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Solar spectroscopy
3". Quant. Spectrosc. Radlat. Transfer. Vol. 3, pp. 519-528. Pergamon Press Ltd., 1963. Printed in Great Britain
SOLAR
SPECTROSCOPY
LEo GOLDBERG Harvard College Observatory, Cambridge, Massachusetts SOLAR spectroscopy is a particularly fascinating subject because of the great variety of conditions under which the sun emits radiation. Thus, temperatures range from a few thousand to several million degrees and densities from below 10-is g/cm3 to 5 x 10-7 g/cms. The presence of magnetohydrodynamicphenomena, some of which are explosively transient in character, adds further spice to the formation of solar spectra. The observable optical spectrum extends continuously from X-rays as short as about 1 A to the beginning of the radio frequency spectrum at millimeter wavelengths. Beginning in the ultraviolet at about 1700 A and extending through the visible and infrared, the spectrum of the solar disc is essentially a continuous spectrum crossed by tens of thousands of absorption lines--the so-called Fraunhofer lines. Below 1700 A, the spectrum of the disc consists almost entirely of emission lines superposed on a very faint emission background. There is a further remarkable difference between the spectra above and below 1700 _~. The Fraunhofer absorption lines are those of neutral and singly-ionized atoms, which would be expected to appear at temperatures of about 4000°-6000°K. The emission lines on the other hand arise from atoms in many different stages of ionization, some typical examples being H I, He I and He II, O I, O VI, Si XII, Mg X, C II, Si I, Fe XV, etc. The appearance of these emission lines implies a continuum of temperatures up to several million degrees. The range and diversity of the solar spectrum can be understood in terms of the following semi-quantitative and rather well-documented model of the solar atmosphere. First, the visible spectrum including most of the Fraunhofer absorption lines originates in the deepest observable layer of the atmosphere, called the photosphere, a zone about 300 km thick. The temperature decreases from about 8000°K at the bottom of this zone to something like 4500°K at the top. Owing to the high opacity of the photospheric gases, no radiation from below can escape to the surface without being totally absorbed. The top of the photosphere is defined as the level at which the gases are just barely beginning to become opaque, and therefore the radiation that escapes from the photosphere suffers partial absorption on the way out. It turns out that each point in the photosphere radiates like a black body at the local temperature; therefore, at each wavelength the outgoing radiation is an average of Planckian intensities corresponding to different temperatures. The resulting spectral energy curve at visible wavelengths rather closely simulates that of a black body with T = 6300°K. At longer infrared wavelengths, the opacity of the photosphere increases with increasing wavelength and therefore the "effective" temperature diminishes and 519
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approaches a boundary value of approximately 4500°K. At shorter wavelengths, the opacity also increases, and the spectral energy curve roughly resembles that of a black body at T = 4500°K. The low temperature of the photosphere explains why its radiation is insignificantly weak at wavelengths below about 1700 A. Directly above the photosphere is an atmospheric fringe about 20,000 km thick, called the chromosphere, and above it is the corona, which has been observed to extend to distances on the order of 10 solar radii and probably does not have a well-defined boundary as it merges into the interplanetary medium. Not very long ago, it was thought that the chromosphere and corona were simple low-temperature extensions of the photosphere, but it has been known for over 20 years that, on the contrary, the corona is a very hot plasma, its temperature being on the order of 1-2 million degrees and that the chromosphere is a transition region in which the temperature increases rapidly outwards. The spectra of the chromosphere and corona are so faint that they cannot be observed unless steps are taken to suppress the enormously greater intensity of the photosphere. At visible wavelengths the suppression is best accomplished by a solar eclipse and less efficiently by an artificial eclipse. At far ultraviolet wavelengths, however, the problem is solved by Planck's law. We have already noted that the intensity of the photosphere is insignificant below h1700, and consequently the emission-line spectra of the chromosphere and corona may be observed directly upon the disc.
