Solar Physics
104 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS
through the efforts of George Ellery Hale, observational solar physics had advanced much more rapidly than the theoretical interpretation of the data. This gap, however, began to close in the late twenties, with the development of theories of ionization equilibrium and of atomic structure.
Although by 1930 a certain number of suc- cesses had been achieved from the application of the new physical theories to the observa- tions, they were far outnumbered by many conspicuous failures. In 1930, numerous road- blocks filled almost every avenue of solar physics. It is useful to survey these barriers from the vantage point of 1956, both to note those that have already been removed, or are in the process of being eliminated, and to assess how far we may now expect to move down the road before new obstacles appear.
The photosphere
One of the most fundamental problems in solar physics concerns the structure and circulation of the gaseous layers comprising the photosphere, the region in which the continuous spectrum is formed and in which most of the Fraunhofer absorption takes place.
The solution of this problem calls for the con- struction of a model photosphere in which the chemical composition and the distribution of temperatures, pressures, gas velocities, and magnetic fields are completely specified every- where in the photosphere. In theory, we can derive all of this information from observations of the continuous spectrum and the Fraunhofer lines. Practically, however, the problem is frightfully complicated. For example, mea- surements of solar limb darkening and spectral energy distribution will yield the distribution of temperature with depth if we know what processes produce the continuous spectrum.
We can then calculate the pressure distribution if the atmosphere is in hydrostatic equilibrium.
This assumption is certainly wrong if the at- mospheric gases are in violent, turbulent motion caused by convective instability or electro- magnetic forces. To construct an accurate model we must evaluate the relative contribu- tions of radiation and convection in the transport of energy through the atmosphere.
Stability depends on the temperature gradient
and the chemical nature of the atmosphere.
The temperature gradient, in turn, must be sufficient to drive the solar radiation through the semiopaque gas. In an idealized atmos- phere, where the atmospheric gases are arti- ficially stirred and where no heat is transferred from or into the moving volume, the tempera- ture gradient must follow the so-called adiabatic law. Such an atmosphere is in neutral equi- librium. Exchanging equal masses of gas at different atmospheric levels produces no effect on the temperature distribution. As the mass from the lower level rises and expands, it assumes the same volume, pressure, and temperature as that of the mass it replaces.
As long as the temperature decreases upward at a rate slower than that specified by the adiabatic condition, the atmosphere will be stable. Radiative transfer will predominate and the flux of energy will be essentially con- stant over the entire solar disk. However, if the natural gradient is steeper than the adiabatic, a mass of gas displaced upward becomes warmer than its surroundings. It will continue to rise, like a hot-air balloon. Analo- gously, a mass displaced downward becomes cooler than its surroundings and thus descends.
An atmosphere, so constituted, becomes un- stable and convection sets in.
When convection is mild, the energy con- veyed upwards will essentially equal that con- veyed downwards. Transfer by radiation may still predominate. However, as convection increases, nonlinear effects enter so that we no longer have a precise balance. We shall then have a net outward transport of energy by moving airmasses. The convective and radia- tion fields may be said to "couple" together.
The radiative flux at the outer boundary will vary from point to point over the solar disk in such a way as to maintain a constant average.
The convective field will carry momentum as well as energy and thus will produce either dimi- nution or increase of the effective gravity, with consequent distention or compression of the atmospheric gases.
Unsold has shown that convective instability tends to exist in two separate levels of the solar atmosphere, one below the photosphere and the other near the top of the reversing layer. The lower one arises from ionization effects of hvdro-
NEW HORIZONS IN ASTRONOMY 105 gen, the dominant chemical constituent of the
solar atmosphere. If a volume consisting largely of ionized gas is displaced upward, it expands and cools. The cooling effects lead to electron capture. The released energy raises the temperature above the value prescribed by the adiabatic relation, and thus we find a hydro- gen convective zone. The second zone is associated with the region where the atmosphere is transparent except in the absorption lines.
The "blanketing effect" of the absorbing atoms again changes the temperature gradient in such a way as to induce convective instability.
When we turn to the Fraunhofer spectrum for information on chemical composition and gas motions, we encounter even more difficult problems. The shape and intensity of a solar absorption line depend in a very complicated manner on a variety of factors, of which the abundance of the responsible element is only one. The "f-value," "line strength," or ab- sorptive power of an atom for a given radiation is also significant. The population of atoms in the two levels responsible for the line formation is also extremely important. The Boltzmann equation fixes these populations if the medium is in thermodynamic equilibrium. The temper- ature is the determining parameter. Likewise, the Saha equation, under similar conditions, fixes the amount of dissociation. However, the very fact that energy is flowing through the medium requires departures from this equilib- rium condition. An exact determination of the significant populations theoretically requires advance knowledge of all the atomic constants, such as areas for absorption of radiation or collisional excitation, and the appropriate transition probabilities. The equations of sta- tistical equilibrium are most cumbersome and difficult to solve. Further progress would seem to depend on the development of new techniques for the obtaining of approximate solutions near thermodynamic equilibrium.
