Kinetic and Structural Evolution of Self‐gravitating, Magnetized Clouds: 2.5‐dimensional Simulations of Decaying Turbulence

Abstract

The molecular component of the Galaxy is comprised of turbulent, magnetized clouds, many of which are self-gravitating and form stars. To develop an understanding of how these clouds' kinetic and structural evolution may depend on their level of turbulence, mean magnetization, and degree of self-gravity, we perform a survey of direct numerical MHD simulations in which three parameters are independently varied. Our simulations consist of solutions to the time-dependent MHD equations on a two-dimensional grid with periodic boundary conditions; an additional "half" dimension is also incorporated as dependent variables in the third Cartesian direction. Two of our survey parameters, the mean magnetization parameter β≡ c 2 sound / v 2 Alfven and the Jeans number n J ≡ L cloud / L Jeans , allow us to model clouds that either meet or fail conditions for magneto-Jeans stability and magnetic criticality. Our third survey parameter, the sonic Mach number ≡σ velocity / c sound , allows us to initiate turbulence of either sub- or super-Alfvénic amplitude; we employ an isothermal equation of state throughout. We evaluate the times for each cloud model to become gravitationally bound and measure each model's kinetic energy loss over the fluid-flow crossing time. We compare the evolution of density and magnetic field structural morphology and quantify the differences in the density contrast generated by internal stresses for models of differing mean magnetization. We find that the values of β and n J , but not the initial Mach number , determine the time for cloud gravitational binding and collapse: for mean cloud density n H 2 =100 cm -3 , unmagnetized models collapse after ~5 Myr, and magnetically supercritical models generally collapse after 5-10 Myr (although the smallest magneto-Jeans stable clouds survive gravitational collapse until t ~15 Myr), while magnetically subcritical clouds remain uncollapsed over the entire simulations; these cloud collapse times scale with the mean density as t g ∝ n −½ H 2 . We find, contrary to some previous expectations, less than a factor of 2 difference between turbulent decay times for models with varying magnetic field strength; the maximum decay time, for B ~14 μG and n H 2 =100 cm -3 , is 1.4 flow crossing times t cross = L /σ velocity (or 8 Myr for typical giant molecular cloud parameters). In all models we find turbulent amplification in the magnetic field strength up to at least the level β pert ≡ c 2 sound /δ v 2 Alfven =0.1, with the turbulent magnetic energy between 25% and 60% of the turbulent kinetic energy after one flow crossing time. We find that for non-self-gravitating stages of evolution, when clouds have =5-10, the mass-averaged density contrast magnitudes ⟨log(ρ/ )⟩ are in the range 0.2-0.5, with the contrast increasing both toward low and high β. Although our conclusions about density statistics may be affected by our isothermal assumption, we note that only the more strongly magnetized models appear to be consistent with estimates of clump/interclump density contrasts inferred in Galactic giant molecular clouds.