Since the application of simple X-ray reflection arguments led us to deduce an unacceptably large black hole mass, we must examine alternative avenues. Indeed, the spectral fitting of Lee et al. (1999b) forces us to consider complications beyond the simple reflection picture -- In their spectral fitting, they found that the Compton reflection continuum fails to show the expected correlation with the iron line equivalent width (in fact, they are anti-correlated; Lee et al. 1999b). Very similar behaviour is also seen in NGC 5548 (Chiang et al. 1999)
Ionization of the disk surface is one of the few physical phenomenon that can (partially) decouple the strength of the Compton reflection continuum from the strength of the iron line. Matt, Fabian & Ross (1993) demonstrated that the iron emission line is more sensitive to ionization effects than the general form of the Compton reflection continuum. In other words, patches of the disk with certain (surface) ionization parameters can produce a Compton reflection continuum without producing appreciable iron fluorescence.
We use this fact to construct the following simple model. Let the X-ray flux illuminating the surface layers of the accretion disk be
A variety of X-ray source geometries give
at large radii,
and
as one approaches the innermost parts of the disk. Now, the
ionization parameter of at the surface of the disk is given by
where n(r) is the density of the surface layers of the disk. We suppose
that
. Hence, we have
Standard disk models (Shakura & Sunyeav 1973) give
at
large radii, and
near the inner part of the disk. Now, suppose
that there exists a critical ionization parameter
above
which there is no iron line produced. For reasonable values of
and
, this gives a critical radius
within which no
iron line is produced. The total iron line flux expected from the object
is then given by
which is readily manipulated to give
For our canonical values of
and
, this gives
. Thus, this simple model produces an iron
line flux which is anti-correlated with the flux of the illuminating
source. Provided a strong Compton reflection continuum can still
originate from the ionized portions of the disk, this type of picture may
explain the spectral behavior that we observe.
One simple prediction of this model is that the velocity width of the line profile gets smaller as the continuum flux increases (due to an outward migration in the inner radius of the line emitting region). Of course, the toy model presented above only captures the crudest aspects of the problem. Fully self-consistent ionized reflection models must be calculated (taking into account the vertical structure of the disk; e.g. see Nayakshin, Kazanas & Kallman 1999) and compared with the data in order to test whether the picture sketched here is reasonable or not.
Even if global, flux-correlated changes in the ionization of the disk
surface are responsible for the observed spectral changes, we would still
expect reverberation signatures on short timescales. We have set upper
limits of
s on the timescale of any reverberation delay. If
the black hole mass is
, the light
crossing time of the iron line producing region is
s, and
hence we need to infer a disk-hugging corona (with
) in order
to be compatible with the reverberation limits. If, instead, the black
hole is
, the light crossing time of the
entire line producing region is only
and so the X-ray source
geometry is unconstrained by our reverberation limits. The corresponding
Eddington ratios are
and
for black hole masses of
and
respectively.