VISIBLE SOLAR SPECTRUM The term "visible" is used loosely here to include the spectral region from about 3000 to 9000 _A, which can be photographed from the ground with very high resolution. Modern observations of the visible spectrum had their beginning in the work of H. A. Rowland, whose spectra obtained just prior to 1900 were not substantially surpassed in spectral purity and resolving power until the late 1940's. The major improvements in the intervening period were in the establishment of accurate wavelength standards and in the provision of photometric calibration for intensity measurements. The introduction to solar spectroscopy of modern high-quality gratings, especially those ruled by H. W. Babcock at the Mt. Wilson and Palomar Observatories, has been responsible for some rather spectacular new developments in the field. A good example of the performance of modern solar spectroscopic equipment is that of the 50 ft vacuum spectrograph of the McMath-Hulbert Observatory, completed in 1955. Measurements by Pierce of the performance of an 8 in., 600 groove/mm Babcock grating show a resolution of 630,000 in the fifth order, the dispersion being about 1 A/cm. The half width of the instrumental profile is about 0.01 A, and the total intensity of ghosts is 1.8 per cent in the fifth order. The half width of the narrowest solar absorption lines is 0"03 A, and therefore the profiles of even very weak lines may be obtained directly by photoelectric scanning, with little or no correction for instrumental distortion. A number of solar observatories in this country and abroad now have equipment with comparable performance. Studies of the solar photosphere are based upon intensity measurements on both continuous and line spectra.
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A. The continuous spectrum Measurements of the intensity of the continuous spectrum can give information on the temperature gradient in the photosphere and on the wavelength dependence of the continuous absorption coefficient at various depths in the atmosphere. The necessary measurements are: (1) the absolute spectral energy distribution of radiation from the center of the sun's disc and (2) measurements of the rate of darkening to the limb at monochromatic wavelengths, spaced so as to give complete coverage of the spectrum. With the assumption of hydrostatic equilibrium, the analysis of such data leads to the derivation both of the temperature and pressure gradients in the photosphere and of the wavelength dependence of the continuous absorption coefficient. Studies of this type have proved that bound-free and free-free transitions in the fields of negative hydrogen ions are the major contributor to the opacity of the photosphere at visible wavelengths. Continuous absorption by neutral hydrogen is also of considerable importance in the deep layers. It is also possible that some of the apparent discrepancy between theory and observation at the shorter wavelengths below ~5000 may be caused by H2 molecules absorbing while in the lowest repulsive electronic state. Empirical models of the photosphere derived from limb darkening observations are uncertain at both the upper and lower boundaries, the upper because of the blurring of the solar limb by the earth's atmosphere and the lower because of uncertainties in estimating the proportion of the energy flux that is transported by convection rather than by radiation. B. The absorption line spectrum The Fraunhofer lines are not a primary source of information on temperature and pressure models of the photosphere, but they may serve to verify or disprove such models. Study of the shapes of Fraunhofer lines also provides a basis on which to decide among alternative mechanisms for the formation of lines, such as coherent or noncoherent scattering, or pure absorption, and to determine the conditions under which local thermodynamic equilibrium is a valid assumption. Currently, the most fruitful investigations of Fraunhofer lines are the chemical composition of the photosphere and the spatial distribution of velocities and magnetic fields. Because of its implications for stellar evolution and element building, the accurate determination of the chemical composition of the sun is one of the central problems of solar physics. Unfortunately, the derivation of solar abundances is not as straightforward a problem as might appear to the non-specialist, who often treats published results with more respect than they deserve. To begin with, only about 60 of the chemical elements have been identified in the sun, although additional ones may soon be discovered in the far ultraviolet. Of the observable sixty, twenty have been insufficiently measured in the laboratory, and ten others show but one or two faint lines, which can hardly be measured with any reasonable degree of accuracy. Even when an element is represented by numerous well-measured lines, the abundance can be derived from the line intensity only by a rather complicated theory involving numerous assumptions as to the structure of the atmosphere, the mechanism of line formation, and the transition probabilities or oscillator strengths. Thus, abundances are a continuing problem. Information on velocity fields in the sun may be inferred from the widths of line
