Radiation Transport Around Kerr Black Holes Jeremy David ...

190 CHAPTER 7. CONCLUSIONS AND FUTURE WORK
years, there have been a number of very exciting observations of Sgr A ∗ , home to
the supermassive black hole at the center of our galaxy [see, e.g. Baganoff et al.
(2001); Genzel et al. (2003)]. Tsuchiya et al. (2004) and Aharonian et al. (2004) have
both reported significant detection of extremely high energy γ-ray emission from the
vicinity of Sgr A ∗ . One speculative but extremely exciting possible explanation for this
TeV emission could be the annihilation of dark matter particles in the central cusp of
the galactic halo [Bergstrom et al. (2004) and references therein]. The very same code
used to trace hot spot photons could also calculate the redshift and energy distribution
of the annihilation γ-rays, assuming a simple model for their production. Eventually,
with the proper theoretical foundation, these observations may also be used to map
out the spacetime around black holes, and even understand the fundamental particle
physics of dark matter.
7.5 Development of New Models
While it is definitely a useful achievement to develop a post-processor ray-tracing code
capable of analyzing any general accretion disk model, what would be really exciting
is to develop a new physical model that could predict the existence of HFQPOs from
first principles. The very fact that there are currently so many alternative (and
certainly not completely convincing) models in the literature was what motivated us
to focus on the post-processor approach in the first place. But as they often say, “the
more the merrier,” so we propose to add a couple more possibilities to this growing
list.
Perhaps the simplest to analyze would be a set of spiral density waves forming in
a relatively cold, thin disk of test particles on geodesic orbits. Much like the sweeping
spiral arms that make up many galaxies (Toomre, 1964; Toomre & Toomre, 1972),
these accretion disk density waves would be produced around regions in phase space
where the epicyclic orbits overlap and form caustic sheets (Gottlieb, 2002). While the
individual particles in the disk will be orbiting at the same geodesic frequencies as the
hot spot model, the spiral density arms may appear to be moving at quite a different
velocity, perhaps even explaining the low frequency QPOs. Also, the formation of
these waves may be closely related to the resonant interaction between azimuthal
and radial coordinate frequencies, just as in the forced resonance model for hot spot
formation.
As we mentioned at the end of Section 6.4, the QPOs may be coming from a
more global oscillation in the inner regions of the corona. We have recently begun to
investigate the possibility of forming radiation “eigenmodes” that can grow in a type
of resonance cavity around the black hole. For example, consider a ring of hot gas
in a planar circular orbit, with a non-axisymmetric m = 2 temperature perturbation