Introduction

One of the main features of turbulence is its multi-scale nature (e.g., Scalo 1987; Lesieur 1990).

Introduction

More than their large sizes, the key defining property of Giant HII regions (GHIIRs), as a distinct class of objects, is the supersonic velocity widths of their integrated emissionline profiles (Smith & Weedman 1972; Melnick 1977; Melnick et al. 1987 and references therein). Since supersonic gas motions will rapidly decay due to the formation of strong radiative shocks, the detection of Mach numbers greater than 1 in the nebular gas poses an astrophysically challenging problem.

Melnick (1977) suggested that the ionized gas is made of dense clumps moving in an empty or very tenuous medium, so that the integrated profiles reflect the velocity dispersion of discrete clouds rather than hydrodynamical turbulence. In this model, the relevant time scale for radiative decay of the kinetic energy is the crossing-time of the HII regions which turns out to be comparable to the ages of the ionizing clusters.

The isothermal gravitational collapse and fragmentation of a molecular cloud region and the subsequent formation of a protostellar cluster is investigated numerically. The clump mass spectrum which forms during the fragmentation phase can be well approximated by a power law distribution dN/dM ∝ M−1.5. In contrast, the mass spectrum of protostellar cores that form in the centers of Jeans unstable clumps and evolve through accretion and N-body interaction is best described by a log-normal distribution. Assuming a star formation efficiency of ∼ 10%, it is in excellent agreement with the IMF of multiple stellar systems.

Introduction

Understanding the processes leading to the formation of stars is one of the fundamental challenges in astronomy and astrophysics. However, theoretical models considerably lag behind the recent observational progress. The analytical description of the star formation process is restricted to the collapse of isolated, idealized objects (Whitworth & Summers 1985). Much the same applies to numerical studies (e.g. Boss 1997; Burkert et al. 1997 and reference therein). Previous numerical models that treated cloud fragmentation on scales larger than single, isolated clumps were strongly constrained by numerical resolution. Larson (1978), for example, used just 150 particles in an SPH-like simulation. Whitworth et al. (1995) were the first who addressed star formation in an entire cloud region using high-resolution numerical models. However, they studied a different problem: fragmentation and star formation in the shocked interface of colliding molecular clumps.

Introduction

Spiral galaxies, quasars, active galactic nuclei, X-ray binaries, cataclysmic variables, and young stars: these are a few of the astronomical objects that contain disks. Disks are common in astrophysics because it is usually difficult to change the specific angular momentum of gas, but easy to radiate away its thermal energy. Gas injected into in a spherically symmetric potential thus naturally shocks, radiates, and settles down into a plane normal to its mean angular momentum.

Because they are so common, disks occupy a lot of the astronomical community's time and energy (that would otherwise be entirely dissipated in attempting to measure Ω0). Although there are enormous differences between individual disk systems in global structure and observational appearance, there are a number of fluid dynamical processes common to all disks. These processes are worth understanding in detail.

The most fundamental process in disks, analogous to nuclear reactions in stars, is angular momentum transport. The disk cannot evolve unless gas in the disk can be persuaded to give up some of its angular momentum and spiral down the gravitational potential.

Introduction

Cosmic rays are very fast charged particles which are accelerated to high energies by plasma processes, principally collisionless shock waves, occuring in astrophysical plasmas. The acceleration at collisionless shock waves relies on the interaction of the charged particles with turbulence, which causes spatial diffusion both along and perpendicular to the magnetic field. This allows some of the particles to cross the the shock many times, to gain many times their original energy.

