Fabian Heitsch

Gravitational Collapse in Turbulent Molecular Clouds. I. Gasdynamical Turbulence

Observed molecular clouds often appear to have very low star formation efficiencies and lifetimes an order of magnitude longer than their free-fall times. Their support is attributed to the random supersonic motions observed in them. We study the support of molecular clouds against gravitational collapse by supersonic, gasdynamical turbulence using direct numerical simulation. Computations with two different algorithms are compared: a particle-based, Lagrangian method (smoothed particle hydrodynamics [SPH]) and a grid-based, Eulerian, second-order method (ZEUS). The effects of both algorithm and resolution can be studied with this method. We find that, under typical molecular cloud conditions, global collapse can indeed be prevented, but density enhancements caused by strong shocks nevertheless become gravitationally unstable and collapse into dense cores and, presumably, stars. The occurrence and efficiency of local collapse decreases as the driving wavelength decreases and the driving strength increases. It appears that local collapse can be prevented entirely only with unrealistically short wavelength driving, but observed core formation rates can be reproduced with more realistic driving. At high collapse rates, cores are formed on short timescales in coherent structures with high efficiency, while at low collapse rates they are scattered randomly throughout the region and exhibit considerable age spread. We suggest that this naturally explains the observed distinction between isolated and clustered star formation.

Gravitational collapse in turbulent molecular clouds. II. Magnetohydrodynamical turbulence

Hydrodynamic supersonic turbulence can only prevent local gravitational collapse if the turbulence is driven on scales smaller than the local Jeans lengths in the densest regions, which is a very severe requirement (see Paper I). Magnetic fields have been suggested to support molecular clouds either magnetostatically or via magnetohydrodynamic (MHD) waves. Whereas the first mechanism would form sheetlike clouds, the second mechanism not only could exert a pressure onto the gas counteracting the gravitational forces but could lead to a transfer of turbulent kinetic energy down to smaller spatial scales via MHD wave interactions. This turbulent magnetic cascade might provide sufficient energy at small scales to halt local collapse. We test this hypothesis with MHD simulations at resolutions up to 2563 zones done with ZEUS-3D. We first derive a resolution criterion for self-gravitating, magnetized gas: to prevent collapse of magnetostatically supported regions caused by numerical diffusion, the minimum Jeans length must be resolved by four zones. Resolution of MHD waves increases this requirement to roughly six zones. We then find that magnetic fields cannot prevent local collapse unless they provide magnetostatic support. Weaker magnetic fields do somewhat delay collapse and cause it to occur more uniformly across the supported region in comparison to the hydrodynamical case. However, they still cannot prevent local collapse for much longer than a global free-fall time.

The Birth of Molecular Clouds: Formation of Atomic Precursors in Colliding Flows

Molecular cloud complexes (MCCs) are highly structured and turbulent. Observational evidence suggests that MCCs are dynamically dominated systems, rather than quasi-equilibrium entities. The observed structure is more likely a consequence of the formation process than something that is imprinted after the formation of the MCC. Converging flows provide a natural mechanism to generate MCC structure. We present a detailed numerical analysis of this scenario. Our study addresses the evolution of an MCC from its birth in colliding atomic hydrogen flows up until the point when H2 may begin to form. A combination of dynamical and thermal instabilities breaks up coherent flows efficiently, seeding the small-scale nonlinear density perturbations necessary for local gravitational collapse and thus allowing (close to) instantaneous star formation. Many observed properties of MCCs come as a natural consequence of this formation scenario. Since converging flows are omnipresent in the ISM, we discuss the general applicability of this mechanism, from local star formation regions to galaxy mergers.

Cooling, Gravity, and Geometry: Flow-driven Massive Core Formation

We study numerically the formation of molecular clouds in large-scale colliding flows including self-gravity. The models emphasize the competition between the effects of gravity on global and local scales in an isolated cloud. Global gravity builds up large-scale filaments, while local gravity, triggered by a combination of strong thermal and dynamical instabilities, causes cores to form. The dynamical instabilities give rise to a local focusing of the colliding flows, facilitating the rapid formation of massive protostellar cores of a few hundred M☉. The forming clouds do not reach an equilibrium state, although the motions within the clouds appear to be comparable to virial. The self-similar core mass distributions derived from models with and without self-gravity indicate that the core mass distribution is set very early on during the cloud formation process, predominantly by a combination of thermal and dynamical instabilities rather than by self-gravity.

Formation of structure in molecular clouds: A Case study

Molecular clouds (MCs) are highly structured and turbulent. Colliding gas streams of atomic hydrogen have been suggested as a possible source of MCs, imprinting the filamentary structure as a consequence of dynamical and thermal instabilities. We present a two-dimensional numerical analysis of MC formation via converging H I flows. Even with modest flow speeds and completely uniform inflows, nonlinear density perturbations arise as possible precursors of MCs. Thus, we suggest that MCs are inevitably formed with substantial structure, e.g., strong density and velocity fluctuations, which provide the initial conditions for subsequent gravitational collapse and star formation in a variety of Galactic and extragalactic environments.

