Possible scenarios for state transitions

We can organize possible scenarios for Deep Minimum state transitions by considering the three components of the X-ray continuum that might be relevant to inner disk X-ray reflection; (1) the normal accretion-powered X-ray emission from the corona of the accretion disk, (2) the torque-powered X-ray emission from the corona of the inner accretion disk, and (3) X-ray emission from a high latitude source (maybe the base of a Blandford-Znajek powered jet) near the black hole spin-axis (we shall refer to this as the jet-component, although this emitting material may not necessarily be moving rapidly). We can then elucidate three scenarios for normal/Deep-Minimum state changes in MCG$-$6-30-15 by considering the dominance of these three X-ray continuum components.

1. Constant-torque, variable-accretion case: Suppose that the inner disk torque is long-lived and changes in inner disk accretion rate drive the observed changes. In particular, the Deep Minimum state would correspond to a temporary but dramatic decline in the accretion rate through the inner disk. This naturally explains the drop in continuum flux during Deep Minima as well as the broadening of the disk reflection features. On the other hand, this scenario does not straightforwardly explain why the strength of the X-ray reflection features appears to saturate in the normal state (i.e. maintain a constant flux rather than equivalent width). As discussed by Reynolds (2000) and Lee et al. (2000), flux-correlated ionization changes in the disk surface might be responsible for this effect. A potentially more problematic issue for this scenario is the rate at which MCG$-$6-30-15 can transit into a Deep Minimum state. One naively expects the accretion rate to change on the viscous timescale $t_{\rm visc}=(r/h)^2\alpha^{-1}t_{\rm dyn}$, where $r$ is the radius of the disk, $h\sim 0.1r$ is its thickness, $t_{\rm dyn}$ is the dynamical timescale and $\alpha=0.1\alpha_{0.1}$ (with $\alpha_{0.1}\sim 0.1-1$) is the usual dimensionless angular momentum transport parameter of Shakura & Sunyaev (1973). If the mass of the black hole is $M=10^6M_6M_\odot$ (with $M_6\sim 1$-10; Reynolds 2000) we can deduce $t_{\rm dyn}\sim 50M_6{\rm\thinspace s}$. Thus, we have $t_{\rm visc}\sim 50M_6\alpha_{0.1}$ksec. Although the actual time required to transit to the Deep Minimum state is poorly characterized, the ASCA study of Iwasawa et al. (1996) suggest that it is rather more rapid ($<5$ksec). Thus, this model has may have problems reproducing the rapid transition. More detailed modelling, which is beyond the scope of this paper, is required to assess whether changes in accretion rate can really occur on such rapid timescales.

2. Sporadic-torque, constant-accretion case: Motivated by the timescales noted above, we consider a model in which the accretion rate in the inner disk is constant, but the torque exerted on the inner boundary by the plunging region or the spinning black hole is sporadic on a short timescale. In this case, the Deep Minimum state corresponds to rather rare intervals (duty cycle of $\sim 20\%$) in which the torque is ``engaged'' and strongly energizing the inner disk (the fact that F02 also observe a steep emissivity profile in the very innermost disk suggests that the torque is engaged, albeit more weakly, even in the normal state). This model successfully explains the changes in the line profile and (by construction through the assumed time-dependence of the torque) the rapid transition timescale. As before, flux-correlated ionization changes would have to be invoked to explain the saturation of the reflection features seen in the normal state. However, all other things being equal, the torqued disk would be expected to be more luminous than the untorqued disk due to the work done by the torque. This is in contrast with the observed continuum drop when the source enters the Deep Minimum state. However, more theoretical work on the physics of sporadically-torqued accretion disks is required to assess the true time-dependence of the luminosity.

3. Time variable height of a jet X-ray source: As discussed by Fabian & Vaughan (2003), an interesting possibility is that a classical accretion powered disk corona is (even if it exists) unimportant for producing the X-ray reflection features. Following the work of Martocchia & Matt (1996) and Martocchia, Matt & Karas (2002), Fabian & Vaughan (2003) suggest that the X-ray source is located close to the spin-axis of the black hole and at some height from the accretion disk. If one further supposes that the long term ($f<10^{-4}$Hz) variability of MCG$-$6-30-15 is driven by changes in the height and not intrinsic luminosity of this source, general relativistic effects (predominantly gravitational lightbending) can reproduce the observed relation of continuum and X-ray reflection intensities. We can extend the Fabian & Vaughan (2003) scenario into the Deep Minimum state in two ways. Firstly, there might be a separate X-ray component due to the inner disk torque (which would be emitted in a disk corona) that is responsible for the extreme red wing seen at all times in this source. The Deep Minimum state then corresponds to times when the jet source fades to low levels. Secondly, it is possible that there is only one X-ray emitting component. In the normal state, this is the jet component as discussed by Martocchia & Matt (1996) and Fabian & Vaughan (2003). The Deep Minimum state could correspond to times when the height of the jet component goes to zero in a continuous manner, i.e., the jet component touches-down on the disk and transits over to become a viscously mediated torque-component. This latter event might accompany a change in the structure of the black hole magnetosphere.

The key to distinguishing between these models is application of physical disk models similar to those described in this paper to all available high-quality data of MCG$-$6-30-15 and similar sources. This will allow us to determine observationally whether the torqued component varies dramatically when the source enters into a Deep Minimum state. We also need more realistic spectral models so that the physics of the accretion disk can be probed with confidence. Obvious improvements are to develop models in which the black hole spin is a free parameter of the fit (since we have no right to believe that all real black holes have dimensionless spin parameters of $a=0.998$) which also take into account that the inner edge of the fluorescing part of an accretion disk is not sharp (Krolik & Hawley 2002). MHD simulations will be invaluable for guiding development of such models.

It might be difficult to disentangle the possible role of an on-axis jet using current data alone. Observationally decomposing the X-ray continuum into its coronal and jet components may have to await the next generation of large-area observatories (principally Constellation-X and XEUS) which will allow one to assess the time delay between rapid X-ray variability and responses in the X-ray reflection spectrum. A measurement of this reverberation timescale would place strong constraints on the location of the X-ray source. We note that an X-ray source close to the spin axis of the black hole is the most favourable geometry for probing very strong relativistic effects (including a robust measure of the black hole's spin parameter) through X-ray iron line reverberation (Stella 1990; Matt & Perola 1992; Campana & Stellar 1993, 1995; Reynolds et al. 1999; Young & Reynolds 2000).