Physical properties of the atomic gas in spiral galaxies are briefly considered. Although both Warm (WNM, 104 K) and Cool (CNM, ∼ 100 K) atomic phases coexist in many environments, the dominant mass contribution within a galaxy's star-forming disk (R25) is that of the CNM. Mass fractions of 60 to 90% are found within R25. The CNM is concentrated within moderately opaque filaments with a face-on surface covering factor of about 15%. The kinetic temperature of the CNM increases systematically with galactocentric radius, from some 50 to 200 K, as expected for a radially declining thermal pressure in the galaxy mid-plane. Galaxies of different Hubble type form a nested distribution in TK(R), apparently due to the mean differences in pressure which result from the different stellar and gas surface densities. The opaque CNM disappears abruptly near R25, where the low thermal pressure can no longer support the condensed atomic phase. The CNM is apparently a prerequisite for star formation. Although difficult to prove, all indications are that at least the outer disk and possibly the inter-arm atomic gas are in the form of WNM, which accounts for about 50% of the global total. Median line profiles of the CNM display an extremely narrow line core (FWHM ∼ 6 km s−1) together with broad Lorentzian wings (FWHM ∼ 30 km s−1). The line core is consistent with only opacity broadening of a thermal profile.

A synopsis of results stemming from the analysis of the radial velocity fluctuation fields of 6 HII regions (Sh 142, M 17, Sh 158, Sh 170, Orion and Sh 212) are presented. In addition new data from the DENSITY fluctuation fields of the HII region Sh 269 will also be shown. The analysis was done using the well known two-point correlation functions. However I innovated by using the higher order structure functions on the Sh 269 data. PDF increment calculations were also done hinting at the presence of intermittency in Sh 269.

Introduction

HII regions were the first interstellar objects where scale dependent brightness and velocity fluctuations were identified and attributed to turbulent motions (von Hoerner 1951; Courtes 1955; Münch 1958). The study of turbulent motions in HII regions was then forgotten for many years until the work of Roy & Joncas (1985) and of O'Dell and collaborators later on. The discovery of such motions in HII regions should not come as a surprise. These objects possess large scale velocity gradients that are explained by ionized gas flows produced by the erosion of the parent molecular cloud. The newly born massive stars produce the necessary UV photon flux. Turbulence becomes a natural companion of the kinematics of HII regions since the ionized gas flows can reach twice the speed of sound enabling the Reynolds number to reach high values (ℜ > 105).

We present two-dimensional MHD numerical simulations for the interaction of high-velocity clouds (HVC) with a magnetized gaseous disk. The initial magnetic field is oriented parallel to the disk. The impinging clouds move in oblique trajectories and fall toward the disk with different initial velocities. The B-field lines are distorted and compressed during the collision, increasing the field tension and preventing the cloud material from penetrating into the disk. The perturbation, however, creates a complex, turbulent, pattern of MHD waves that are able to traverse the galactic disk and, for unstable disks, can trigger the Parker instability.

Introduction

High velocity clouds (HVC) are atomic H I clouds located at high latitudes in our Galaxy, and moving at velocities ∣VLSR∣≥ 90 km/s (see Bajaja et al. 1985, and Wakker & van Woerden 1997). Their distance is unknown, but limits to the locations of some particular clouds indicate z-heigths of a few kiloparsecs, setting a possible mass range of 105-106 M⊙. Thus, a HVC complex moving with a speed of 100 km/s has a kinetic energy of about 1052−53 erg. These values indicate that the bulk motion of the HVC system could represent a rich source of energy and momentum for the interstellar medium (equivalent to that from several generations of superbubbles).

There is evidence for possible collisions between HVCs and gaseous disks, both in our Galaxy and in external galaxies.

Introduction

Molecular clouds (MCs) are recognized to be the sites of present day star formation in our galaxy. The description of their dynamics is an essential ingredient for the theory of star formation.

A lot of work has been devoted to understand i) how super-sonic random motions in MCs can persist for at least a few dynamical times and ii) why MCs do not collapse, or fragment gravitationally into stars, on a free–fall time–scale. The magnetic field has been advocated as the solution for both problems. Magneto–hydrodynamic (MHD) waves were believed to dissipate at a significantly lower rate then super–Alfvénic and super–sonic random motions.

