Radiation Transport Around Kerr Black Holes Jeremy David ...

1.3. OUTLINE OF METHODS AND RESULTS 25
a measure of how the disk emission is relativistically redshifted, beamed, and lensed,
and is a classic means of simulating the shape of broadened iron emission lines seen by
many X-ray observations. We show how the transfer function is sensitive to the disk
inclination, but not the black hole spin. Only when truncating the disk at the ISCO
and scaling the emission by a power law (e.g. g(r) ∼ r −α ), thus giving more weight
to the inner regions, are the line profiles noticeably different for different spin values.
However, since both the ISCO-truncation and r −α scaling are only conjectures as of
this writing, the broadened emission lines do not seem to be an unambiguous means
for measuring black hole spin. Hence we turn our attention in the direction of timing
observations and QPOs.
1.3.2 The Hot Spot Model
Recent observations of commensurate integer ratios in the high-frequency QPOs of
black hole accretion disks (Miller et al., 2001; Remillard et al., 2002), as well as
the longstanding puzzles of the frequency variability of low-frequency QPO peaks
and their correlations with X-ray flux and energy, motivate more detailed study of
the QPO phenomenon as a means to determining the black hole parameters [for
reviews, see Lamb (2003) and Psaltis (2004b)]. We have developed a model that is a
combination of many of the above approaches (see Section 1.2.1), in which additional
physics ingredients can be added incrementally to a framework grounded in general
relativity. The model does not currently include radiation pressure, magnetic fields, or
hydrodynamic forces, instead treating the emission region as a collection of cold test
particles radiating isotropically in their respective rest frames. The dynamic model
uses the geodesic trajectory of a massive particle as a guiding center for a small region
of excess emission, a “hot spot,” that creates a time-varying X-ray signal, in addition
to the steady-state background flux from the disk.
An early prototype of the hot spot model was originally proposed by Sunyaev
(1972) as a means for identifying the black hole horizon (as opposed to a NS surface)
as the emitter spirals in towards the horizon and then fades away to infinity. Bao
(1992) calculated light curves and power spectra for a collection of random hot spots in
an AGN disk to model the variability seen on time scales of hours or days. Our version
of the hot spot model described in Chapter 3 is motivated by the similarity between
the QPO frequencies and the black hole (or neutron star) coordinate frequencies near
the ISCO (Stella & Vietri, 1998, 1999) as well as the suggestion of a resonance leading
to 3:2 integer commensurabilities between these coordinate frequencies (Abramowicz
& Kluzniak, 2001, 2003; Kluzniak & Abramowicz, 2001; Rebusco, 2004; Horak, 2004).
Stella & Vietri (1999) investigated primarily the QPO frequency pairs found in lowmass
X-ray binaries (LMXBs) with a neutron star (NS) accretor, but their basic
methods can be applied to black hole systems as well. Both NS and BH binaries