An accretion disk simulation.
A turbulent magnetic field produced by an accretion disk simulation.
Luminosity profiles of simulated disks (solid curves) and analytical, Novikov-Thorne disks (dashed curves), for accretion onto black holes with spin parameters a/M = 0, 0.7, 0.9 and 0.98 (bottom to top).
Dimensionless viscosity parameter α as a function of radius. Simulation data (gray points) inspired a one-dimensional model for α(r) (red curve). This model is the sum of a mean magnetic field component (dashed green) and a turbulent component (dashed blue).

Accretion onto black holes involves turbulence, magnetic fields, and general relativity. I run simulations that include all of these things and then I look for insights from the simulation data that I can use to improve accretion disk theories.

A typical simulation begins with a magnetized torus of fluid in hydrostatic equilibrium orbiting a spinning black hole. The torus solution is obtained by solving Euler's equations in the Kerr metric and I recently found a family of torus solutions that is more physical than those used previously [Penna et al. 2012b].

Early on in the simulation, differential rotation shears the magnetic field and triggers the magnetorotational instability. This drives turbulence, which transports energy and angular momentum outwards and allows the gas to accrete inwards. Eventually, the accreting gas reaches a quasi-steady state. The orbital velocity of the gas is higher in the inner regions of the disk than in the outer regions, so the fluid at small radii equilibrates before the fluid at large radii. Magnetic buoyancy lifts fields out of the disk and creates a low density, highly magnetized, laminar corona. I have shown how black hole spin, disk thickness, magnetic field strength and topology, and other parameters affect the properties of the accretion flow [Penna et al. 2010].

The standard theory of thin, relativistic accretion disks (Novikov and Thorne 1973), an analytical model developed long before the current simulations were possible, gives a fairly good description of the simulation data. However, the Novikov-Thorne model predicts zero luminosity inside the radius of the innermost stable circular orbit (ISCO), whereas simulations show that disks produce a modest amount of luminosity there (of order 10% the total disk luminosity). I found an analytical solution that generalizes the Novikov-Thorne disk by including luminosity inside the ISCO [Penna et al. 2012a].

Since the pioneering work of Shakura and Sunyaev (1973), analytical accretion disk models have folded the complicated physics of turbulence and magnetic fields into a dimensionless viscosity parameter, α. This parameter is always assumed to be a constant, however simulations show that it varies with radius. Drawing on my simulations, I developed a one-dimensional model for α(r) [Penna et al. 2012c]. This brings theory and simulations closer together.

Advances in theory have applications to observational work. In collaboration with others, I have used my results to estimate the errors in black hole spin estimates [Kulkarni et al. 2011], characterize the accretion flow onto the galactic center black hole [Shcherbakov et al. 2012], and elucidate the hard power law emission from black hole X-ray binaries [Zhu et al. 2012].

At the same time, I am interested in questions about black holes which have no immediate applications to astronomy, but are interesting because they provide physical intuition. I solved for the motion of a spherical shell with finite thickness as it collapses onto a black hole, and showed that an external observer sees the entire shell freeze just outside the horizon [Penna 2012]. This corrected an earlier claim that all but an infinitesimal surface layer would appear to cross the horizon in finite time (Liu and Zhang 2009). I have made a speculative suggestion for the interpretation of Carter's constant [Penna 2011].