Introduction

Electromagnetic radiation from astronomical objects encounters different turbulent zones in its way to Earth-based telescopes. Interstellar turbulence, for instance, provokes phase fluctuations of radio waves which are exploited to study the interstellar medium, as presented by several authors in this volume. In the optical domain, wave perturbations occur in the Earth's atmosphere, due to turbulent fluctuations of the refractive-index of air (which is frequently referred to as optical turbulence). This has severe negative effects on astronomical observations as the commonly known “seeing” that strongly limits the achievable angular resolution (Roddier 1981). A number of high angular resolution techniques, like adaptive optics and interferometry, are being developed to overcome this limitation. They owe their good results yet obtained to the knowledge of the optical effects of atmospheric turbulence, and their optimization demands an increasingly high precision of that knowledge.

Introduction

Interstellar turbulence may affect the chemistry of translucent and dense molecular clouds in various ways. Turbulent mixing of material from dense cores to the surface of molecular clouds, and vice versa, may alter the abundances inferred from chemical networks. In particular, turbulent transport and diffusion was invoked to explain the large abundance of atomic carbon and that of complex organic molecules which is observed in dense molecular clouds (Boland & de Jong 1982; Chièze, Pineau des Forêts & Herbst 1991; Xie, Allen & Langer 1995).

The dissipation of turbulence in translucent molecular clouds is another physical process which has recently been considered to alter chemical abundances.

We use the standard, adiabatic shell evolution to predict the size distribution N(R) for populations of SN-driven superbubbles in a uniform ISM. We derive N(R) for simple cases of superbubble creation rate and mechanical luminosity function. We then compare our predictions for N(R) with the largely complete HI hole catalogue for the SMC, with a view toward the global structure of the ISM in that galaxy. We also present a preliminary derivation for N(v), the distribution of shell expansion velocities.

Introduction

Core-collapse supernovae (SNe) tend to be correlated in both space and time because of the clustering of the massive (≳ 8M⊙) star progenitors. These clustered SNe, along with stellar winds of the most massive stars, produce superbubble structures in both the warm ionized (104 K) and atomic H I components of the interstellar medium (ISM) in star-forming galaxies. The hot, coronal component of the ISM is thought to originate largely from the shock heating of material interior to shells of superbubbles and supernova remnants (SNRs). Total kinetic energies deposited into the interstellar environment are in the range 1051 − 1054 erg for OB associations, and ≳ 1055 erg for starburst phenomena. Hence, the large-scale structure and kinematics of the multi-phase ISM could be largely determined by this superbubble activity. Likewise, this effect should influence turbulence on global, macroscopic scales, which then cascades to smaller scales.

H2O masers near young stars show turbulent motions of many times sound speed. These motions appear on scales of 1 to 300 AU, much smaller than the 104 AU sizes of H2O maser clusters. Turbulent velocity differences between the masers are typically 10 to 100 km s−1, much larger than typical sound and Alfven speeds of ∼ 0.8 km s−1. These velocity differences show the powerlaw correlation functions characteristic of fluid turbulence, over several orders of magnitude in separation. The index is close to that predicted by the Kolmogorov theory. Maser features also show internal turbulence, on scales of < 1 AU, consistent with Alfvenic turbulence.

Introduction

H2O masers are among the most spectacular astrophysical masers; they are found near late-type stars, around galactic nuclei, and near young stars. Those near young stars are among the brightest and most numerous. As Strelnitski & Sunyaev (1973) first proposed, the strong winds from these stars accelerate and power the masers. The population inversion required for maser action arises at shocks, in the outflowing wind and where it meets ambient material (Litvak 1969, Strelnitski 1984, Elitzur, Hollenbach, & McKee 1989, Kaufman & Neufeld 1996). Each masing region contains between one and several hundred individual masing cloudlets, known as features.

The kinematics of clusters of H2O masers have been studied in detail with very-long baseline interferometry (VLBI), in part because comparison of proper motions with Doppler shifts can yield trigonometric distances to these objects (Genzel et al. 1981, Reid et al. 1988, Gwinn, Moran, & Reid 1992).

