Mordecai-Mark Mac Low

Control of star formation by supersonic turbulence

Understanding the formation of stars in galaxies is central to much of modern astrophysics. However, a quantitative prediction of the star formation rate and the initial distribution of stellar masses remains elusive. For several decades it has been thought that the star formation process is primarily controlled by the interplay between gravity and magnetostatic support, modulated by neutral-ion drift (known as ambipolar diffusion in astrophysics). Recently, however, both observational and numerical work has begun to suggest that supersonic turbulent flows rather than static magnetic fields control star formation. To some extent, this represents a return to ideas popular before the importance of magnetic fields to the interstellar gas was fully appreciated. This review gives a historical overview of the successes and problems of both the classical dynamical theory and the standard theory of magnetostatic support, from both observational and theoretical perspectives. The outline of a new theory relying on control by driven supersonic turbulence is then presented. Numerical models demonstrate that, although supersonic turbulence can provide global support, it nevertheless produces density enhancements that allow local collapse. Inefficient, isolated star formation is a hallmark of turbulent support, while efficient, clustered star formation occurs in its absence. The consequences of this theory are then explored for both local star formation and galactic-scale star formation. It suggests that individual star-forming cores are likely not quasistatic objects, but dynamically collapsing. Accretion onto these objects varies depending on the properties of the surrounding turbulent flow; numerical models agree with observations showing decreasing rates. The initial mass distribution of stars may also be determined by the turbulent flow. Molecular clouds appear to be transient objects forming and dissolving in the larger-scale turbulent flow, or else quickly collapsing into regions of violent star formation. Global star formation in galaxies appears to be controlled by the same balance between gravity and turbulence as small-scale star formation, although modulated by cooling and differential rotation. The dominant driving mechanism in star-forming regions of galaxies appears to be supernovae, while elsewhere coupling of rotation to the gas through magnetic fields or gravity may be important.

Starburst - driven mass loss from dwarf galaxies: Efficiency and metal ejection

We model the effects of repeated supernova (SN) explosions from starbursts in dwarf galaxies on the interstellar medium of these galaxies, taking into account the gravitational potential of their dominant dark matter halos. We explore SN rates from one every 30,000 yr to one every 3 Myr, equivalent to steady mechanical luminosities of L=0.1-10×1038 ergs s−1, occurring in dwarf galaxies with gas masses Mg=106-109 M☉. We address in detail, both analytically and numerically, the following three questions: 1. When do the SN ejecta blow out of the disk of the galaxy? 2. When blowout occurs, what fraction of the interstellar gas is blown away, escaping the potential of the galactic halo? 3. What happens to the metals ejected from the massive stars of the starburst? Are they retained or blown away?

Rapid planetesimal formation in turbulent circumstellar disks

During the initial stages of planet formation in circumstellar gas disks, dust grains collide and build up larger and larger bodies. How this process continues from metre-sized boulders to kilometre-scale planetesimals is a major unsolved problem: boulders are expected to stick together poorly, and to spiral into the protostar in a few hundred orbits owing to a ‘headwind’ from the slower rotating gas. Gravitational collapse of the solid component has been suggested to overcome this barrier. But even low levels of turbulence will inhibit sedimentation of solids to a sufficiently dense midplane layer, and turbulence must be present to explain observed gas accretion in protostellar disks. Here we report that boulders can undergo efficient gravitational collapse in locally overdense regions in the midplane of the disk. The boulders concentrate initially in transient high pressure regions in the turbulent gas, and these concentrations are augmented a further order of magnitude by a streaming instability driven by the relative flow of gas and solids. We find that gravitationally bound clusters form with masses comparable to dwarf planets and containing a distribution of boulder sizes. Gravitational collapse happens much faster than radial drift, offering a possible path to planetesimal formation in accreting circumstellar disks.

The Energy Dissipation Rate of Supersonic, Magnetohydrodynamic Turbulence in Molecular Clouds

Molecular clouds have broad line widths, which suggests turbulent supersonic motions in the clouds. These motions are usually invoked to explain why molecular clouds take much longer than a free-fall time to form stars. Classically, it was thought that supersonic hydrodynamical turbulence would dissipate its energy quickly but that the introduction of strong magnetic fields could maintain these motions. A previous paper has shown, however, that isothermal, compressible MHD and hydrodynamical turbulence decay at virtually the same rate, requiring that constant driving occur to maintain the observed turbulence. In this paper, direct numerical computations of uniform, randomly driven turbulence with the ZEUS astrophysical MHD code are used to derive the value of the energy-dissipation coefficient, which is found to be with ηv = 0.21/π, where vrms is the root-mean-square (rms) velocity in the region, Ekin is the total kinetic energy in the region, m is the mass of the region, and is the driving wavenumber. The ratio τ of the formal decay time Ekin/kin of turbulence to the free-fall time of the gas can then be shown to be where Mrms is the rms Mach number, and κ is the ratio of the driving wavelength to the Jeans wavelength. It is likely that κ < 1 is required for turbulence to support gas against gravitational collapse, so the decay time will probably always be far less than the free-fall time in molecular clouds, again showing that turbulence there must be constantly and strongly driven. Finally, the typical decay time constant of the turbulence can be shown to be where is the driving wavelength.

