed
The X-ray spectra of BL Lac objects are generally well described by a single power-law absorbed by an amount of matter consistent with the Galactic value. Some BL Lac objects, however, seem to require a model with a broken power-law, Mkn 421 being one of these (Comastri et al. 1997; Takahashi et al. 1996).
A single power-law model provides an unacceptable fit for both the total (reduced ) and the intensity resolved spectra (; ). Fig. 4 demonstrates that this is not due to a localized feature but to a incorrect modeling of the spectrum in the whole 0.1-30 keV energy range. Although a broken power-law yields a dramatic improvement of the quality of the fit, the fit is still unacceptable for the T and B datasets (; ; ). A good fit can be obtained if a pair of photoabsorption edges is added to the broken power-law, with threshold energies keV and keV. The addition of both edges is statistically required in the time-averaged spectrum ( and 29 for their subsequent inclusion in the spectral model). The best-fit threshold energies are broadly consistent with those expected from highly ionized Neon species NeIX ( keV) and NeX ( keV). No Oxygen edges are, however, detected, with the 90% upper limit on the optical depth of an OVII (OVIII ) edge of 0.13 (0.12). This makes such a model unlikely (see the discussion in Sect. 4), despite an acceptable .
If a narrow (i.e.: intrinsic width equal to 0) Gaussian line is instead employed to model the "bump" in the residuals around 1 keV, the improvement in the quality of the fit is much less, albeit formally still highly significant (, corresponding to chance occurrence likelihood of ), with best fit parameters: cm-2; ; ; keV; keV; eV.
An alternative explanation for the relatively poor fit of the broken power-law model is that the intermediate X-ray spectrum undergoes a gradual and smooth steepening with energy, which cannot be described by an abrupt (and unphysical) switch in the spectral photon index. A gradual steepening with energy on the other hand agrees with the Synchrotron Self Compton (SSC) scenario, which is nowadays widely accepted to explain the Spectral Energy Distribution (SED) of BL Lac objects (Ghisellini, Maraschi & Treves 1985; Ghisellini 1989). We have therefore parameterized the gentle concave curvature in the spectra with the function:
where , and are the low and high energy asymptotic slopes and is a "curvature radius" in the energy space. This model has only one degree of freedom more than the simple broken power-law. This model has already successfully fit the BeppoSAX spectrum of PKS 2155-304 (Giommi et al. 1998). It was impossible to obtain a significant constraint on from the fitting, the nominal best fit value being 0.30 for all datasets. In Table 2 the results for and are shown. The former case is strongly favored from the statistical point of view and will be therefore discussed in the following. The is comparable with that from the broken power-law + edges model for all datasets (; ; ). The asymptotic spectral indices are and , with a folding energy keV. Interestingly, the best-fit absorbing photoelectric column density ( cm-2) is well consistent with the Galactic contribution along the line of sight to Mkn 421 ( cm-2, Dickey & Lockman 1990). The average 0.1-2 keV and 2-10 keV fluxes are erg cm-2 s-1 and erg cm-2 s-1, corresponding to rest frame luminosities of 7.4 and erg s-1, respectively.
Using this physically reasonable description of the continuum, both in the time averaged and intensity resolved spectra, the next step is to understand which model parameter(s) (and therefore which physical quantities) can be considered responsible for the spectral changes observed in Mkn 421. If all the parameters are left free, there is a suggestion that and vary between Phase A and B spectra, but they are still marginally consistent within the statistical uncertainties. The fits on the intensity resolved spectra were therefore repeated, after fixing the other two parameters (i.e.: and ) to their best-fit values obtained from the time averaged spectrum fitting. The asymptotic high energy slopes are different at the 90% confidence level, while the folding energies are still consistent. However, whatever the detailed reason for the spectral change is, it is what happens above 4 keV that determines the observed spectral variability. In Fig. 5 the best-fit model and residuals are shown for all the datasets.
Narrow-band features such as Gaussian lines, absorption edges or saturated absorption lines were added to the best-fit power-law with variable curvature model. The largest improvement in fit quality is obtained in the last case ( for 2 degrees of freedom, which is significant at the 90% level of confidence only), with centroid energy keV. If the notch energy is held fixed at 0.654 keV (L resonant absorption of OVIII ), following the discovery of such feature in the Einstein spectra of several BL Lac objects (Canizares & Kruper 1984; Madejski et al. 1991), only a 90% upper limit of 10 eV on the EW can be set.
© European Southern Observatory (ESO) 1999
Online publication: December 22, 1998