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profiles, which are usually found to be larger than those due to thermal broadening alone and from local Doppler shifts in the positions of the lines. It has been found, for example, that the half widths of faint Fraunhofer lines are about twice as large as would be expected from thermal Doppler broadening at T = 6000°K. This suggests that the photosphere is turbulent, the r.m.s, value increasing with depth from about 0-6 km/sec at the top of the photosphere to about 1.55 km/sec in the deep layers. It should be mentioned in passing that although the chromosphere is completely transparent even at the very centers of most Fraunhofer lines, the central cores of the strongest absorption lines appear to be formed entirely in the chromosphere, and measurements of their shapes suggest that for these lines the turbulent velocity increases from just under 1 km/sec at the top of the photosphere to about 6 kin/see at a height of about 3000 km. Thus the turbulent velocity appears to pass through a minimum and to increase both inward and outward from the top of the photosphere. Furthermore, the turbulent velocity field in the photosphere appears to be anisotropic; from observations made at points near the limb, the ratio of horizontal to vertical velocities is found to be just under two. The scale of the microturbulence is probably smaller than the thickness of the photosphere, and therefore cannot be resolved no matter how high the angular resolution of the image. There is a second type of motion, on a size scale ranging from 1000 to 5000 km (1 sec of arc = .750 km), which manifests itself as local Doppler shifts in the positions of Fraunhofer lines, the r.m.s, value of the velocity being a few tenths of a kilometer per second. The detection and measurement of such tiny ~/elocities implies the measurement of wavelength shifts on the order of one part in a million. Actually, the performance of modern grating solar spectrographs is such that velocity shifts as small as one part in five million can be detected with relative ease. Although local Doppler shifts have been systematically measured in the solar spectrum since 1950, their real nature was not understood until 1960 when Leighton and his associates at the California Institute of Technology discovered that the local velocity field is periodic in the form of a damped oscillation with a period of about five minutes, which happens to correspond to the characteristic frequency of the atmosphere. Similar results have also been obtained independently by Evans and Michard at the Sacramento Peak Observatory. The oscillations appear to be excited by convective motions originating in an unstable layer below the photosphere. These oscillatory velocities seem to be largely radial in direction. Leighton has also called attention to a second flow pattern, the scale of which is about 15,000 km. This large scale motion is predominantly horizontal with a mean lifetime of about 10 hr. The distribution of velocities over the surface of the sun strongly suggests that the flow pattern of the large scale motion is shaped by the lines of force of the sun's magnetic field. There are also many other lines of evidence which show that praetieaUy all solar phenomena--sunspots, faculae, prominences, flares, etc.--are either caused or influenced in a major way by solar magnetic fields. Thus, solar phenomena must be interpreted'in the framework of magnetohydrodynamics, and clearly the measurement of magnetic fields with high accuracy is essential in this context. The measurement of magnetic fields on the sun is based upon the splitting of spectral lines by the Zeeman effect. For the sake of simplicity, simple Zeeman triplets with large g-factors are selected for measurement and usually only the longitudinal component of the field is measured. Thus the
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problem reduces to measuring the separation of two Zeeman components circularly polarized in opposite directions. The classical method of observation, as first applied to the sun by George Ellery Hale in 1908, makes use of a Nicol prism and compound quarter wave plate in front of the slit of a spectrograph. The spectrum then consists of a series of parallel strips in which circular polarization of a given sign is alternately transmitted and extinguished. The direct method is well suited to the measurements o f the relatively intense fields, from a few hundred to a few thousand gauss, found in sunspots. But even a field Of 100 gauss causes a shift of only 0.004 A in the magnetically sensitive line Fe I A5250. Since the half width of this line is in the neighborhood of 0.10 A, it is obvious that direct measurement of line shifts is impractical for solar fields as small as tens of gauss, to say nothing of a few tenths of a gauss, for which the Zeeman shifts are as small as 0.0005 of the half width. Solar magnetographs, which are capable of measuring fields as small as a few tenths of a gauss, with automatic recording of the sign and intensity of the field over the entire solar image, were first perfected by H. D. and H. W. Babcock at the Mr. Wilson and Palomar Observatories about 1952. When a pair of exit slits is placed on opposite sides of a line profile and when the circular polarization in the line profile is modulated at a fixed frequency by an optical analyzer, the profile will appear to shift back and forth, and the light passing through the slits will fluctuate slightly in intensity. Magnetographs are now in operation at a number of solar observatories here and abroad. The systematic mapping of the entire sun by the Babcocks has led to the definite detection of a general or poloidal field with an intensity of I to 2 gauss, and to new insights into the origin and development of the solar cycle. The fine scanning of magneticallyactive regions, which has been intensively pursued at the Crimean Astrophysical Observatory, seems destined to throw light on the origin of solar flares. The future development of magnetographs should be in the direction of still higher angular resolution, in the near future on the order of 1 see of arc, and ultimately from a balloon or satellite on the order of 0.1 sec of arc. The scientific goal of such high resolution would be the measurement of magnetic fields associated with the so-called granulation, the bright-dark pattern caused by convection, which has a scale as small as half a second of arc and less.
