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.

Control of star formation by supersonic turbulence

▪ Abstract Turbulence affects the structure and motions of nearly all temperature and density regimes in the interstellar gas. This two-part review summarizes the observations, theory, and simulations of interstellar turbulence and their implications for many fields of astrophysics. The first part begins with diagnostics for turbulence that have been applied to the cool interstellar medium and highlights their main results. The energy sources for interstellar turbulence are then summarized along with numerical estimates for their power input. Supernovae and superbubbles dominate the total power, but many other sources spanning a large range of scales, from swing-amplified gravitational instabilities to cosmic ray streaming, all contribute in some way. Turbulence theory is considered in detail, including the basic fluid equations, solenoidal and compressible modes, global inviscid quadratic invariants, scaling arguments for the power spectrum, phenomenological models for the scaling of higher-order structu...

http://www.ifa.hawaii.edu/%7Ereipurth/reviews/elmegreen1_araa.pdf

Interstellar Turbulence I: Observations and Processes

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Control of Star Formation by Supersonic Turbulence

Understanding massive stars is essential for a variety of branches of astronomy including galaxy and star cluster evolution, nucleosynthesis and supernovae, pulsars, and black holes. It has become evident that massive star evolution is very diverse, being sensitive to metallicity, binarity, rotation, and possibly magnetic fields. Although the problem to obtain a good statistical observational database is alleviated by current large spectroscopic surveys, it remains a challenge to model these diverse paths of massive stars toward their violent end stage. I show that the main sequence stage offers the best opportunity to gauge the relevance of the various possible evolutionary scenarios. This also allows sketching the post-main-sequence evolution of massive stars, for which observations of Wolf-Rayet stars give essential clues. Recent supernova discoveries owing to the current boost in transient searches allow tentative mappings of progenitor models with supernova types, including pair-instability supernova...

Presupernova Evolution of Massive Single and Binary Stars

Context. Density and velocity fluctuations on virtually all scales observed with modern telescopes show that molecular clouds (MCs) are turbulent. The forcing and structural characteristics of this turbulence are, however, still poorly understood.Aims. To shed light on this subject, we study two limiting cases of turbulence forcing in numerical experiments: solenoidal (divergence-free) forcing and compressive (curl-free) forcing, and compare our results to observations.Methods. We solve the equations of hydrodynamics on grids with up to 10243  cells for purely solenoidal and purely compressive forcing. Eleven lower-resolution models with different forcing mixtures are also analysed.Results. Using Fourier spectra and Δ -variance, we find velocity dispersion-size relations consistent with observations and independent numerical simulations, irrespective of the type of forcing. However, compressive forcing yields stronger compression at the same rms Mach number than solenoidal forcing, resulting in a three times larger standard deviation of volumetric and column density probability distributions (PDFs). We compare our results to different characterisations of several observed regions, and find evidence of different forcing functions. Column density PDFs in the Perseus MC suggest the presence of a mainly compressive forcing agent within a shell, driven by a massive star. Although the PDFs are close to log-normal, they have non-Gaussian skewness and kurtosis caused by intermittency. Centroid velocity increments measured in the Polaris Flare on intermediate scales agree with solenoidal forcing on that scale. However, Δ -variance analysis of the column density in the Polaris Flare suggests that turbulence is driven on large scales, with a significant compressive component on the forcing scale. This indicates that, although likely driven with mostly compressive modes on large scales, turbulence can behave like solenoidal turbulence on smaller scales. Principal component analysis of G216-2.5 and most of the Rosette MC agree with solenoidal forcing, but the interior of an ionised shell within the Rosette MC displays clear signatures of compressive forcing.Conclusions. The strong dependence of the density PDF on the type of forcing must be taken into account in any theory using the PDF to predict properties of star formation. We supply a quantitative description of this dependence. We find that different observed regions show evidence of different mixtures of compressive and solenoidal forcing, with more compressive forcing occurring primarily in swept-up shells. Finally, we emphasise the role of the sonic scale for protostellar core formation, because core formation close to the sonic scale would naturally explain the observed subsonic velocity dispersions of protostellar cores.

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Comparing the statistics of interstellar turbulence in simulations and observations - Solenoidal versus compressive turbulence forcing

We study the mixing of chemical species in the interstellar medium (ISM). Recent observations suggest that the distribution of species such as deuterium in the ISM may be far from homogeneous. This raises the question of how long it takes for inhomogeneities to be erased in the ISM, and how this depends on the length scale of the inhomogeneities. We added a tracer field to the three-dimensional, supernova-driven ISM model of de Avillez (2000) to study mixing and dispersal in kiloparsec-scale simulations of the ISM with different supernova rates and different inhomogeneity length scales. We find several surprising results. Classical mixing length theory fails to predict the very weak dependence of mixing time on length scale that we find on scales of 25-500 pc. Derived diffusion coefficients increase exponentially with time, rather than remaining constant. The variance of composition declines exponentially, with a time constant of tens of megayears, so that large differences fade faster than small ones. The time constant depends on the inverse square root of the supernova rate. One major reason for these results is that even with numerical diffusion exceeding physical values, gas does not mix quickly between hot and cold regions.

