The outer region of a star in which the optical spectrum is formed is referred to as the atmos- phere. This definition delimits a shell lying between the deeper regions, which cannot be directly observed, and the higher regions, which contribute very little energy to the optical spectrum (but which may be all-important in the radio spectrum). Although it is convenient to treat this shell separately, it is certainly not independent of the layers lying below and above it.
Any discussion of stellar atmospheres logically begins with the sun. Here is a star on our doorstep; and the variety and accuracy of the solar data we can accumulate far surpasses that for any other star. We may examine the radiation received from every point on the sun's disk and for every wavelength that penetrates the earth's atmosphere.
In spite of centuries of solar observation, new techniques continue to introduce new phenomena. To mention only two of the most interesting: the Babcocks' magnetograph, which gives a tracing of the atmosphere's magnetic field point by point; and the McMath- Hulbert vacuum spectrograph, which has re- vealed a remarkable complexity of line struc- ture. Both of these innovations are triumphs of observational technique and will create challenges to the theoretician.
The theoretical models that have been ex- plored until recently may be characterized as being in "hydrostatic and radiative equilib- rium"; that is, the atmosphere is supported by hydrostatic pressure and radiation is the sole means of energy transport. The logical chain is this: the temperature distribution is found either theoretically or by limb darkening measurements, and it depends on the broad continuous absorption characteristics of the gas.
A complete physical description of the atmos-
1 Indiana University, Bloomlngton, Ind.
phere follows from the temperature distribution by using the hydrostatic equation, the absorp- tion coefficient, the ionization equation, etc.
The resulting "model atmosphere" combined with the theory of the formation of absorption lines is used to predict the observed spectrum.
The only adjustable parameters of such a solar model are the abundances of the elements which are determined by a comparison with observa- tions.
Although the reasoning is straightforward, many problems arise even in the static model.
To list only a few:
(1) The temperature distribution of the upper layers is uncertain because of the difficulty of observation close to the limb of the sun.
(2) The abundance of the second most abundant element, helium, cannot be deter- mined directly since it is effectively "dead weight" in a low-temperature atmosphere.
(3) The fundamental data of transition probabilities for many lines are still missing.
The great emphasis on nuclear and molecular physics in recent years has attracted physicists away from research in atomic spectra. A possible solution is for some young astronomers to learn the laboratory techniques and to do the work themselves.
(4) The theories of the shape of the line- absorption coefficient, i. e., broadening, absorp- tion versus scattering and noncoherent proc- esses, are not in satisfactory form. Of partic- ular interest in this connection is the recent use of a shock tube at the University of Michigan to obtain laboratory data on broadening.
(5) The problem of predicting the profile of an absorption line formed when radiation passes through many layers of different physical characteristics has been solved only for very special cases.
(6) The cumulative effect of many absorp- 119
120 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS
tion lines (blanketing effect) is difficult to evaluate.
However, overshadowing all these difficulties today is the problem of describing a dynamic atmosphere. The theoretician no longer can avoid including large-scale motions in his solar models but the kinematical description is far from clear. One important source of informa- tion is the "granulation"; but the details are obscured by "seeing" in the earth's atmos- phere. It is to be hoped that Schwarzschild's unorthodox plan to photograph the sun from above the "seeing" will be successfully carried out in the near future.
Although simple models (such as those used by de Jager) involving temperature inhomo- geneities in adjacent columns of the atmosphere may prove serviceable for a while, eventually we must have a model obeying the hydro- dynamical laws (better still the hydromagnetic laws) and including the transport of energy by a combination of convection and radiation.
Increasing use will undoubtedly be made of high-speed electronic computers to obtain numerical solutions to these difficult problems.
Computers can certainly not create ideas, but they can explore the consequences of various assumptions to an extent previously impossible.
It is a challenge to find efficient machine pro- cedures for calculating model atmospheres and line profiles under a variety of physical con- ditions. Computer techniques will probably be second nature to astrophysicists a few academic generations hence; at the moment, however, theoreticians have been very con- servative in adopting these new methods.
As if the existing observations do not provide sufficient problems, astronomers have watched with great interest as rocket spectrographs and radio telescopes have broadened the limits of the observable spectrum. Lyman a has at last been photographed and even soft X-rays have been detected. Observations such as these will have a profound effect on future models of the sun.
There is very little generally accepted theory concerning the spectacular transient solar phenomena. Many solar observatories are in- volved in the accumulation and classification of data from which theories will eventually arise, and a highly coordinated effort in this
direction is being planned for the forthcoming International Geophysical Year. Many prob- lems in this particular field are treated in- dividually in other articles of this volume.
The techniques developed to describe the solar atmosphere have been applied with some success to "normal" atmospheres of other spectral types. In some cases it is possible to obtain information that the sun will not provide directly: for example, the abundance of hydrogen relative to helium can be found in principle from the spectra of hot stars.
Unfortunately, no conclusive value can as yet be given.
Problems immediately arise because of ob- servational limitations. There is just not enough light to work with. Photoelectric techniques for the absolute spectrophotometry of stars are currently being developed by several observers and should yield important astro- physical data. Nevertheless we have only indirect measurements of limb darkening, and these for only a few eclipsing binaries.
As the available light goes down, so does the possible dispersion, and observations become less reliable. Some objects are out of reach of all except the largest reflectors.
Surveys can be carried through by using rough curve-of-growth methods based on ideal- ized models, but eventually we need detailed model atmospheres for a wide variety of spectral types. These are constructed by using theoret- ical temperature distributions and are tested by requiring the flux to be constant at every depth. However, it is difficult to apply this criterion in early-type stars where the flux is jagged due to the absorption edges of hydro- gen and helium.
As we go toward the cool stars, the im- portance of the blanketing effect grows and a premise upon which other models are founded breaks down—it is not possible to separate the lines from the continuum. Entirely new theoretical techniques will have to be combined with laboratory data on the absorption of mole- cules before we will have as detailed an inter- pretation of the atmospheres of stars of late spectral type as we have for the sun.
Nature has provided a unique tool for study- ing the outer regions of late-type giants.
Binary systems like 31 Cygni, in which a small
NEW HORIZONS IN ASTRONOMY 121 hot component is gradually eclipsed by the
extended atmosphere of its giant companion, provide a wealth of detailed information. The observations indicate a "network of prom- inences" far more extensive than that of the sun; and if an understanding of a dynamic atmosphere is important in the sun, it is vital here.
As the spectroscopic peculiarities become more unusual, the extrapolation of normal tech- niques becomes less successful. Thus, our present understanding of the atmospheres of pulsating variables, magnetic stars, Wolf- Rayet stars, etc., is rudimentary at best.
Nevertheless, the tendency is to make quantita- tive measurements whenever possible and not to be satisfied with visual estimates.
It is obviously impossible to cover all aspects of such a varied subject in a short survey.
Fortunately several detailed discussions of solar and stellar atmospheres have recently appeared, and references to individual papers will be found there.
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