C. Solar rotation The observation of details on the surface of the sun shows that the sun is rotating and furthermore that the angular velocity decreases with latitude as follows: = 14.°38-2.°77 s i n ~
(1)
This unusual relationship has been confirmed by the measurement of Doppler shifts at the east and west limbs where the line of sight velocity arising from the rotation at the equator is about 2 km/sec. It may be possible to explain most of the observed features of the sunspot cycle as a consequence of the action of the differential rotation in amplifying an initially weak dipole field.
D. The infrared solar spectrum Observations of the infrared solar spectrum are generally inferior in quality to those in the visible owing to the relative insensitivity of detecting systems and to absorption
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by the earth's atmosphere, which is total in many large regions of the spectrum and partial in others. The photographic plate is not an efficient detector for infrared wavelengths longer than about 9000 A, although it may be useful for some purposes up to 13,500 A. Photoconductive cells have given good results up to about 5 p, and thermocouples out to the infrared cutoff of the atmosphere at about 23.7/~. The spectroscopic resolving power attained so far decreases more or less regularly from about 200,000 at 1 /~ to about 2000 at 20 /z. The time seems ripe to undertake new observations, especially in the region 8 to 13/z, with some of the recently developed detectors such as the superconducting bolometer. The continuous absorption coefficient of the negative hydrogen ion increases toward wavelengths longer than 1-6/~. Consequently, observations of the infrared continuous radiation from the sun can give important information on the temperature distribution of the highest layers of the photosphere. In the vicinity of 1.6/~, the wavelength dependence of the opacity of the photosphere passes through a minimum, and consequently intensities are relatively high for many of the high excitation lines that occur in this portion Of the spectrum. At longer wavelengths, the increasing opacity coupled with the tendency of infrared atomic lines to arise from highly excited levels causes the solar Fraunhofer spectrum, at least the atomic component, to fade out rapidly from 2.0/~ to longer wavelengths. On the other hand, the infrared solar spectrum should be rich in vibration-rotation bands of a number of molecules known to be abundant on the sun. To date only the fundamental and first overtone bands of CO have been studied in detail; the detection of the vibration-rotation bands of other molecules such as CH, CN, NH, NO, OH is impeded by insufficient spectroscopic resolving power and by atmospheric absorption. The spectra of sunspots should be rich in infrared bands and may offer the best possibility for the detection of the rare isotopes of C, N, and O. THE CHROMOSPHERE The spectrum of the chromosphere may be viewed in three different ways. First, although the chromosphere is completely transparent to visible radiation at nearly all wavelengths, its lowest layers are opaque to radiation at the centers of a number of strong Fraunhofer lines. The cores of these lines therefore originate in the low chromosphere, mostly at heights on the order of a few hundred kilometers and in the case of the very strongest lines, at heights up to five or six thousand kilometers. Second, the emission spectrum of the chromosphere may be observed when the radiation from the photosphere is occulted--most effectively by the moon during a total eclipse but also by an occulting disc under good seeing conditions. Third, the far ultraviolet emission spectrum of the chromosphere may be observed from high altitudes in rockets or satellites. A. The spectrum of the chromosphere on the disc One of the most interesting and puzzling phenomena connected with the spectrum of the chromosphere on the disc is the so-called double reversal in the cores of the H and K lines of Ca II. The emission reversals are also observed in other cool stars in which a remarkable correlation--the Wilson-Bappu effect--has been found between the width of the emission feature and the intrinsic luminosity of the star, a correlation that holds
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over a range of over a factor of a million in luminosity. There is no satisfactory explanation as yet either for the origin of the double reversal or for the correlation between the width of the emission and stellar luminosity. It is not unlikely that the effect will ultimately be explained as a magnetohydrodynamic phenomenon. We have referred already to the broadening of the cores of strong Fraunhofer lines by thermal or non, thermal motions in the chromosphere. Although the r.m.s, velocity of the motion clearly increases with height, we are still not able to specify the exact heights to which the measurements refer. Solar spectrographs are also frequently used to make spectroheliograms, or photographs of the sun in a very narrow band of wavelengths, say 0.1 A. Ordinarily, the wavelength selected is at or close to the center of a very strong Fraunhofer line, e.g. the H~ line of H and the H and K lines of Ca +. This is a powerful technique for studying solar activity at different heights in the chromosphere, even though the heights themselves are not well known. Solar flares are almost always detected and studied on spectroheliograms, usually in H~, since only a small number of the very brightest flares have been known to emit detectable amounts of continuous radiation. Aside from the spectacular forms of solar activity such as the flares, and the dark filaments, spectroheliograms of the so-caUed quiet chromosphere also show a wealth of detail, both in the form of apparently random bright and dark mottling and a kind of coarse network that seems to delineate a celJular structure. Some interesting variants of the spectroheliogram have recently been designed by Leighton. One is a so-caUed velocity map of the sun, in which the bright and dark regions represent matter with velocities of approach and recession respectively. The second is a magnetic map in which the field intensity is measured by the degree of blackness or whiteness, one denoting negative polarity and the other positive. The brightness fluctuations of spectroheliograms seem to be intimately related to the distribution of magnetic and velocity fields in the chromosphere.