The Formation of Self-Gravitating Cores in Turbulent Magnetized Clouds

We use ZEUS-MP to perform high-resolution, three-dimensional, super-Alfvenic turbulent simulations in order to investigate the role of magnetic fields in self-gravitating core formation within turbulent molecular clouds. Statistical properties of our super-Alfvenic model without gravity agree with previous similar studies. Including self-gravity, our models give the following results. They are consistent with the turbulent frag- mentation prediction of the core mass distribution of Padoan & Nordlund. They also confirm that local gravitational collapse is not prevented by magnetohydrodynamic waves driven by turbulent flows, even when the turbulent Jeans mass exceeds the mass in the simulation volume. Comparison of results between 256 3 and 512 3 zone simulations reveals convergence in the collapse rate. Analysis of self-gravitating cores formed in the simulation shows the following: (1) All cores formed are magnetically supercritical by at least an order of magnitude. (2) A power-law relation between central magnetic field strength and density Bc / � 1=2 c is observed despite the cores being strongly supercritical. (3) Specific angular momentum j / R 3=2 for cores with radius R. (4) Most cores are prolate and triaxial in shape, in agreement with the results of Gammie and coworkers. We find a weak correlation between the minor axis of the core and the local magnetic field in our simulation at late times, different from the uncorrelated results reported by Gammie and coworkers. The core shape analysis and the power-law relationship between core mass and radius M / R 2:75 suggest the formation of some highly flattened cores. We identified 12 cloud cores with disklike appearance at a later stage of our high-resolution simulation. Instead of being tidally truncated or disrupted, the core disks survive and flourish while undergoing strong interactions. We discuss the physical properties of these disklike cores under the constraints of resolution limits. Subject headings: ISM: clouds — ISM: kinematics and dynamics — ISM: magnetic fields — methods: numerical — stars: formation — turbulence On-line material: mpeg animation

RAPID MOLECULAR CLOUD AND STAR FORMATION : MECHANISMS AND MOVIES

We demonstrate that the observationally inferred rapid onset of star formation after parental molecular clouds have assembled can be achieved by flow-driven cloud formation of atomic gas, using our previous three-dimensional numerical simulations. We postprocess these simulations to approximate CO formation, which allows us to investigate the times at which CO becomes abundant relative to the onset of cloud collapse. We find that global gravity in a finite cloud has two crucial effects on cloud evolution. (1) Lateral collapse (perpendicular to the flows sweeping up the cloud) leads to rapidly increasing column densities above the accumulation from the one-dimensional flow. This in turn allows fast formation of CO, allowing the molecular cloud to appear rapidly. (2) Global gravity is required to drive the dense gas to the high pressures necessary to form solar-mass cores, in support of recent analytical models of cloud fragmentation. While the clouds still appear supersonically turbulent, this turbulence is relegated to playing a secondary role, in that it is to some extent a consequence of gravitational forces.

THE FATE OF HIGH-VELOCITY CLOUDS: WARM OR COLD COSMIC RAIN?

We present two sets of grid-based hydrodynamical simulations of high-velocity clouds (HVCs) traveling through the diffuse, hot Galactic halo. These H I clouds have been suggested to provide fuel for ongoing star formation in the Galactic disk. The first set of models is best described as a wind-tunnel experiment in which the HVC is exposed to a wind of constant density and velocity. In the second set of models, we follow the trajectory of the HVC on its way through an isothermal hydrostatic halo toward the disk. Thus, we cover the two extremes of possible HVC trajectories. The resulting cloud morphologies exhibit a pronounced head-tail structure, with a leading dense cold core and a warm diffuse tail. Morphologies and velocity differences between head and tail are consistent with observations. For typical cloud velocities and halo densities, clouds with H I masses <104.5 M ☉ will lose their H I content within 10 kpc or less. Their remnants may contribute to a population of warm ionized gas clouds in the hot coronal gas, and they may eventually be integrated in the warm ionized Galactic disk. Some of the (still overdense, but now slow) material might recool, forming intermediate or low-velocity clouds close to the Galactic disk. Given our simulation parameters and the limitation set by numerical resolution, we argue that the derived disruption distances are strong upper limits.

Gravity or turbulence? Velocity dispersion–size relation

We discuss the nature of the velocity dispersion versus size relation for molecular clouds. In particular, we add to previous observational results showing that the velocity dispersions in molecular clouds and cores are not purely functions of the spatial scale but involve surface gas densities as well. We emphasize that hydrodynamic turbulence is required to produce the first condensations in the progenitor medium. However, as the cloud is forming, it also becomes bound, and gravitational accelerations dominate the motions. Energy conservation in this case implies |Eg |∼ Ek, in agreement with observational data, and providing an interpretation for two recent observational results: the scatter in the δv–R plane, and the dependence of the velocity dispersion on the surface density δv 2 /R ∝ � . We argue that the observational data are consistent with molecular clouds in a state of hierarchical and chaotic gravitational collapse, i.e. developing local centres of collapse throughout the whole cloud while the cloud itself is collapsing, and making equilibrium unnecessary at all stages prior to the formation of actual stars. Finally, we discuss how this mechanism need not be in conflict with the observed star formation rate.

DRIVING TURBULENCE AND TRIGGERING STAR FORMATION BY IONIZING RADIATION

We present high-resolution simulations on the impact of ionizing radiation of massive O stars on the surrounding turbulent interstellar medium (ISM). The simulations are performed with the newly developed software iVINE which combines ionization with smoothed particle hydrodynamics (SPH) and gravitational forces. We show that radiation from hot stars penetrates the ISM, efficiently heats cold low-density gas and amplifies overdensities seeded by the initial turbulence. The formation of observed pillar-like structures in star-forming regions (e.g. in M16) can be explained by this scenario. At the tip of the pillars gravitational collapse can be induced, eventually leading to the formation of low-mass stars. Detailed analysis of the evolution of the turbulence spectra shows that UV radiation of O stars indeed provides an excellent mechanism to sustain and even drive turbulence in the parental molecular cloud.