Modelling the 2-10keV spectrum assuming an underlying power-law continuum

Initially, we consider only the 2-10keV part of the spectrum and, furthermore, assume that the underlying continuum spectrum (i.e., prior to the effects of any reflection/reprocessing) is well described by a power-law. The restriction on the energy band is intended to avoid complexities associated with the well-known dusty warm absorber displayed by this object (Nandra & Pounds 1992; Reynolds 1997; Reynolds et al. 1997; George et al. 1998; Lee et al. 2001), as well as any oxygen and nitrogen recombination lines that may originate from the accretion disk (Branduardi-Raymont 2001; Sako et al. 2002). The power-law assumption is justified since, over this spectral range, almost all detailed models of thermal Comptonisation in AGN disk coronae predict a very good power-law form. The principal reason for this is that the 2-10keV band is well above energies characterizing the seed photons (believed to be generically in the optical/UV/EUV band for AGN) but is well below the thermal cutoff of a typical disk corona (above $\sim 100{\rm\thinspace keV}$). We shall relax both the energy restriction and power-law assumption later.

These spectral fits are reported in Table 1. All fits include absorption by the Galactic material along the line of sight to MCG$-$6-30-15 (with column density $N_{\rm H}=4.1\times 10^{20}\hbox {${\rm cm}^{-2}\,$}$; Elvis et al. 1989), modelled using the tbabs model of Wilms, Allen & McCray (2000). As shown in Paper I, a simple power-law is a poor fit, with residuals clearly indicating a rather narrow emission line at 6.4keV in addition to a broad excess between 3-7keV. The 6.4keV feature is well fit by a narrow Gaussian, resulting in a formal measurement of $6.40^{+0.01}_{-0.02}$keV for its energy. Thus, we can be secure in identifying this as the fluorescent K$\alpha$ emission line of iron which is in a rather low ionization state (less than FeXVII).

Figure 2: Fits of the joint EPIC-pn and RXTE-PCA data set with the partial-covering model (ABS*PCABS[PO+NFE]; panel a) and the relativistic ionized accretion disk model (ABS[PO+NFE+KDISK{iREFL}]; panel b). Although the partial covering model provides an adequate fit to the 0.5-10keV EPIC-pn spectrum, it requires a rather steep underlying continuum (with photon index $\Gamma \sim 2.3$) which is in strong disagreement with the higher-energy spectral data from the PCA. On the other hand, the relativistic disk model adequately describes the joint pn-PCA spectrum from 0.5-17keV. In both panels, the soft X-ray spectrum has been described using the ``absorber+emitter'' model from Section 3.2.

As can be seen from Table 1, there are two rather different models that fit the EPIC-pn data equally well: the partial covering model and the relativistic ionized disk model. This degeneracy can be broken by looking at the simultaneous higher energy data from the RXTE-PCA. To allow for any possible cross-calibration problems, we permit both the normalization and power-law index of the PCA spectral model to vary independently of the EPIC-pn spectral model. Indeed, we find that the PCA data require a photon index that is flatter by $\Delta\Gamma\sim 0.1$ than the EPIC-pn data, as is expected for the pre-LHEASOFT-5.3 PCA response matrix . Figure 2 shows the joint pn-PCA fit using each of these two spectral models. For completeness, these figures show the fit to the full 0.5-10keV EPIC-pn band employing the ``absorber+emitter'' soft X-ray model discussed in the next section, although similar conclusions are reached by modelling just the 2-10keV EPIC-pn spectrum in conjunction with the 3-15keV PCA spectrum. It can clearly be seen that the partial covering model grossly fails to reproduce the spectrum of this source above 10keV. To further examine this issue, we perform a joint pn-PCA fit of a combined spectral model that contains both relativistic disk features and partial covering. It is found that the column density of the partial absorber (assuming $f=0.4$) has an upper limit of $N_{\rm H}=3\times 10^{21}\hbox{${\rm cm}^{-2}\,$}$ and is consistent with zero; we conclude that a partial absorber, if present at all, has a negligible effect on the part of the X-ray spectrum relevant to accretion disk studies.

Having shown that the partial covering model is not viable, we conclude that the spectral complexity in the 2-10keV band of this source is primarily due to X-ray reflection from an ionized disk. The data require the disk component to be strongly broadened and redshifted. Our spectral model includes these effects by convolving the ionized reflection spectrum with the relativistic shifts expected from a thin accretion disk around a near-extremal Kerr black hole with dimensionless spin parameter $a=0.998$ (Laor 1991). In addition to using updated calibrations, these fits extend the previous work reported in Paper I by employing the self-consistent models of X-ray reflection from ionized material by Ballantyne, Ross & Fabian (2001).

Confirming the principal result of Paper I, the degree of relativistic broadening required by these data pushes one to a high value of the emissivity index and a low value of the inner disk radius. If one fixes the inclination of the accretion disk at $i=28^\circ$ (i.e., the value derived from ASCA data by Tanaka et al. 1995 and used in Paper I), the required emissivity index and inner radius are $\beta=4.29^{+0.15}_{-0.16}$ and $r_{\rm in}=1.78^{+0.14}_{-0.11}\,r_{\mathrm g}$), respectively. Allowing the inclination to be a free parameter, the best fitting values are even more extreme ($i=56\pm 4^\circ$, $\beta=7.7\pm 0.15$ and $r_{\rm in}=1.30^{+0.21}_{-0.06}\,r_{\mathrm g}$).