I describe the multivariate technique of Principal Component Analysis and its application to spectroscopic imaging data of the molecular interstellar medium. The technique identifies differences in line profiles with respect to the noise level at various scales. It is assumed that such differences arise from fluctuations within turbulent flows. From the resultant eigenvectors and eigenimages, a size line width relationship, (δv ∼ τα), can be constructed which describes the relationship between the magnitude of velocity fluctuations and the angular scale over which these occur for a given region. From a sample of selected molecular regions in the outer Galaxy, I find the power law exponent varies from 0.4 to 0.7. Thus, the turbulent flows within molecular regions of the Galaxy do not follow the Kolmogorov-Obukhov relation for incompressible turbulence. Implications of these results are discussed with respect to the injection and dissipation of kinetic energy in molecular regions.

Introduction

In the early, pioneering days of millimeter wave astronomy, the presence of turbulent flows within molecular regions of the Galaxy was inferred from the supersonic line widths of CO spectra. Since that time, telescope and detector technology has advanced such that one can now routinely construct detailed images of molecular emission from which the properties of interstellar turbulence can, in principle, be derived. In practice, statistical descriptions of the observations are required to fully exploit the available information.

Introduction

The density and velocity structure within a molecular cloud is a remnant of its formation environment and the starting point for the creation of stars. It determines how deeply radiation can propagate through the cloud, and is a critical parameter for understanding the evolution of the ISM. How is it best described?

Beginning with Larson (1981), correlations between cloud properties such as linewidth and size have been fit by power laws. Since a power law does not have a characteristic scale, the implication is that clouds are scale-free and self-similar. This has led to statements in the literature that clouds are best described as fractals (e.g. Falgarone, Phillips, & Walker 1991; Elmegreen 1997). On the other hand, other recent studies (Larson 1995; Simon 1997; Goodman et al. 1998; Blitz & Williams 1997) suggest that there are characteristic size and velocity scales in star-forming regions.

Interstellar Turbulence, the second conference organized by the Guillermo Haro International Program on Advanced A strophysical Research, was an excellent forum to review and discuss one of the most intriguing features of cosmic and terrestrial fluids. Turbulence is universal and mysterious, and remains one of the major unsolved problems in physics and astrophysics. It is present in all terrestrial and astrophysical environments: close to our telescopes, it blurs and distorts our view of the skies, and in the interstellar and intergalactic media, somehow, it creates fluctuations and redistributes angular momentum, leading to star formation and large scale structure.

The Guillermo Haro Program was created in 1995 at the Instituto Nacional de Astrofísica, Optica y Electrónica (INAOE), and is named in honor of its founder, the remarkable astronomer-lawyer Guillermo Haro. This second conference was aimed at revising our conceptions on the properties of turbulence, and at summarizing the present status in observational, theoretical, and computational research in interstellar turbulence. It was held in Puebla, México, at the Benemérita Universidad Autónoma de Puebla, during the week of January 12th to 16th, 1998. There were 130 participants, from four continents, and a large fraction of them were very young scientists. The program covered a wide variety of topics, ranging from atmospheric and interstellar turbulent flows, to magnetic fields and cosmic ray transportation, and energy dissipation, fragmentation and star formation.

Introduction

Over the last several decades it has become clear that the dynamics and evolution of star-forming interstellar clouds are difficult to explain without magnetic effects. A principal problem involves support of dense clouds against their own gravity. In general, such clouds are observed to be in approximate virial equilibrium between gravity and internal motions. Seemingly, therefore, they should be stable against collapse. However, observed line widths are almost invariably much greater than the sound speed. Therefore the internal motions that support the clouds are highly supersonic, and simple estimates indicate that shock-induced dissipation of mechanical energy should occur on about the free-fall time. In such a case, non-magnetic turbulence offers no effective support for the clouds (unless, of course, it can somehow be continuously regenerated).

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).