We need to know the mechanism that the atoms employ for removing energy from the line.
The process may involve pure absorption, coherent scattering, or noncoherent scattering, and it is usually not obvious which mechanism or combination of mechanisms operates for a given line at a given height in the atmosphere.
The character of the line depends critically on
the assumed atmospheric model. Third, we must know or determine what processes cause the broadening of the spectral lines. The most important broadening mechanisms include ran- dom Doppler effects caused by thermal agita- tion or by macro- or micro-turbulence, colli- sions, Stark effect, and radiation damping.
Widening from hyperfine structure and Zeeman effect may not always be negligible. The parameters necessary for calculating the Stark and collisional broadening are very difficult to come by, theoretically or experimentally.
Twenty-five years ago only a rough beginning had been made towards the quantitative inter- pretation of the solar spectrum. Virtually all analyses of the Fraunhofer spectrum were based on the idealized assumption that the continuous spectrum originated in a sharply bounded radiating surface, the photosphere, and that the lines were produced in a cooler super- imposed layer, the reversing layer, which was supposed to be at constant temperature and pressure. Only very crude guesses were avail- able for most f-values and line-broadening parameters, and accurate intensity measure- ments had been made for but a mere handful of solar lines. Nevertheless, H. N. Russell (1929) accomplished a remarkable feat in achieving what he has called the "zero-th approximation"
to the chemical composition of the sun, espe- cially in view of the fact that only recently have astrophysicists displayed any general agreement that the "first approximation" has finally been reached.
No one doubted the existence of large tem- perature and pressure gradients in the solar photosphere, but attempts to construct a model solar atmosphere were frustrated by a total lack of knowledge concerning the origin of the con- tinuous spectrum. Calculations by Menzel and Pekeris (1935) gave too low a figure for the absorption by transitions involving the negative hydrogen ion. In 1938 Wildt (1939) noted the existence of a bound state of H —, and suggested that photoelectric ionizations and free-free transitions of this negative ion were the major causes of the sun's continuous opacity. Wildt's suggestion was confirmed by the work of Chandrasekhar and associates (Chandrasekhar and Breen, 1946) and Chalonge and Kourganoff (1946).
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Numerous calculations of model solar photo- spheres followed. Even now, we must admit that the photospheric model is known only in the first approximation. Although most workers agree on the temperature distribution in the intermediate layers, the structure of the deepest and uppermost layers remains uncer- tain. Since most of the radiation from these regions is absorbed by the overlying gases, we must use theory rather than direct observation for the analysis. In consequence, the location and extent of the convective zone are not precisely known. Indeed, the magnitude of what appear to be convective processes in the outer atmosphere suggests that even the inter- mediate layer may not be free from effects of the hydrogen zone. Radiation from the upper layers can best be observed at the extreme limb of the sun, where terrestrial atmospheric seeing hampers observation. The blanketing effect of the absorption lines and possible departures from thermodynamic equilibrium further com- plicate the problem.
Additional difficulties of even more basic character stand in the way of a definitive model of the photosphere. Just a few years ago it seemed possible that a straightforward analysis of measurements of solar limb darkening and absolute spectral energy distribution would de- termine an accurate solar model. I t was hoped that the model could be tested and further re- fined by calculation of absorption-line profiles in terms of a specific chemical composition of the atmosphere. For several reasons, this hope now seems to have been optimistic. First, no existing model has succeeded in reproducing in detail the profiles of strong absorption lines. In particular, the observed central intensity has always been greater than the calculated, but the discrepancy has usually been attributed to in- perfections in the theory of line formation.
Various devices such as fluorescence effects and noncoherent scattering have been employed to fill in the line center, but none has proved quite satisfactory. Second, the empirical dependence of the continuous opacity upon wavelength, de- rived from Pierce's (in press) latest measures of limb darkening, differs significantly from the values calculated in terms of currently accepted electron pressure distributions and the theory of continuous absorption by neutral hydrogen at-
oms and negative hydrogen ions. Errors evi- dently exist either in the model or in the theory of the continuous absorption, or perhaps in both.
