SESSION III

STELLAR AERODYNAMICS

SESSION CHAIRMAN: JOHN T. JEFFERIES Institute for Astronomy, University of Hawaii

[facing p. 190

J, Quant. Spectrosc. Radiat, Transfer. Vol. 8, pp. 191-192. Pergamon Press, 1968. Printed in Great Britain

S T E L L A R A E R O D Y N A M I C S

I N T R O D U C T O R Y R E M A R K S

JOrIN T. JEVVERmS

Institute for Astronomy, University of Hawaii, Honolulu, Hawaii

As DR. KING pointed out yesterday, radiative transfer has been for many years a subject of intense interest to astronomers. Today, we are to hear a number of presentations reflecting some aspects of the more recent work on the subject in the context of astrophysics.

Let me say a few preliminary words for perspective. You will find, as the meeting pro- gresses, that a great deal of attention is to be given to the problem of radiative transfer in spectral lines and in the free-bound continua of atoms. These aspects constitute, of course, a central problem in the interpretation of astronomical spectra, where the appearance of many emission or absorption features in atomic, rather than molecular, transitions makes the problem somewhat simpler in many respects and certainly different from those discussed in the first two sessions, which concentrated mainly on the interpretation of molecular spectra. The papers in this session will increasingly reflect a point of view which has recently become prevalent in astronomical work; namely, that the strong spectral lines are not formed in local thermodynamic equilibrium.

For LTE to hold, it is sufficient, and in general it is necessary, that the collisional pro- cesses take place at a greater rate than their radiative counterparts. This condition is in general necessary if the temperature structure of the atmosphere is complicated, even at high optical depths. For the tenuous gas in a stellar atmosphere, however, and par- ticularly for strong radiative transitions, this condition does not in general obtain. The radiative rates are usually greater than the collisional rates, since the collisional transition rates depend on the density whereas the radiative spontaneous transition rates do not so depend, and the density is in general relatively low. Thus, we find ourselves in general facing a position where LTE is not applicable. As Dr. Hummer will mention, the excitation state of a gas can be described by a certain function, a source function, whose specification allows us immediately to compute the emergent intensity from a column of gas. That is, we have the following expression for the emergent intensity.

~v

f e- rvlu Iv = Sv dzv 0

Iv is the intensity emerging from a plain parallel slab of gas at an angle, whose cosine is #, with respect to the normal to this plain parallel slab. The quantity S is the source function defined as the ratio of the emission coefficient to the absorption coefficient.

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192 JOHN T. JEFFERIES

The quantity z~ is an optical depth variable. Thus, the fundamental problem is the specifica- tion of the source function S~ as a function of position in the gas.

In conditions which depart from local thermodynamic equilibrium, the source function is not necessarily equal to the Planck function. In general, it depends on the ratio of the population of the upper state of the transition to the lower state of the transition. Thus, the determination of the source function involves a detailed microscopic discussion of the rates of transition back and forth between the energy levels from which the line is formed. If radiative rates are large, we thus have the source function for the radiative field depending upon the radiative field.

In the solution of such a complicated problem certain simplifications have to be made. Many of the earlier studies in this particular non LTE field (as it is now known) dealt solely with the one line problem, i.e., an atom consisting of two levels; and the solution of this problem is still a very vital one. Within the past year or so, much attention has been given to the solution of a somewhat more general multilevel problem, where we have more than two levels to the atom and more than one line present ; some of these cases will be discussed in this session. The solution of this multilevel problem brings into prominence a very important question as to the relationship between the source functions of two lines formed in the same atom; for example, one may think of the relationship between the source function and two D lines of neutral sodium, lines which are very important in astronomical spectra. We will hear some discussion as to exactly why this is an important problem and, later on, to what extent it is being solved.