Mixing Timescales in a Supernova-driven Interstellar Medium

We study the mixing of chemical species in the interstellar medium (ISM). Recent observations suggest that the distribution of species such as deuterium in the ISM may be far from homogeneous. This raises the question of how long it takes for inhomogeneities to be erased in the ISM, and how this depends on the length scale of the inhomogeneities. We added a tracer field to the three-dimensional, supernova-driven ISM model of Avillez (2000) to study mixing and dispersal in kiloparsec-scale simulations of the ISM with different supernova (SN) rates and different inhomogeneity length scales. We find several surprising results. Classical mixing length theory fails to predict the very weak dependence of mixing time on length scale that we find on scales of 25--500 pc. Derived diffusion coefficients increase exponentially with time, rather than remaining constant. The variance of composition declines exponentially, with a time constant of tens of Myr, so that large differences fade faster than small ones. The time constant depends on the inverse square root of the supernova rate. One major reason for these results is that even with numerical diffusion exceeding physical values, gas does not mix quickly between hot and cold regions.

Mixing Time Scales in a Supernova-Driven Interstellar Medium

The results of a three-dimensional model for disk-halo interaction are presented here. The model considers explicitly the input of energy and mass by isolated a nd correlated supernovae in the disk. Once disrupted by the explosions, the disk never returns to its initial state. Instead it approaches a state where a thin HI disk is formed in the Galactic plane overlayed by thick HI and HII gas disk w ith scale heights of 500 pc and of 1 to 1.5 kpc, respectively. The upper parts o f the thick HII disk (the diffuse ionized medium) act as a disk-halo interface a nd its formation and stability are directly correlated to the supernova rate per unit area in the simulated disk.

Disk-Halo Interaction - I. Three-Dimensional Evolution of the Galactic Disk

We study, by means of adaptive mesh refinement hydro- and magnetohydrodynamic simulations that cover a wide range of scales (from kiloparsec to subparsec), the dimension of the most dissipative structures and the injection scale of turbulent interstellar gas, which we find to be about 75 pc, in agreement with observations. This is, however, smaller than the average size of superbubbles but consistent with significant density and pressure changes in the ISM, which leads to the breakup of bubbles locally and hence to the injection of turbulence. The scalings of the structure functions are consistent with log-Poisson statistics of supersonic turbulence, where energy is dissipated mainly through shocks. Our simulations are different from previous ones by other authors, since (1) we do not assume an isothermal gas but have temperature variations of several orders of magnitude, and (2) we have no artificial forcing of the fluid with some ad hoc Fourier spectrum but drive turbulence by stellar explosions at the Galactic rate, self-regulated by density and temperature thresholds imposed on the ISM gas.

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The Generation and Dissipation of Interstellar Turbulence: Results from Large-Scale High-Resolution Simulations

Observations have suggested substantial departures from pressure equilibrium in the interstellar medium (ISM) in the plane of the Galaxy, even on scales under 50 pc. Nevertheless, multiphase models of the ISM assume at least locally isobaric gas. The pressure then determines the density reached by gas cooling to stable thermal equilibrium. We use numerical models of the magnetized ISM to examine the consequences of supernova driving for interstellar pressures. In this paper we examine a (200 pc)3 periodic domain threaded by magnetic fields. Individual parcels of gas at different pressures reach widely varying points on the thermal equilibrium curve: no unique set of phases is found but rather a dynamically determined continuum of densities and temperatures. A substantial fraction of the gas remains entirely out of thermal equilibrium. Our results appear consistent with observations of interstellar pressures. They also suggest that the high pressures observed in molecular clouds may be due to ram pressures in addition to gravitational forces. Much of the gas in our model lies far from equipartition between thermal and magnetic pressures, with ratios ranging from 0.1 to 104 and ratios of uniform to fluctuating magnetic field of 0.5-1. Our models show broad pressure probability distribution functions with log-normal functional forms produced by both shocks and rarefaction waves rather than power-law distributions produced by isolated supernova remnants. The width of the distribution can be described quantitatively by a formula derived from the work of Padoan, Nordlund, & Jones.

Miguel A. de Avillez

Papers

Mixing Timescales in a Supernova-driven Interstellar Medium

Mixing Time Scales in a Supernova-Driven Interstellar Medium

Disk-Halo Interaction - I. Three-Dimensional Evolution of the Galactic Disk

The Generation and Dissipation of Interstellar Turbulence: Results from Large-Scale High-Resolution Simulations

The Distribution of Pressures in a Supernova-Driven Interstellar Medium. I. Magnetized Medium