Third, no spherically symmetrical model of the photosphere appears capable of representing the center-to-limb variation in the intensities of both low and high excitation lines of Fe I (Bohm, 1954). Nor can the center-limb vari- ation in the CO line intensities be accounted for on such a model (Newkirk, 1953). Similar re- sults have been obtained by Elste (1955) at Gottingen and by others.
The evidence is accumulating that the line- intensity observations can be reconciled with theory only when account is taken of temper- ature and velocity fluctuations in the photo- sphere and chromosphere. The recognition of temperature fluctuations is not new, since they are reflected in the brightness fluctuations of the granules, but their influence on the Fraun- hofer spectrum represents a second-order effect which could not be detected before the advent of modern techniques of observation and analy- sis. I t is now generally agreed that the phe- nomenon of the granules is a consequence of turbulent convection in the photosphere and that, on the average, the bright and presumably hot granules are ascending and the cooler, inter- granular regions are descending in the photo- sphere. If the convection is sufficiently violent, however, coupling of the mechanical and radi- ative fields may occur, with nonlinear effects.
The optical thickness of the atmosphere might vary significantly between the bright and dark areas, with an appreciable change of line in- tensity.
Another consequence of the turbulence is the excessive broadening of the centers of the Fraunhofer lines as compared with that to be expected from thermal Doppler effect at a temperature of 6,000° K. The root-mean- square turbulent velocity derived from indi- vidual line profiles and from the curve of growth is about 2 km/sec. Richardson and Schwarzs- child (1950) supposed that the radial velocities of individual granules could be obtained from the measurement of minute Doppler shifts from point to point along the length of Fraunhofer lines, under conditions of high spectroscopic resolution and exceptional seeing. Careful measurement of selected Mount Wilson plates
NEW HORIZONS IN A8TRONOMY
107
did indeed reveal irregularities in the lines, which, upon measurement, yielded a root-mean- square velocity of about 0.4 km/sec. This effect was interpreted as arising from the macroturbu- lence of relatively large elements, the higher velocity of 2 km/sec being attributed to the microturbulence of elements smaller than the thickness of the "reversing layer."
It had been supposed that the observation of the random Doppler shifts was limited by the resolution of the solar image; i. e., by the external seeing. Recent work by McMath (1956) and McMath, Mohler, and Pierce (1955) at the McMath-Hulbert Observatory has revealed, however, that limitations in spectroscopic resolution are at least of equal importance and that air turbulence within the spectrograph may "wash out" the small Doppler effects. On McMath-Hulbert photo- graphs made with the vacuum spectrograph, all photospheric lines show a characteristic
"zigzag" appearance even when the seeing quality is less than average. Further, when the seeing is good, the lines fluctuate in in- tensity from point to point along the solar disk. Thus the temperature and velocity fluctuations in the solar atmosphere may now be directly observed in the Fraunhofer spectrum, at least for elements about 2 seconds of arc in diameter or larger.
Several inferences may be drawn from these results, the most general of which is that the interpretation of photospheric and chromo- spheric observations on the basis of spherical symmetry should now be abandoned, and the observational emphasis directed towards de- termining the nature of the velocity and temperature fluctuations in the solar at- mosphere. The impact of this new develop- ment upon the National Science Foundation is likely to be very great. First, important funds will be required both to modernize existing solar spectrographs and to construct new ones.
Second, an enormous quantity of new and valuable data will become available for analysis, which will necessitate funds for assistance in reduction and analysis. Third, new impetus will be provided for the development and refinement of image-tube techniques. At pres- ent photographic exposure times are not less than 10-20 seconds, whereas the image tube
may be expected to reduce exposures to a small fraction of a second. Such a reduction would greatly reduce the effects of atmospheric scintillation and improve our determinations of the lifetimes of small-scale solar phenomena.
Finally, it is already apparent that spectroscopic resolution has far exceeded the image resolution and that limitations in external seeing quality will seriously hinder the discovery of the details of solar atmospheric structure.
Poor external seeing is caused both by dis- turbances inherent in the atmosphere and by local disturbances of the air produced by solar heating of the telescope and mirrors. The Nation- al Science Foundation panel for a national as- tronomical observatory, under the chairmanship of R. R. McMath, has recently considered this problem and has concluded that two courses of action should be taken. First, the present site survey for the national observatory should be extended to include observations of daytime as well as nighttime seeing. Second, an in- vestigation of instrumental seeing should be undertaken at the earliest possible moment with the goal of designing a solar telescope in which heating effects would be minimized.
It is probable that the solution of the problem of telescopic seeing is now the most important instrumental challenge in the field of solar physics.
