Can Nonlinear Hydromagnetic Waves Support a Self-Gravitating Cloud?

Using self-consistent magnetohydrodynamic (MHD) simulations, we explore the hypothesis that nonlinear MHD waves dominate the internal dynamics of galactic molecular clouds. We employ an isothermal equation of state and allow for self-gravity. We adopt ``slab-symmetry,'' which permits motions $\bf v_\perp$ and fields $\bf B_\perp$ perpendicular to the mean field, but permits gradients only parallel to the mean field. The Alfv\'en speed $v_A$ exceeds the sound speed $c_s$ by a factor $3-30$. We simulate the free decay of a spectrum of Alfv\'en waves, with and without self-gravity. We also perform simulations with and without self-gravity that include small-scale stochastic forcing. Our major results are as follows: (1) We confirm that fluctuating transverse fields inhibit the mean-field collapse of clouds when the energy in Alfv\'en- like disturbances remains comparable to the cloud's gravitational binding energy. (2) We characterize the turbulent energy spectrum and density structure in magnetically-dominated clouds. The spectra evolve to approximately $v_{\perp,\,k}^2\approx B_{\perp,\,k}^2/4\pi\rho\propto k^{-s}$ with $s\sim 2$, i.e. approximately consistent with a ``linewidth-size'' relation $\sigma_v(R) \propto R^{1/2}$. The simulations show large density contrasts, with high density regions confined in part by the fluctuating magnetic fields. (3) We evaluate the input power required to offset dissipation through shocks, as a function of $c_s/v_A$, the velocity dispersion $\sigma_v$, and the scale $\lambda$ of the forcing. In equilibrium, the volume dissipation rate is $5.5(c_s/v_a)^{1/2} (\lambda/L)^{-1/2}\times \rho \sigma_v^3/L$, for a cloud of linear size $L$ and density $\rho$. (4) Somewhat speculatively, we apply our results to a ``typical'' molecular cloud. The mechanical power input requiredComment: Accepted for publication in Ap.J. 47 pages, 13 postscript figures. Report also available at http://cfa-www.harvard.edu/~gammie/MHD.p

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