Can Nonlinear Hydromagnetic Waves Support a Self-Gravitating Cloud?

Abstract

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 Alfvén speed $v_A$ exceeds the sound speed $c_s$ by a factor $3-30$. We simulate the free decay of a spectrum of Alfvén 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 Alfvén- 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 $v_{\perp,\,k}^2\approx B_{\perp,\,k}^2/4πρ\propto k^{-s}$ with $s\sim 2$, i.e. approximately consistent with a ``linewidth-size'' relation $σ_v(R) \propto R^{1/2}$. 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 $σ_v$, and the scale $λ$ of the forcing. In equilibrium, the volume dissipation rate is $5.5(c_s/v_a)^{1/2} (λ/L)^{-1/2}\times ρσ_v^3/L$, for a cloud of linear size $L$ and density $ρ$. (4) Somewhat speculatively, we apply our results to a ``typical'' molecular cloud. The mechanical power input required