Numerical Models of Accretion Disks

I review recent numerical studies of accretion disks, focusing on measurements of the turbulent shear stress, or $\alpha$, in the shearing box model. I conclude with a list of astronomically relevant open questions that can be settled via future numerical experiments.Comment: 9 pages, LaTeX, aipproc.sty, invited review at "Accretion Processes in Astrophysical Systems: Some Like It Hot", eds. S. Holt and T. Kallma

Photon Bubbles in Accretion Discs

We show that radiation dominated accretion discs are likely to suffer from a ``photon bubble'' instability similar to that described by Arons in the context of accretion onto neutron star polar caps. The instability requires a magnetic field for its existence. In an asymptotic regime appropriate to accretion discs, we find that the overstable modes obey the remarkably simple dispersion relation \omega^2 = -i g k F(B,k). Here g is the vertical gravitational acceleration, B the magnetic field, and F is a geometric factor of order unity that depends on the relative orientation of the magnetic field and the wavevector. In the nonlinear outcome it seems likely that the instability will enhance vertical energy transport and thereby change the structure of the innermost parts of relativistic accretion discs.Comment: 7 pages, LaTeX, 1 eps figure, mn.sty, submitted to MNRA