B. The flash spectrum The intensity of the visible emission of the chromosphere is only about one tenthousandth that of the photosphere. Therefore, if the chromosphere is to be observed at the solar limb, both instrumental and atmospheric scattering present very severe problems. Although the chromospheric spectrum may be photographed on any clear day when seeing conditions are good, by far the best results are obtained when the sun's disc is occulated by the moon at a total solar eclipse. Known as the flash spectrum because it is observable for just a few seconds immediately before and after totality, this type of observation has yielded most of the information we now have about the physical state of the chromosphere. At visible wavelengths, the flash spectrum is in most respects an emission-line reversal of the Fraunhofer spectrum. A striking exception is the presence of fairly strong lines of both neutral and ionized He, which are not present in the spectrum of the photosphere. There are also relatively faint continua comprising the free-free and capture continua of both H and H - as well as photospheric radiation scattered by free electrons. Eclipse sPectrographs may be used in both slit and slitless forms. When accurate line profiles are desired, it is better to use slit spectra, b u t it is then difficult to determine the height at which the observation was made. In the slitless form, which is most commonly used, the edge of the moon defines the slit, and each line contains all chromospheric
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radiation above the moon's limb. Since the position of the moon at any instant is known with high accuracy, a series of spectra taken in rapid succession can in principle lead to a determination of the variation with height of densities, temperatures, pressures, and other conditions in the atmosphere. Unfortunately, such analyses are not entirely unambiguous and therefore the structure of the chromosphere is still highly controversial. First, the observations do not give the volume emission straight away but its double integral over the radial and tangential directions. The volume emission can only be extracted unambiguously if the atmosphere is spherically symmetric whereas in fact inhomogeneities in density and temperature appear to be the rule rather than the exception. Second, the chromosphere deviates strongly from thermal equilibrium, and therefore the usual ionization and excitation equations are invalid. Thus, although it may be possible to derive the height distribution of the number density of atoms in a given excited state and in a given stage of ionization, there is no obvious way of translating this number into the total density of atoms in all stages of excitation and ionization. A third complication is that the chromosphere appears to be in a state of violent hydrodynamic motion in which magnetic fields may also play a role, and it is not an easy matter to incorporate such motion into a theory of line formation. C. The corona
The visible radiation of the corona is still fainter than that of the chromosphere, by about two orders of magnitude. Thus, while important observations of the corona can be carried out from mountain stations with coronagraphs, the corona is best studied during total eclipses. About 97 per cent of the visible radiation of the corona is in a continuous spectrum, the remainder being in the form of bright emission lines which result from magnetic dipole and quadrupole transitions in very highly ionized atoms, typical of which are Ca XII, Fe XIV, Ni XVI, etc. Obviously, the occurrence of such high stages of ionization signifies temperatures in the neighborhood of one or two million degrees. In the inner parts of the corona, the continuous spectrum is simply radiation from the photosphere scattered by the free electrons in the highly-ionized corona. The outer parts of the corona also show a contribution arising from the scattering of solar light by the dust in interplanetary space. The relative contributions of dust and electrons may be assessed by taking account of the fact that the electron scattered radiation is polarized while the dust scattered component is not. Although there is no doubt that 106 degrees is the correct order of magnitude for the coronal temperature, the exact value, or even whether the corona is in fact spatially uniform in temperature remains both unknown and controversial. There are many different ways of deducing the temperature of the corona, among which are: (1) the widths of coronal emission lines, assumed to be thermally widened; (2) the distribution of electron density, assuming hydrostatic equilibrium; (3) the intensity of radio-frequency radiation interpreted as black body emission; and (4) the relative intensities of lines from different stages of ionization together with an appropriate theory of ionization equilibrium. Values of the temperature derived by these different methods show a spread of between 500,000 ° and 4,000,000 °. The temperatures derived from the shapes and intensities of emission lines show two systematic trends. First, the temperature increases with ionization potential, and second, for the same stage of ionization, the
