Introduction

Almost 40 years ago, it was suggested that the centres of galaxies host supermassive black holes and, further, that accretion onto those black holes powers active galactic nuclei (AGN; Salpeter 1964; Zeldovich 1964; Lynden-Bell 1969). Nowadays, the observational evidence in support of this picture is substantial. Proper motion studies of the stars in the centralmost regions of the Milky Way provide compelling evidence for the presence of a supermassive black hole with a mass of about $3\times 10^6\hbox{$\rm\thinspace M_{\odot}$}$ (Eckart & Genzel 1997; Ghez et al. 1998, 2000, 2003; Eckart et al. 2002; Schödel et al. 2002). The kinematics of rotating central gas disks in several nearby low-luminosity AGN has also provided some of the most convincing evidence for supermassive black holes (for example, M87: Ford et al. 1994, Harms et al. 1994; NGC 4258: Miyoshi et al. 1995; Greenhill et al., 1995). Finally, spectroscopic studies of stellar kinematics reveal that almost all galaxies studied to date do indeed possess a central supermassive black hole. The very strong correlation between the stellar velocity dispersion of a galaxy's bulge and the mass of the black hole it hosts (Gebhardt et al. 2000; Ferrarese & Merritt 2000) argues for an intimate link between supermassive black hole and galaxy formation, a result of fundamental importance.

With the existence of supermassive black holes established, it is clearly of interest to study them in detail. While of crucial importance for establishing the presence of supermassive black holes, all of the kinematic studies mentioned above probe conditions and physics at large distances from the black hole, $r>10^3r_{\mathrm g}$, where $r_{\mathrm g}=GM/c^2$ and where $M$ is the mass of the black hole. However, the energetically dominant region of an AGN accretion flow is very close to the central black hole, $r<20r_{\mathrm g}$, where general relativistic effects become strong. This is the region we must consider if we are to truly understand these systems. Luckily, nature has provided us with an extremely useful probe of this region. X-ray irradiation of relatively cold material in the vicinity of the black hole can imprint characteristic features into the X-ray spectra of black hole systems, most notably the K$\alpha$ fluorescent line of iron. Detailed X-ray spectroscopy of these features can be used to study Doppler and gravitational redshifts, thereby providing key information on the location and kinematics of the cold material. This is a powerful tool that allows us to probe within a few gravitational radii, or less, of the event horizon. See Fabian et al. (2000) and Reynolds & Nowak (2003) for general reviews of relativistic iron line studies of accreting black holes.

The Seyfert 1 galaxy MCG$-$6-30-15 ($z=0.008$) holds a special place in the history of relativistic iron line studies (e.g., see discussion in Reynolds & Nowak 2003). It was the first object for which observations by the Advanced Satellite for Cosmology and Astrophysics (ASCA) clearly revealed an iron emission line with a profile sculpted by strong relativistic effects (Tanaka et al. 1995; Fabian et al. 1995). Since then, studies of the iron line in this object have given us a window into some of the most exotic black hole physics observed to date. By identifying and then examining the so-called ``Deep Minimum'' state of this object, Iwasawa et al. (1996) used the iron line profile as measured by ASCA to demonstrate the need for iron fluorescence from within $r=6r_{\mathrm g}$, the radius of marginal stability around a Schwarzschild black hole. This suggested that the central black hole was rapidly rotating (in order that the radius of marginal stability lie at $r_{\rm ms}<6r_{\mathrm g}$; Iwasawa et al. 1996, Dabrowski et al. 1997), although the possibility of fluorescence from within $r=r_{\rm ms}$ prevented these arguments from being made rigorous (Reynolds & Begelman 1997).

More recently, XMM-Newton observations have provided strong support for the hypothesis of a rapidly rotating black hole. The first XMM-Newton observation of MCG$-$6-30-15 caught the object in a prolonged Deep Minimum state, allowing a high signal-to-noise spectrum to be obtained. The iron line was found to be extremely broadened and redshifted (Wilms et al. 2001; hereafter Paper I), in agreement with the previous results of Iwasawa et al. (1996). Using the scenario of Reynolds & Begelman (1997), even these new data could be (formally) described with emission around a non-rotating black hole. However, one would need essentially all of the emission to originate inside of $r=3r_{\mathrm g}$, i.e. half of the radius of marginal stability. This is an unreasonable emission pattern in any current accretion model. Thus, while uncertainties within the radius of marginal stability still hamper attempts to make these arguments absolutely rigorous, the data presented in Paper I make a compelling case that the supermassive black hole in MCG$-$6-30-15 is rapidly rotating.

The principal result of Paper I was the extreme central concentration of the iron line emission required to describe the observed breadth and redshift of the line profile. Even within the context of a rapidly-rotating Kerr black hole (with dimensionless spin parameter $a=0.998$), a phenomenological model in which the line emissivity varied as a power-law in radius ($\epsilon \propto r^{-\beta }$) required an inner emitting radius of $r<2.1r_{\mathrm g}$ and an emissivity index of $\beta=4.7\pm 0.3$. Assuming that the iron line emissivity tracks (even approximately) the underlying dissipation in the disk, this is in serious conflict with standard radiatively-efficient accretion disk models. In Paper I, we suggested that the central disk is being torqued by magnetic interaction with either the plunging region (Gammie 1999; Krolik 1999; Agol & Krolik 2000) or the rotating event horizon (Blandford & Znajek 1977; Li 2002). In both cases, the magnetic torque does work on the central accretion disk thereby producing a very centrally concentrated energy source.

In this paper, we further explore the XMM-Newton/EPIC data set first presented in Paper I. After describing our updated data reduction and calibration in Section 2, we present two distinct but related investigations. Firstly, in Section 3, we re-analyze the time-averaged X-ray reflection features investigated in Paper I. We show that the principal conclusions of Paper I, especially the need for a very high emissivity index, are robust to the application of a self-consistent ionized reflection model as well as the continuum curvature introduced by the inclusion of a physical thermal Comptonisation model or a complex absorber. By explicitly fitting the torqued disk model of Agol & Krolik (2000), we strengthen the hypothesis that this accretion disk is extracting the black hole's spin energy. In Section 4, we proceed to examine variability of the iron line features. Our results for the Deep Minimum state are put into a wider context, and implications for models of this source are discussed, in Section 5.

Throughout this paper, we shall assume a Hubble constant of $71\hbox{$\hbox{${\rm\thinspace km}{\rm\thinspace s}^{-1}\,$}{\rm\thinspace Mpc}^{-1}$}$ (from the Wilkinson Microwave Anisotropy Probe; Spergel et al. 2003). The corresponding distance to MCG$-$6-30-15 is $32.9{\rm\thinspace Mpc}$ ($z=0.00779$; Reynolds et al. 1997), assuming negligible motion of this galaxy relative to the Hubble flow. All uncertainties are quoted at the 90% level for one significant parameter ($\Delta \chi ^2=2.71$).