Superbubbles in disk galaxies

Correlated supernovae from an OB association create a superbubble: a large, thin, shell of cold gas surrounding a hot pressurized interior. Because supernova blast waves usually become subsonic before reaching the walls of the shell or cooling radiatively, the energy input from supernovae may be reasonably approximated as a continuous luminosity. Using the Kompaneets (thin-shell) approximation, the growth of superbubbles in various stratified atmospheres is numerically modeled. A dimensionless quantity predicts whether a superbubble will blow out of the H I disk of a spiral galaxy (and begin to accelerate upward) or collapse. Superbubbles blow out of the H I layer when they have a radius in the plane between one and two scale heights. They blow out only one side of a disk galaxy if their centers are more than 50-60 p above the plane and the gas layer has density and scale height typical of the Milky Way. Fingers of warm interstellar gas intrude into the hot interior when the superbubble overtakes dense clouds. 23 references.

Kinetic Energy Decay Rates of Supersonic and Super-Alfvenic Turbulence in Star-Forming Clouds

We compute 3D models of supersonic, sub-Alfvenic, and super-Alfvenic decaying turbulence, with an isothermal equation of state appropriate for star-forming interstellar clouds of molecular gas. We find that in 3D the kinetic energy decays as t-?, with 0.85 < ? < 1.2. In ID magnetized turbulence actually decays faster than unmagnetized turbulence. We compared different algorithms, and performed resolution studies reaching 2563 zones or 703 particles. External driving must produce the observed long lifetimes and supersonic motions in molecular clouds, as undriven turbulence decays too fast.

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.

Turbulent Structure of a Stratified Supernova-driven Interstellar Medium

To study how supernova feedback structures the turbulent interstellar medium, we construct 3D models of vertically stratified gas stirred by discrete supernova explosions, including vertical gravitational fields and parameterized heating and cooling. The models reproduce many observed characteristics of the Galaxy, such as global circulation of gas (i.e., galactic fountain) and the existence of cold dense clouds in the galactic disk. Global quantities of the model such as warm and hot gas filling factors in the midplane, mass fraction of thermally unstable gas, and the averaged vertical density profile are compared directly with existing observations and shown to be broadly consistent. We find that energy injection occurs over a broad range of scales. There is no single effective driving scale, unlike the usual assumption for idealized models of incompressible turbulence. However, >90% of the total kinetic energy is contained in wavelengths shortward of 200 pc. The shape of the kinetic energy spectrum differs substantially from that of the velocity power spectrum, which implies that the velocity structure varies with the gas density. Velocity structure functions demonstrate that the phenomenological theory proposed by Boldyrev is applicable to the medium. We show that it can be misleading to predict physical properties such as the stellar initial mass function based on numerical simulations that do not include self-gravity of the gas. Even if all the gas in turbulently Jeans-unstable regions in our simulation is assumed to collapse and form stars in local free-fall times, the resulting total collapse rate is significantly lower than the value consistent with the input supernova rate. Supernova-driven turbulence inhibits star formation globally rather than triggering it.

Modelling CO formation in the turbulent interstellar medium

We present results from high-resolution three-dimensional simulations of turbulent interstellar gas that self-consistently follow its coupled thermal, chemical and dynamical evolution, with a particular focus on the formation and destruction of H 2 and CO. We quantify the formation time-scales for H 2 and CO in physical conditions corresponding to those found in nearby giant molecular clouds, and show that both species form rapidly, with chemical time-scales that are comparable to the dynamical time-scale of the gas. We also investigate the spatial distributions of H 2 and CO, and how they relate to the underlying gas distribution. We show that H 2 is a good tracer of the gas distribution, but that the relationship between CO abundance and gas density is more complex. The CO abundance is not well-correlated with either the gas number density n or the visual extinction Av : both have a large influence on the CO abundance, but the inhomogeneous nature of the density field produced by the turbulence means that n and A v are only poorly correlated. There is a large scatter in A v , and hence CO abundance, for gas with any particular density, and similarly a large scatter in density and CO abundance for gas with any particular visual extinction. This will have important consequences for the interpretation of the CO emission observed from real molecular clouds. Finally, we also examine the temperature structure of the simulated gas. We show that the molecular gas is not isothermal. Most of it has a temperature in the range of 10-20 K, but there is also a significant fraction of warmer gas, located in low-extinction regions where photoelectric heating remains effective.

Superbubble blowout dynamics

Multiple supernovae and stellar winds from OB associations carve large holes filled with hot gas in the galactic disk. These superbubbles sweep up H I into cold, thin, dense shells and eventually grow large enough to blow completely out of the galactic H I disk. When superbubbles blow out of the disk, they vent hot gas and supernova energy into the galactic corona. In this paper ZEUS, a two-dimensional hydrodynamics code, is used to model the blowout of a superbubble from exponential and Gaussian models for the vertical density stratification. The results are compared to those from the Kompaneets (thin-shell) approximation. It is found that this approximation works very well, and that most of the mass of the shell remains in the plane, with 5 percent of it accelerating upward. The venting of the hot gas and the stability of the shell depends strongly on the model of the density distribution. It is suggested that the low galactic halo actually consists of a froth of merged superbubbles. 37 references.