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temperature derived from the line width is about 1.3 million degrees greater than that derived from ionization theory. These apparent discrepancies may be reconciled if it is assumed (1) that the different emissions come f r o m regions of different temperature, as was first suggested by Shklovsky; and (2) that the abnormally high widths of the line profiles are due in part to large scale motions. The required r.m.s, velocity of turbulent motion is about 35 km/sec. The Doppler spectrum of radar echoes from the sun reported by the Lincoln Laboratory at 38 Mc has a total width of 18 kc, which seems to confirm the presence of large scale motions of about the same size suggested by the optical line widths.
D. The far ultraviolet solar spectrum The high temperature of the upper chromosphere and corona was not discovered until 20 years ago, despite the fact that excellent spectra of both the chromosphere and the corona were taken as early as the beginning of the century. There were many reasons why the high temperature was overlooked for so long, but one of them is that the visible spectrum of the chromosphere is in most respects that of a gas of a temperature of 5000 ° to 6000 °. Aside from the anomalous intensities of the He lines, the existence of a temperature that increases outwards can be inferred only after rather intricate and sophisticated analysis of eclipse spectra. At first sight, it may seem strange that the visible spectrum of the chromosphere should not show any lines of more than once-ionized elements. The reason seems to be that the temperature of the chromosphere at first increases only very slowly with height and rises very steeply in a region of relatively low density. The steepness of the temperature gradient is such that the abundance of any one ionization stage is too small for it to radiate any but the resonance lines, which fall in the far ultraviolet. After all, the transition probability depends on the cube of the frequency, and this fact alone explains why the permitted lines of highly-ionized atoms are not observed at visible wavelengths. This suggests that the low chromosphere can best be studied through the medium of its visible spectrum, but that the zone of transition to the corona, the region of steep temperature gradient, should be investigated by its far ultraviolet spectrum. Thanks to the pioneering work of groups at the Naval Research Laboratory, the University of Colorado, the Air Force Cambridge Research Laboratories, and the Goddard Space Flight Center of NASA, the far ultraviolet spectrum has been observed in its entirety to a short wave limit somewhat below 100 A. Most investigations to date have been carried out from rockets, but the G o d d a r d group has obtained more than 10,000 scans of the solar spectrum between 100 and 400 A in the first Orbiting Solar Observatory. The spectra obtained with the first OSO refer to integrated solar radiation. The second OSO, to be launched in the Fall of 1963, will record spectra in the region 5001500 A of solar radiation from a small region of the disc and will also make time-lapse spectroheliograms in a number of far ultraviolet wavelengths. An up-to-date review of developments in far ultraviolet solar spectroscopy will be found in the review by H. Friedman cited below. This review has been necessarily brief and incomplete and has either omitted many important subjects or mentioned them only briefly. For example, the spectroscopy of solar activity is a special field by itself, requiring rather specialized instruments and techniques, as is the investigation of the far ultraviolet spectrum f r o m high altitudes. 9
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T h e r e a d e r wishing to p u r s u e these subjects a n d others m a y do so with the aid o f the references below. GENERAL REFERENCES 1. Articles by C. DE JAGERand by L. GOLDBERGand A. K. PIERCEin Encyclopaedia of Physics, vol. LII (Ed. H. FLOGCE), Springer, Berlin (1959). 2. Annual Review of Astronomy and,4strophysics, vol. I (Ed. L. GOLDBERG).Articles by H. W. BAaCOCK, R. B. LEI~ITON, and H. FRIEDMAN,Annual Reviews, Inc., Palo Alto (1963) 3. R. N. THOMASand R. G. ATHAY,Physics of the Solar Chromosphere, Interscience, New York (1961).
