**2.2. The profile of the broad iron line**

The iron K line is intrinsically a rather narrow line. Hence, we can use broadening of the line to study the dynamics of the accretion disk. The line profiles is shaped by the effects of Doppler shifts and gravitational redshifting. Figure 3 demonstrates these effects at work in a schematic way. In a non-relativistic disk, each radius of the disk produces a symmetric double-horned line profile corresponding to emission from material on both the approaching (blue-shifted) and receding (red-shifted) side. The inenr regions of the disk, where the material is moving the fastest, produce the broadest parts of the line. Near a black hole, where the orbital velocities of the disk are mildly relativistic, special relativistic beaming enhances the blue peak of the line from each radius (second panel of Fig. 3). Finally, the comparable influences of the transverse Doppler effect (i.e. ``moving clocks run slowly'') and gravitational redshifting (i.e. ``clocks near black holes run slowly'') shifts the contribution from each radius to a lower energy. Summing the line emission from all radii of the relativistic disk gives a skewed and highly broadened line profile. It has been suggested by Pariev & Bromley (1998) that turbulence in the accretion disk may also significantly broaden the line. While a detailed assessment of this possibility must await future magneto-hydrodynamic disk simulations, it seems unlikely that the turbulent velocity field in a thin accretion disk will be large enough to broaden the line.

Some fully relativistic model line profiles are plotted in
Figs. 4 and
5. In Fig. 4, we show
the line profile from an accretion disk in orbit
around a non-rotating black hole (described by the Schwarzschild
metric). The line is assumed to be emitted from an annulus of the disk
extending between 6 *r*_{g} and 30 *r*_{g}
from the black hole, where
*r*_{g} = *GM / c*^{2} is the standard
gravitational radius. It is seen that the
high energy ``bluewards'' extent of the line is a strong function of the
inclination of the disk. In fact, the blue extent of the line is almost
entirely a function of the inclination, thereby providing a robust way
to measure the inclination of the disk. On the other hand, the redward
extent of the line is a sensitive funcion of the inner radius of the
line emitting annulus. In Fig. 5, we show model
iron lines from a
Schwarzschild black hole and a rapidly rotating black hole (described by
a near extremal kerr metric). In this figure, we have made the
assumption that the line emission extends down to the innermost stable
orbit of the acretion disk. For these purposes, the principal
difference between these two space-time geometries is the location of
the innermost stable orbit (and hence the inner edge of the line
emission) - this critical radius is at 6 *r*_{g} in the
Schwarzschild case, and *r*_{g} in the extremal kerr case.

Model line profiles are given in the Schwarzschild case by Fabian et al (1989) and for the maximal Kerr (spinning black hole) case by Laor (1991). Iron lines in extreme kerr metrics are also computed by Bromley, Miller & Pariev (1998), and Martocchia, Karas & Matt (2000). These last two sets of authors have presented diagnostics that can be used by observers who wish to avoid full spectral fitting of complex relativistic models. The formalism of computing relativistic line profiles is also discussed by ] Fanton et al. (1997).