Thin, Keplerian accretion disks generically become gravitationally unstable at large radii. I investigate the nonlinear outcome of such instability in cool disks using razor-thin, local, numerical models. Cooling, characterized by a constant cooling time drives the instability. I show analytically that if the q c , disk can reach a steady state in which heating by dissipation of turbulence balances cooling, then the dimensionless angular momentum Ñux density Numerical experiments show a \ [(9/4)c(c [ 1))q c ]~1. that (1) if then the disk reaches a steady, gravitoturbulent state in which Q D 1 and cooling is q c Z 3)~1 balanced by heating due to dissipation of turbulence ; (2) if then the disk fragments, possibly q c [ 3)~1, forming planets or stars ; (3) in a steady, gravitoturbulent state, surface density structures have a characteristic physical scale D64G&/)2 that is independent of the size of the computational domain.

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When surrounded by a transparent emission region, black holes are expected to reveal a dark shadow caused by gravitational light bending and photon capture at the event horizon. To image and study this phenomenon, we have assembled the Event Horizon Telescope, a global very long baseline interferometry array observing at a wavelength of 1.3 mm. This allows us to reconstruct event-horizon-scale images of the supermassive black hole candidate in the center of the giant elliptical galaxy M87. We have resolved the central compact radio source as an asymmetric bright emission ring with a diameter of 42±3 μas, which is circular and encompasses a central depression in brightness with a flux ratio 10:1. The emission ring is recovered using different calibration and imaging schemes, with its diameter and width remaining stable over four different observations carried out in different days. Overall, the observed image is consistent with expectations for the shadow of a Kerr black hole as predicted by general relativity. The asymmetry in brightness in the ring can be explained in terms of relativistic beaming of the emission from a plasma rotating close to the speed of light around a black hole. We compare our images to an extensive library of ray-traced general-relativistic magnetohydrodynamic simulations of black holes and derive a central mass of M=(6.5±0.7)×10 9 M e . Our radiowave observations thus provide powerful evidence for the presence of supermassive black holes in centers of galaxies and as the central engines of active galactic nuclei. They also present a new tool to explore gravity in its most extreme limit and on a mass scale that was so far not accessible.

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We describe a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, and van Leer scheme. A variant of constrained transport, proposed earlier by T\'oth, is used to maintain a divergence free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. We describe code performance on a full suite of test problems in both special and general relativity. On smooth flows we show that it converges at second order. We conclude by showing some results from the evolution of a magnetized torus near a rotating black hole.Comment: 38 pages, 18 figures, submitted to Ap