Introduction

The Probability Density Function of mass density is an important statistical property of the ISM that relates, for example, to gravitational collapse and star formation. Log-Normal PDFs have been discussed occasionally in both the cosmological and interstellar contexts (Hubble 1934, Peebles 1980, Ostriker 1984, Zinnecker 1984, Coles & Jones 1991). Vázquez-Semadeni (1994) noticed that the density PDFs in his 2-D numerical simulations of turbulence were consistent with a Log-Normal, and discussed possible reasons for the lognormality. Padoan et al. (1997) showed that the standard deviation of the Log-Normal PDFs in their isothermal 3-D simulations was approximately equal to half the rms Mach number. Scalo et al. (1998) raised the questions of how a polytropic equation of state, and more generally a realistic ISM cooling function, might influence the PDF.

In this contribution we investigate the question of the shape of the PDF for isothermal and polytropic equations of state, using analytical methods and by looking at results from 3-D simulations of supersonic turbulence.

Introduction

Is the core difficulty in the so-called convective term of the equation, i.e. in the simple fact that moving matter is self-advected? In which case, the understanding of threedimensional (3D) incompressible turbulence would be the key to our own case of compressible MHD turbulence (CMT). Or will the many added features – such as Alfvén and magnetosonic waves and a preferred direction in the presence of a strong uniform magnetic field – change the behavior of CMT flows altogether? How far does the concept of universality carry out? This is one of the questions that the detailed observations of astrophysical flows can help settle. In this short review, I shall begin by giving the humongus list of parameters that have to be considered a priori, the rule of the game being to determine which parameters are relevant and which can be ignored. In the next Section, some of the key features of the temporal and spatial development of compressible flows and MHD flows will be recalled. Section 4 is devoted to the formation of large scales (as opposed to small scales), the agent being here the magnetic helicity and Section 5 deals with intermittency and its measure through high-order structure functions.

Introduction

Numerical tools are likely to play an important role in the investigation of MHD turbulence in cold molecular clouds if for no other reason than because the observed linewidths are highly supersonic, and as of yet there does not exist a comprehensive analytic theory of compressible MHD turbulence. Our group (C. Gammie, E. Ostriker, and myself) has begun a project to study systematically the internal dynamics of magnetized, self-gravitating molecular clouds in two- and three-dimensions. Our motivations are two-fold: not only do we wish to understand the dynamics of compressible MHD turbulence as a well-defined physics problem, but also we would like to use the dynamical models as a basis with which to interpret the enormous collection of astronomical observations of molecular clouds that have been collected over the past several decades.

The viscous dissipation process in supersonic flows is known to be highly intermittent in space and time. It means that the volume over which the turbulent energy is released is as small as the character of intermittency is pronounced. In the interstellar medium, this phenomenon is predicted to induce large fluctuations at small scales of the gas properties. Since the interstellar viscous dissipation scale is out of reach of current observational capabilities, indirect signatures of the presence of this process in the interstellar medium would be valuable. A few possible indirect signatures are presented here.

Introduction

On average in our Galaxy, about 10−3 L⊙/M⊙ are permanently driven into heat due to the viscous dissipation of supersonic turbulence. On average again, this is negligible compared to the heating due to the UV stellar radiation which is about 1 L⊙/M⊙. But it is now known that a large fraction of the energy released by the dissipation of turbulence is not distributed evenly but is concentrated in localized regions of space and time because most of the dissipation occurs in bursts. This phenomenon is known as the intermittency of turbulent dissipation. In those regions of interstellar space where viscous dissipation occurs, the corresponding heating term becomes temporarily dominant, even in regions poorly shielded from the ambient interstellar radiation field. This significantly modifies the subsequent evolution of the gas which has received this energy, in comparison to that of gas of its neighborhood which has not received it.