Is the black hole rapidly spinning?

There has been a great temptation within the X-ray astrophysics community to interpret very broad iron lines, with $r_{\rm in}<6M$ , as direct evidence for black hole rotation. However, when one attempts to make these arguments rigorous, a loophole is rapidly discovered. By its basic nature, one can see that it is possible to produce arbitrarily redshifted spectral features from around any black hole if any region of the disk (even those within the plunging region) is permitted to produce observable line emission [216]. As the emitting region tends to the event horizon, the redshifts grow arbitrarily large. Thus, an attempt to determine the space-time geometry (and, in particular, the spin parameter of the black hole) from the time-averaged iron line profile necessarily involves considerations of the astrophysics of the inner accretion disk and, in particular, the extent to which emission/reflection from the plunging region of the disk might be important.

Within the standard model for black hole accretion (i.e., that of Page, Novikov and Thorne [115,114]), there is no angular momentum transport and no dissipation of energy within the plunging region. Hence, this region of the disk cannot support an X-ray active corona. Furthermore, if the corona of the dissipative part of the disk has a small scale-height, the surface of the plunging region will not be subjected to X-ray irradiation for purely geometric reasons, and will not produce X-ray reflection signatures. These considerations would validate the assumption of no X-ray reflection signatures from within the plunging region thereby allowing the spin of the black hole to be determined in the manner discussed above. However, there are two scenarios in which appreciable X-ray reflection might occur from part of the plunging region. Firstly, it is possible that the outer disk corona might be geometrically-thick, thereby allowing it to irradiate a dissipationless plunging region. Given this scenario, the ASCA data for the DM-state of MCG-6-30-15 data could be consistent with even a non-rotating (Schwarzschild) black hole [216]. Secondly, as discussed in §3.2.4, the accretion flow within the plunging region may well be able to dissipate a significant fraction of its binding energy. One could easily imagine the formation of a powerful X-ray emitting corona sandwiching the plunging region of the disk. Although this scenario has not been worked out in detail, such an inner corona might be responsible for locally produced X-ray reflection within the plunging region. It should be noted that the plunging region is likely to be highly ionized, and so any detailed study of X-ray reflection from this region must use self-consistent ionized reflection models as were discussed in §3.5.2 [217].

**Figure 13:** *XMM-Newton* data from the first observation of MCG-6-30-15. Panel (a) shows the ratio between the data and a simple model consisting of a power-law fitted to the 0.5-11keV data. Panel (b) shows the ratio of data to a more detailed model which also accounts for line-of-sight absorption towards the accreting black hole. The residuals in this plot are attributed to X-ray reflection from the relativistic disk. (c) Deconvolved spectrum of the iron K band portion of the spectrum, showing a very broadened and redshifted iron line. Figure from [218]
$\begin{figure}\centerline{ \psfig{figure=mcg6_xmm.ps,width=0.8\textwidth}} \end{figure}$

The above history made MCG-6-30-15 a prime target for study with the high-throughput EPIC instruments on board the XMM-Newton observatory. The first XMM-Newton observation of this source happened to catch it in a prolonged DM state. The superior sensitivity of these instruments allowed a much more detailed study of this enigmatic state to be conducted [218].

In agreement with the ASCA-based conclusions of Iwasawa, the X-ray reflection features were found to be very broad and very strong (see Fig. 13). The detailed modeling of the XMM-Newton/EPIC spectrum required the modeling of the full reflection spectrum, not just the fluorescent iron line, with relativistic shifting/smearing applied to both the fluorescent line and the reflection continuum. Again, the reflection features were found to be so broad and redshifted as to require reflection from within

. Assuming a background spacetime corresponding to a near-extremal Kerr black hole (with $\hbox{$a^*$}=0.998$ , giving $r_{\rm ms}=1.23M$ ), the data constrain the inner edge of the reflecting region to lie closer than $r_{\rm in}<2M$ , with a steep emissivity profile outside of that radius of $4.5<\beta<6.0$ . This line profile can be successfully modeled assuming a Schwarzschild (non-rotating black hole) background (see discussion in § 6.1.2), but very extreme parameters are demanded -- the inner edge of the reflection region is constrained to be $r_{\rm in}<3M$ , very deep within the plunging region, with an extremely large emissivity index $\beta>10$ . Thus, in the Schwarzschild scenario, essentially all of the fluorescence has to originate from an annulus in the innermost parts of the plunging region,

So, the possibility of X-ray reflection signatures from within the radius of marginal stability remains a wild-card affecting the detailed interpretation of these data. While there are no models that treat such emission in detail, the extreme parameters required to explain the XMM-Newton data within the context of a Schwarzschild black hole ( $r_{\rm in}<3M$ and $\beta>10$ ) seem entirely unreasonable. At the very least, one would expect this material to be in an extremely high ionization state and incapable of producing iron fluorescence and other X-ray reflection features. Thus, the case for a rapidly spinning black hole in this object is now very strong, even accounting for the possibility that there may be some emission from the plunging region.