One dominant stroke transformed thousands of years of increasingly refined speculation on the structure of our Universe into fact. Hubble (1925a,b,c, 1926, 1929a,b) clinched the extragalactic nature of the “white nebulae” by discovering their Cepheid variable stars. This vastly expanded the known distance scale.

Cepheids are unusually bright stars that pulsate with regular periods ranging from about 10 to 30 days. (The first onewas found in the constellation Cepheus in the Milky Way.) Their crucial property is the relation between a Cepheid's period and its peak intrinsic luminosity, recognized in 1908 (Leavitt, 1912; Hertzsprung, 1913). Brighter Cepheids have longer periods. From the observed periods of Cepheids in nebulae, Hubble could obtain their intrinsic luminosity and thus find the distance from their observed apparent luminosity. The main uncertainty was in calibrating their period–luminosity relation from the independently known distances of Cepheids in our Galaxy. Early calibrations turned out to be wrong, mainly because there are different types of Cepheids, which give somewhat different period–luminosity relations. (Occam's Razor fails again.)

How to observe the dark matter of our Universe remains a primary puzzle of astronomy. Many searches over the radiative spectrum from radio to Xrays have uncovered much of great interest, but not enough to close the Universe. Many laboratory experiments have searched directly for exotic weakly interacting massive particles (WIMPS) streaming through space, but to no avail. Gravitational lensing of more distant sources reveals dark matter in clusters along the line of sight; its amount and detailed location are quite model dependent. So far, the main direct evidence for dark matter comes from the gravitational motions of stars within galaxies and galaxies within clusters. All of it adds up to only Ω0 ≲ 0.3. Its nature, form, and distribution still are unknown.

Close agreement between the form of the GQED and the observed spatial and velocity distributions of galaxies suggests methods for constraining dark matter. It is relatively easy to start with the cosmological many-body model and formulate dark matter variations around it. These variations should not destroy the observed agreement unduly, nor attract epicycles.

As an illustration (Fang and Saslaw, 1999), consider the peculiar velocity distribution function f(v). This is especially sensitive to local dark matter. In the simplest case, the dark matter is closely associated with each galaxy (e.g., in its halo) as it clusters, and (29.4) describes the velocities. This is consistent with observations.

In hierarchical models of galaxy production, many protogalaxies merge at high redshifts. Each merger results in a spectacular wreck, which gradually restructures itself into a more unified system. Collisions engender vast conflagrations of stars as unstable gas clouds collapse and ignite thermonuclear fires. This process repeats and repeats until galaxies form as we know them today.

We see many galaxies still merging at present. In hierarchical models these late mergers are all that remain of earlier more active combining, or they result from encounters in recent dense groups. The long history of merging changes the observed galaxy distribution by destroying the conservation of galaxy numbers and by modifying the luminosity function. The first of these is easier to model; the second, at present, is really a guess. Galaxy luminosities depend on their unknown stellar initial mass functions, their subsequent star formation by merging or other violent activity, their nonthermal radiation, their production and distribution of dust, and their stellar evolution. Of these factors, only stellar evolution is reasonably well understood. On the other hand, number nonconservation depends on galaxy velocities, densities, and collision cross sections. These too must be modeled, but they seem more straightforward.

By describing the evolution of both the luminosity and the spatial distribution functions with one common formalism, we can use their mutual self-consistency to help constrain free parameters.

In stars with a convection zone just below the photosphere, the convective motions might create acoustic waves which propagate outwards through the photosphere. These sound-waves produce an extra pressure, i.e. ‘wave pressure’ in the atmosphere. This pressure will depend on the density and on the amplitudes of the waves. The gradient of the wave pressure results in a force that can drive a stellar wind. If a stellar wind is driven by acoustic wave pressure it is called a ‘sound wave driven wind’.

In this chapter we will first explain the concept of wave pressure by studying the motion of a particle in the presence of an oscillating force. This simple case, first developed by Landau and Lifshitz (1959) shows that oscillations may result in a net force in the direction of the oscillations. In § 6.1 we discuss the motions of particles in an oscillatory field, such as in a sound wave, and we show that this produces a ‘wave pressure’. In § 6.2 we introduce the concepts of the ‘wave action density’ and the ‘acoustic wave luminosity’. These are useful concepts for describing sound wave driven winds. The pressure due to acoustic waves is described in § 6.3. Section (6.4) descibes sound wave driven wind assuming no dissipation of acoustic energy. This results in estimates of the both the mass loss rate and the wind velocity. In § 6.5 we discuss sound wave driven winds with dissipation of the acoustic energy.

During the last thirty years astronomers have discovered that nearly all stars are losing mass in the form of stellar winds through a major fraction of their lives. This mass loss affects their evolution from their origin to their death. It also leads to spectacular interactions between the supersonic stellar winds and the interstellar medium in the form of planetary nebulae and ring nebulae and in the form of interstellar bubbles and superbubbles. The return of matter from stars into the interstellar medium and the formation of bubbles and superbubbles changes the chemical composition of the galaxies and affects their kinematical properties.

