This paper is an introduction to the astronomical material underlying the Varenna Symposium on Aerodynamical Phenomena in Stellar Atmospheres. The term « aerodynamical phenomena » rather than simply « velocity fields » is used in the title of the symposium to imply that primary concern centers as much on the physical phenomena and consequences associated with the presence of velocity fields as it does simply on the velocity fields themselves. To fully appreciate this distinction between aerodynamical phenomena and velocity fields from the astronomer's viewpoint, one must consider it against the background of the classical theory (*) of stellar atmospheres, which assumes that all the properties of the atmosphere are strictly controlled by the radiation field. The thermodynamic state of the classical atmosphere is fixed by the three conditions of radiative equilibrium (no energy transport other than by radiation), hydrostatic equilibrium (no mechanical momentum transport), and local thermodynamic equilibrium at a temperature fixed by the local energy-density of the radiation field (complete coupling between radiation field and atomic degrees of freedom). Analyses of stellar spectra under the framework of this classical atmospheric model take account of the presence of velocity fields (other than thermal) only in their effect upon the atomic absorption coefficient, not in their energetic or momentum coupling to the thermodynamic state of the atmosphere. Thus, if we become interested in aerodynamic phenomena in stellar atmospheres, we must investigate the possible perturbation these velocity fields may have upon the thermodynamic state of the atmosphere. We develop a primary concern with differential motions, velocity gradients, and dissipation mechanisms — all quantities which may produce a local non-relative energy source — rather than directing our attention only at stellar rotation and uniform expansion of an atmosphere. Thus, what we call aerodynamic phenomena embraces not only velocity fields but also their influence upon the thermodynamic state of the atmosphere.

The term ≪ astronomical turbulence ≫ may be interpreted in a variety of ways. For the purposes of this paper, it is assumed that this expression is equivalent to the term ≪ velocity fields ≫. Thus this paper will summarize our knowledge of (i) the magnitudes of the velocities occurring in the atmospheres of reasonably stable stars, (ii) the time-dependence, and (iii) the directional characteristics of the velocity fields that exist. Neither motions in the atmospheres of explosive variables, nor motions in the atmospheres of strictly periodic variables, nor solar phenomena will be discussed. This summary is restricted to spectrographic observations of stars that have not changed their character radically since they were first observed some fifty or sixty years ago. The stars which are studied can hardly all be classified as stable stars, for changes do occur in their light and spectrum, but in no case are the changes catastrophic.

By intrinsic variable stars, we mean those stars which present variations in light, spectrum and radial velocity which cannot be accounted for in terms of purely geometrical or orbital factors; so that we have to appeal to some kind of periodic physical modification of the star.

There is astrophysical evidence for the existence of shocks propagating in regions of variable density. We have therefore the choice of discussing first the physics of shocks in a variable density atmosphere, or the astrophysical phenomena. Following Kaplan's preliminary report, we shall describe first the astrophysical facts, for the reader to be able to understand the connection of the physics with the astrophysics.

Gas can be observed to flow from a wide variety of stars into the interstellar medium, and to do so in a fascinating variety of ways. In some flows, the temperature exceeds a million degrees; in others, it cannot be distinguished from zero. Flow velocities range from 5 000 km/s down to one or two km/s at the limit of detection. The particle densities in some flows are at least 109 times larger than in others. The rates of mass-loss span the range from zero to probably more than 1026 g/s.

As discussed by DEUTSCH, the following gas-dynamical problem arises in the study of a stellar atmosphere: find a steady outward flow, originating from a star, which is compatible with the interstellar medium. In what follows, spherical symmetry will be assumed; moreover, the gas will be considered as a perfect gas with constant specific heats.