Radiation Transport Around Kerr Black Holes Jeremy David ...

184 CHAPTER 7. CONCLUSIONS AND FUTURE WORK
disk model, based on the work of Shakura & Sunyaev (1973) and Novikov & Thorne
(1973). While their treatment can be thought of as a one- or two-zone model (uniform
density; temperature defined at disk mid-plane and surface), we actually integrate the
complete set of vertical structure equations for density, temperature, pressure, and
energy flux. Coupled with the Novikov-Thorne equations for radial structure, with
the appropriate selection of boundary conditions for the disk atmosphere, the vertical
structure equations have a unique solution at each radius.
To self-consistently model the torque on the inner edge of the disk, in Section
5.2 we showed how the accreting gas expands and plunges along geodesic trajectories
inside of the ISCO. Following a one-dimensional column of gas in the frame
of the plunging particle, we can model the time-dependent vertical structure of the
innermost disk with a Lagrangian approach to the partial differential equations of
hydrodynamics. We found that the plunging disk pressure falls off at a scale length
of l plunge inside the ISCO. Since the angular momentum transport (torque) acts over
a turbulent length scale of l turb ≈ h, we can solve for the integrated stress (and thus
the surface density Σ and radial velocity p r ) at the ISCO by setting l plunge = l turb .
In Section 5.3 we outlined the numerical methods used to solve for the disk structure
inside and outside of the ISCO. The Lagrangian hydrodynamics is based on an
implicit scheme described in Bowers & Wilson (1991). We found that the density
and temperature profiles of the disk fall off rapidly inside the ISCO, but that even a
small torque can significantly affect the temperature and total efficiency of the α-disk
outside of the ISCO. Given the temperature and scale height of the disk atmosphere,
in Section 5.4 we used the relativistic ray-tracing code (see Chapter 2) to calculate
the modified “multi-colored” spectrum of the disk. The peak of the spectrum occurs
at E max , which is a function of the black hole mass and Eddington-scaled accretion
rate. Defining a high-energy cutoff such that I(E cut ) = 10 −5 I(E max ), we showed that
the ratio E cut /E max may be used to determine the inclination and/or spin of the black
hole system.
7.1.4 Electron Scattering
Motivated by the fact that most black hole HFQPOs are seen in the “Very High”
or “Steep Power-Law” spectral state (McClintock & Remillard, 2004), we replaced
the simple coronal scattering model from Section 4.5 with a more detailed Monte
Carlo treatment, including angular dependence and energy transfer via the inverse-
Compton effect. Reversing the ray-tracing paradigm of Chapter 2, in Chapter 6 we
explained how thermal photons are traced from isotropic hot spot emitters through
an ADAF-type corona, and then detected by a distant observer. Like the radiative
transfer equation in Section 2.2.2, the electron scattering can be treated classically in
the appropriate reference frame, and then the post-scattered photon is transformed