Literature in this field has grown tremendously over the past three decades. On the one hand this is due to the advance of spectroscopic observations over the full range of the spectrum and to the enormous improvements in image resolution from ground based telescopes and the Hubble Space Telescope which results in spectacular images of the nebulae formed by stellar winds. On the other hand it is the result of many theoretical studies to explain the basic mechanisms for stellar winds and the interactions with their surroundings. Many reviews have been published that give an overview of specific aspects of stellar winds or mass loss from stars.

Stellar winds are the continuous outflow of material from stars. The ejection of material plays a major role in the life cycle of stars. In the case of massive stars, the winds remove more than half of the star's original mass before the star explodes as a supernova. In this book we will explore the many mechanisms that can lead a star to eject matter in the form of a steady stellar wind. We will also discuss the interaction of winds with the interstellar medium of our galaxy, and the effects of mass loss on the evolution of a star. We start by giving in this chapter a brief overview of the historical development of the subject, especially focusing on the early observations and theoretical advances that led us to our current level of understanding.

Historical introduction

The early developments

The names ‘solar wind’ and ‘stellar winds’ were both coined by Eugene Parker (1958, 1960). However, the origins of the basic ideas regarding mass loss from stars arose long before that.

The earliest phase in the development of the subject concerns the realization that a few stars are like ‘novae’, in having spectra with very broad emission lines. Novae are sudden outbursts of light from certain types of stars, and the outbursts are also associated with the high speed ejection of material. Tycho Brahe's observation of a ‘new star’ or nova in 1572 marks the birth of stellar astronomy as a study of objects that are not perfect celestial objects, but rather ones that can change in interesting ways.

Stars interact with the surrounding interstellar medium (ISM), both through their ionizing radiation and through the mass, momentum, and energy that is transferred by way of their winds. The extreme ultraviolet radiation from hot stars leads to ionized nebulae or H II regions around young stars. In the case of low mass stars about to become white dwarfs, the radiation leads to the ionization of planetary nebulae.

The mass loss in stellar winds leads to a recycling of matter back to the interstellar medium, and because of the nuclear processing that occurs in the interiors of stars, the matter which is returned is often chemically enriched. In the cases of late type giants and carbon rich Wolf-Rayet stars, dust grains are produced in the winds, so the outflows may carry grain enriched material into the interstellar medium. These grains could play a role in the next generation of star formation. There are also dynamical effects associated with wind-interstellar medium interactions. The collisions of the winds with their surroundings produce ‘wind bubbles’, and the momentum transfer helps to maintain the random velocities of interstellar clouds that otherwise would be damped out by the dissipative effects of cloud collisions.

The winds of ‘massive stars’ tend to have the greatest effect on the ISM, because their mass loss rates are large, and the massive stars that are hot also have winds that are very fast and carry large momentum fluxes.

In the last chapter we have seen that if a star has an open magnetic field in the equatorial region and is also rapidly rotating, a very strong stellar wind can be produced. In this chapter we consider the effects of the magnetic field in absence of rotation. If oscillations are induced in the field at the base of the wind, transverse ‘Alfvén’ waves will be generated. The dissipation of energy and momentum associated with the wave propagation can lead to the acceleration of the outer atmosphere in the form of an ‘Alfvén wave driven wind’. Open field regions can arise in a variety of configurations, depending on the circulation currents or dynamo properties of the interior of the star. Furthermore, the strength and geometry of the magnetic field can vary significantly from one location on the star to another, and the wind flow tubes will vary accordingly.

In the absence of a magnetic field, a star that has a spherically symmetric hot corona will produce a steady, radial, structureless wind, driven by the thermal gas pressure gradients in the corona (Parker, 1958), as discussed in Chapter 5. Within a few years after the solar wind was predicted by Parker, interplanetary space probes proved that indeed there is a wind from the sun that occurs at all times. However, the wind was found to be far from steady and structureless. To understand the spatial and temporal variability of the wind, Parker (1965) considered outflow in open magnetic field structures.

Stars emit not only radiation but also particles. The emission of particles is called the stellar wind.

The two most important parameters regarding a stellar wind that can be derived from the observations are the mass loss rate Ṁ, which is the amount of mass lost by the star per unit time, and the terminal velocity v∞, which is the velocity of the stellar wind at a large distance from the star. By convention, the mass loss rate Ṁ is always positive and it is expressed in units of solar masses per year, with 1 M⊙ yr-1 = 6.303 × 1025 g s-1. A star with Ṁ = 1--6M⊙ yr-1, which is not an unusual value, loses an amount of mass equal to the total mass of the earth in three years. The terminal velocity v∞ of a stellar wind ranges typically from about 10 km s-1 for a cool supergiant star to 3000 km s-1 for a luminous hot star.

The values of Ṁ and v∞ are important because

(1) Ṁ describes how much material is lost by the star per unit of time. This is important for the evolution of the stars, because stars with high mass loss rates will evolve differently from those with low mass loss rates.

(2) Different stellar wind theories predict different mass loss rates and different terminal velocities for a star. So by comparing the observed values with the predictions we can learn which mechanism is responsible for the mass loss from a star.