Coronal winds are stellar winds driven by gas pressure due to a high temperature of the gas. In the case of the sun a coronal temperature of about 2 × 106 K is reached in the outer layers of the solar atmosphere. The solar photosphere, where the visual radiation from the sun is emitted, has a temperature of about 6000 K. Above the photosphere the temperature rises with height to a few times 106 K. The temperature rise beyond the photosphere is due to the dissipation of mechanical energy or the reconnection of magnetic fields that originate in the convection zone below the photosphere. Other forces, such as those produced by Alfvén waves, may play a role in the coronal holes which are regions of lower temperatures and higher mass flux. However in this chapter on coronal winds, we will only consider the effects of gas pressure and heat conduction in the production of a stellar wind.

All non-degenerate stars with effective temperatures less than about 6500 K are expected to have a convection zone below their surface, so in principle chromospheres and coronae could exist around all cool stars. However, very luminous cool stars can also have winds driven by other mechanisms such as wave pressure or radiation pressure on dust grains. If these stars have a high mass loss rate, then the heating cannot compete with the cooling of the outflowing gas.

The outer atmospheres of luminous cool giant stars and early-type stars can be driven outward by the strong radiation fields from the stellar photospheres. In the case of the cool stars, radiative driving occurs because of absorption of photons by dust grains that can form in the outer atmospheres. The grains can absorb radiation over a broad range of wavelengths, so the outflows of the cool stars are said to be ‘continuum driven’ winds. In the case of hot early-type stars the winds are driven by the scattering of radiation by line opacity, so their outflows are called ‘line driven’ winds.

The essential difference between continuum driven and line driven winds is the role of the Doppler shift between a parcel of outflowing matter and the photosphere. In the acceleration of a stellar wind to terminal velocity, the stellar light incident on the parcel of the wind is increasingly redshifted up to the final value of Δλ = λv∞/c. For a cool star with a continuum driven wind, this redshift corresponds to a few Å, which is such a narrow band that within it neither the continuum opacity nor the incident radiation field changes significantly. So the Doppler shifting is not important in continuum driven winds. In the case of line driven winds both the line opacity and the radiation field in the lines change significantly over the Doppler shifts associated with the winds.

The purpose of this chapter is to describe and explain some of the fundamental properties of the stellar wind models. This is done by deriving the equations for idealized simple winds. For these simple models the equation of motion can be solved easily so that the velocity and density structures of the wind are known. The solutions show how the velocities and densities depend on the forces in the wind. They also show that the mass loss rate of a stationary wind model is uniquely determined by the solution of the equations, i.e., given the lower boundary conditions in the wind and the forces and energy gains and losses, a physically realistic solution exists for only one specific value of the mass loss rate. The simple solutions discussed in this chapter show how this so-called critical solution depends on the forces and the energy of the wind. Although only simplified models are considered in this chapter, the conclusions are qualitatively valid for the more complicated and detailed models which will be described in later chapters.

Section 3.1 describes the simplest possible model of an isothermal wind in which gas pressure provides the outward force. In §§ 3.2, 3.3 and 3.4 the effects of additional forces in isothermal wind models are considered; first as simple analytic expressions, such as a force which varies as r-2, or as v dv/dr, and later in more general terms.

Early-type stars often show rotationally broadened photospheric lines that indicate that they are rotating with equatorial speeds in the range 100 to 400 km s-1. These stars have radiatively driven winds owing to the strong line opacities in their outer atmospheres, as described in Chapter 8. The rotation of the stars leads to interesting effects, the most prominent of which is the tendency to concentrate the outflowing material toward regions near the equatorial plane. The equatorial material is moving outwards from a star whose surface is rotating at a speed below the critical speed. Therefore these disks are called outflowing disks or de-cretion disks, in contrast to the ‘accretion disks’ around pre-main sequence stars or around the gaining stars in binary systems with mass transfer.

In this chapter we consider only the formation of outflowing disks. For a star that has a stellar wind and also an outflowing disk, the contrast in density from equator to pole is typically about a factor of ten or so. We discuss two basic pictures for producing such a contrast. The first is a piece-wise spherical outflow in which the equatorial density is enhanced because the mass flux from the near-equatorial latitudes is larger or the wind velocity is lower than those in the polar regions. Such a wind could be the result of the ‘rotation induced bi-stability’ (RIB) model of Lamers and Pauldrach (1991). The second is the wind compression picture in which the streamlines of the gas from both hemispheres of a rotating line driven wind are bent towards the equatorial plane.

Mass loss has a profound effect on the evolution of stars. In the case of stars with initial masses greater than about 30 M⊙, mass loss occurs at a considerable rate throughout their whole life. So it affects their evolution from the beginning to the end. In the case of lower mass stars, mass loss is only important in the late stages of their evolution. For those stars only their late evolution is changed dramatically by mass loss. In this chapter we discuss some of the important effects of mass loss on the evolution of the stars. We first discuss the effects in general terms. Later we discuss the evolution of massive stars and of low mass stars under the influence of mass loss. We describe two characteristic examples in some detail: the evolution of a massive star of 60 M⊙ in § 13.2 and of a low mass star of 3 M⊙ in § 13.3. The effect of mass loss on stellar evolution has been described in several reviews: e.g. Iben and Renzini (1983), Chiosi and Maeder (1986) and at several conferences: e.g. Mennessier and Omont (1990) and Leitherer et al. (1996).

The main effects of mass loss

Changes in the surface composition

The outer layers of stars are peeled off by mass loss. Nuclear fusion occurs in the interior of stars. This nuclear fusion changes the chemical composition and the abundance ratios of the elements in the layers where the fusion occurs.

The winds of luminous hot stars are driven by absorption in spectral lines and they are called line driven winds.

Hot stars emit the bulk of their radiation in the ultraviolet where the outer atmospheres of these stars have many absorption lines. The opacity in absorption lines is much larger than the opacity in the continuum. The opacity of one strong line, say the C IV resonance line at 1550 Å, can easily be a factor of 106 larger than the opacity for electron scattering.

The large radiation force on ions due to their spectral lines would not be efficient in driving a stellar wind if it were not for the Doppler effect. In a static atmosphere with strong line-absorption, the radiation from the photosphere of the star will be absorbed or scattered in the lower layers of the atmosphere. The outer layers will not receive direct radiation from the photosphere at the wavelength of the line, and so the radiative acceleration in the outer layers of the atmosphere due to the spectral lines is strongly diminished. However, if the outer atmosphere is moving outward, there is a velocity gradient in the atmosphere allowing the atoms in the atmosphere to see the radiation from the photosphere as redshifted. This is because in the frame comoving with the gas the photosphere is receding. As a result the atoms in the outer atmosphere can absorb radiation from the photosphere which is not attenuated by the layers in between the photosphere and the outer atmosphere.

Introduction

Numerical experiments are making important contributions to the study of turbulence in the interstellar medium (ISM). Since any numerical simulation is restricted in the range of spatial and temporal scales which it can describe, it is important to develop a prescription for treating the effects of turbulence at the smallest scales, which are generally omitted from this range. Although very little energy resides at the smallest scales, the small scale motions dramatically increase momentum and magnetic flux transport in the ISM, and can also produce rapid thermal and chemical mixing. The most common way to account for these subgridscale effects is to simply assume that the viscosity, electrical resistivity, and other transport coefficients are much larger than their molecular values. The difficult problem of justifying this approach and calculating the so-called eddy diffusivities has received more attention in the atmospheric and stellar turbulence communities than it has, so far, among interstellar turbulence theorists.

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.