The vacuum spectrograph or other spectro- graphs that may be designed to eliminate instrumental turbulence will initiate a new phase of research in solar spectroscopy that will take many years to run its course. The end result should be a much finer elucidation of the structure of the solar atmosphere, including its composition and circulation, than is possible at present. As a valuable byproduct we may also expect a better understanding of the mechanisms of absorption-line formation. As previously mentioned, the fact that the observed central intensity of a very strong line is always greater than that calculated from theory has been a major difficulty. However, it is already obvious from the vacuum spectrograms that some if not all of the discrepancy between theory and observation will vanish when we allow for fluctuations in observed central intensity, which have generally been blurred by poor seeing inside the spectrograph. In
108 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. 1
addition, theorists will have to include effects of mechanical as well as radiations! transfer of energy.
Finally, it may not be out of place to point out that if temperature fluctuations are present in the solar photosphere they undoubtedly occur also in stellar atmospheres, especially in the highly turbulent atmospheres of the supergiant stars.
Chromosphere and corona
By definition, the beginning of the chromo- sphere is the upper boundary of the photosphere.
It is also the transition region, perhaps 20,000 km thick, in which the electron temperature increases from its photospheric boundary value of 4,000°-4,500° K to 1,000,000° K or higher, in the inner corona. I t is therefore of strategic importance, since within its confines probably occur the processes that maintain the corona at its high temperature. More than 20 years ago Menzel (1931) called attention to the anomaly posed by the coexistence in the flash spectrum of emission lines of both neutral metals and ionized helium. Menzel pointed out that the observed intensity of He+X4686 could not be explained by a temperature of 6,000° K even if the chromosphere were composed of pure he- lium, and suggested that the required ionizing radiation might come from a hypothetical ultraviolet excess in the solar spectrum.
The problem posed by Menzel is still para- mount for theories of chromospheric structure, even though the solution in terms of an ultra- violet excess has been ruled out. Since the 1930's, at least three important developments have paved the way for a renewed attack on the chromospheric problem. First, the discovery of the high-temperature corona inevitably re- quires the existence of large temperature gradi- ents somewhere in the chromosphere. Second, the observation from rockets of the far ultra- violet solar spectrum has shown that the hypo- thetical ultraviolet excess does not exist.
Third, the observations clearly show that the chromosphere is not a static phenomenon and that hydrodynamic or aerodynamic processes play an important role in fixing its physical state.
Evidence bearing on the structure of the chromosphere comes from observation of the
optical spectrum during eclipses, from motion pictures in Ha obtained with large corona- graphs, from observation of the radio emission at high frequencies, from observation of the central intensities of certain strong Fraunhofer lines and of the XI0830 absorption line of He I.
from observation of emission lines in the rocket ultraviolet, and from observations of the earth's ionosphere. Interpretation of the observations from the conventional point of view of spheri- cally symmetrical chromospheric models leads to serious discrepancies. In particular, one set of observations has seemed to require a tempera- ture for the low chromosphere in the neighbor- hood of 5,000°-6,000° K, whereas another set seems to demand much higher temperatures of about 20,000° K or greater.
A possible path out of the dilemma was pointed out in 1949 by Giovanelli (1949), who suggested that the chromosphere is nonuniform and that it consists of alternate "hot" and
"cold" columns. Hagen's (1954) measurements of the center-limb variation of the radio emis- sion also point to a model of this general type.
Strong support for the nonuniform model has recently been provided by the detailed analysis of flash spectra by the Harvard-High Altitude Observatory group (Athay, Evans, and Roberts, 1953; Athay, Billings, Evans, and Roberts, 1954; Athay and Roberts, 1955; Pecker and Athay, 1955; Matsushima, 1955; Athay, Men- zel, Pecker, and Thomas, 1955; Athay and Thomas, 1955, 195Ga, 1956b; Athay and Men- zel, 1956; Billings, Cooper, Evans, and Lee, 1954) and by studies of the structures of Fraunhofer lines at the McMath-Hulbcrt Ob- servatory (McMath, Mohler, Pierce, and Gold- berg, 1956; Mohler and Goldberg, 1956).
Although the exact geometry and physical properties of the hot and cold regions have not yet been clearly established, interesting working hypotheses have been suggested whicli clearly indicate the lines along which future researches should be planned. Observations of the flash spectrum at future eclipses will con- tinue to play a leading role in the investigations of the chromospheric structure, but they may now be supplemented by additional new tech- niques which have recently been developed.
Of great importance are observations of micro- wave radio emission, which should be carried