Abstract: |
Accretion onto a black hole is the most efficient known process to convert gravitational energy into radiation. Some gamma-ray bursts (GRBs), some X-ray binaries, and all active galactic nuclei (AGN) are likely powered by accretion onto a rotating black hole. I model the global, timedependent
accretion flow around a black hole using the nonradiative viscous hydrodynamic (VHD), Newtonian magnetohydrodynamic (MHD), and general relativistic MHD (GRMHD) equations of motion, which are integrated numerically. I wrote the VHD and nonrelativistic MHD numerical codes, and coauthored the GRMHD code (Gammie et al., 2003).
I first studied VHD accretion disk models, such as those studied by Igumenshchev et al. (1999, 2000) and Stone et al. (1999), hereafter IA and SPB. IA and SPB use the VHD model of accretion, but they gave qualitatively different measurements of the energy per baryon accreted, angular momentum per baryon accreted, and the radial scaling law for various quantities. While there was concern in the community that the different results were due to numerical error, I found that the different results could be reproduced using my single VHD code to model the accretion flow (McKinney and Gammie, 2002). The differences in their results were due to differences in their experimental designs. Seemingly small changes to the VHD model introduced nonnegligible changes to the results. This suggests that a self-consistent MHD, rather than phenomenological VHD, model for turbulence is required to study accretion flow.
First discovered during the VHD study described above, I found that VHD, nonrelativistic MHD, and GRMHD numerical accretion disk models can produce significant numerical artifacts unless the flow near the inner radial boundary condition, at r in, is out of causal contact with the flow at r > r in. For the VHD model, this corresponds to setting Tin so the flow there is always ingoing at supersonic speeds. For the MHD models, this corresponds to setting Tin so the flow there is always ingoing at superfast speeds. For the GRMHD model, this is easily constructed by using Kerr-Schild (horizon-penetrating) coordinates. In this case, r in is chosen to be inside the horizon, where all waves are ingoing.
I next studied MHD and GRMHD numerical accretion disk models to test the results of previously studied phenomenological disk models. These models are based on the Shakura & Sunyaev a-disk model and suggest the disk should terminate at the innermost stable circular orbit (ISCO) of a black hole. Simplified GRMHD models predict super-efficient accretion due to energy extraction from a rotating black hole. I found that MHD and GRMHD numerical models show that the disk does not terminate at the ISCO, and magnetic fields continue to exert a torque on the disk inside the ISCO. The disk will likely continue to emit radiation inside the ISCO, altering the predicted spectra of accretion disks. GRMHD numerical models of thick and thin disks show that the energy per baryon accreted closely follows the thin disk efficiency, so super-efficient accretion does not seem to be a generic property of thick magnetized relativistic disks (McKinney and Gammie, 2004).
The Blandford-Znajek (BZ) effect, describing the extraction of spin energy of a rotating black hole by the magnetosphere, plausibly powers the jet in some GRBs, some microquasars, and all AGN. I found that GRMHD numerical models of thick disks around a rotating black hole show that an evacuated, nearly force-free magnetosphere develops as predicted by BZ (McKinney and Gammie, 2004). The BZ solution for the energy extracted is remarkably accurate in this region for a black hole with a/M ≤ 0.5 and qualitatively accurate for all a/M, where a is the Kerr spin parameter and M is the mass of the black hole. GRMHD numerical models with a/M ≤ 0.5 show a mildly relativistic (Lorentz factor r ~ 1.5 - 3) collimated Poynting jet around the polar axis. Currently, no self-consistent MHD model of the accretion flow around a black hole shows a jet with r > 3. Additional physics is likely required to obtain r ~ 100 as models predict in GRBs, and to obtain r ~ 3- 10 as seen in some microquasars and AGN.
I studied the VHD, MHD, and GRMHD accretion models by performing numerical simulations on our group's Beowulf computer clusters, which I designed and constructed. For about $50,000, one can buy a private cluster of computers that will provide as much computing power as today's typical time-shared "supercomputer." I give an account of the procedures necessary to design, build, and test a Beowulf cluster. The main conclusion is obvious: test one's code on test nodes before purchasing the entire cluster in order to confirm the performance and reliability of the chosen
components (CPUs, motherboard, network, etc.). |