SOLAR
SPECTROSCOPY
LEo GOLDBERG Harvard College Observatory, Cambridge, Massachusetts SOLAR spectroscopy is a particularly fascinating subject because of the great variety of conditions under which the sun emits radiation. Thus, temperatures range from a few thousand to several million degrees and densities from below 10-is g/cm3 to 5 x 10-7 g/cms. The presence of magnetohydrodynamicphenomena, some of which are explosively transient in character, adds further spice to the formation of solar spectra. The observable optical spectrum extends continuously from X-rays as short as about 1 A to the beginning of the radio frequency spectrum at millimeter wavelengths. Beginning in the ultraviolet at about 1700 A and extending through the visible and infrared, the spectrum of the solar disc is essentially a continuous spectrum crossed by tens of thousands of absorption lines--the so-called Fraunhofer lines. Below 1700 A, the spectrum of the disc consists almost entirely of emission lines superposed on a very faint emission background. There is a further remarkable difference between the spectra above and below 1700 _~. The Fraunhofer absorption lines are those of neutral and singly-ionized atoms, which would be expected to appear at temperatures of about 4000°-6000°K. The emission lines on the other hand arise from atoms in many different stages of ionization, some typical examples being H I, He I and He II, O I, O VI, Si XII, Mg X, C II, Si I, Fe XV, etc. The appearance of these emission lines implies a continuum of temperatures up to several million degrees. The range and diversity of the solar spectrum can be understood in terms of the following semi-quantitative and rather well-documented model of the solar atmosphere. First, the visible spectrum including most of the Fraunhofer absorption lines originates in the deepest observable layer of the atmosphere, called the photosphere, a zone about 300 km thick. The temperature decreases from about 8000°K at the bottom of this zone to something like 4500°K at the top. Owing to the high opacity of the photospheric gases, no radiation from below can escape to the surface without being totally absorbed. The top of the photosphere is defined as the level at which the gases are just barely beginning to become opaque, and therefore the radiation that escapes from the photosphere suffers partial absorption on the way out. It turns out that each point in the photosphere radiates like a black body at the local temperature; therefore, at each wavelength the outgoing radiation is an average of Planckian intensities corresponding to different temperatures. The resulting spectral energy curve at visible wavelengths rather closely simulates that of a black body with T = 6300°K. At longer infrared wavelengths, the opacity of the photosphere increases with increasing wavelength and therefore the "effective" temperature diminishes and 519
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approaches a boundary value of approximately 4500°K. At shorter wavelengths, the opacity also increases, and the spectral energy curve roughly resembles that of a black body at T = 4500°K. The low temperature of the photosphere explains why its radiation is insignificantly weak at wavelengths below about 1700 A. Directly above the photosphere is an atmospheric fringe about 20,000 km thick, called the chromosphere, and above it is the corona, which has been observed to extend to distances on the order of 10 solar radii and probably does not have a well-defined boundary as it merges into the interplanetary medium. Not very long ago, it was thought that the chromosphere and corona were simple low-temperature extensions of the photosphere, but it has been known for over 20 years that, on the contrary, the corona is a very hot plasma, its temperature being on the order of 1-2 million degrees and that the chromosphere is a transition region in which the temperature increases rapidly outwards. The spectra of the chromosphere and corona are so faint that they cannot be observed unless steps are taken to suppress the enormously greater intensity of the photosphere. At visible wavelengths the suppression is best accomplished by a solar eclipse and less efficiently by an artificial eclipse. At far ultraviolet wavelengths, however, the problem is solved by Planck's law. We have already noted that the intensity of the photosphere is insignificant below h1700, and consequently the emission-line spectra of the chromosphere and corona may be observed directly upon the disc.
VISIBLE SOLAR SPECTRUM The term "visible" is used loosely here to include the spectral region from about 3000 to 9000 _A, which can be photographed from the ground with very high resolution. Modern observations of the visible spectrum had their beginning in the work of H. A. Rowland, whose spectra obtained just prior to 1900 were not substantially surpassed in spectral purity and resolving power until the late 1940's. The major improvements in the intervening period were in the establishment of accurate wavelength standards and in the provision of photometric calibration for intensity measurements. The introduction to solar spectroscopy of modern high-quality gratings, especially those ruled by H. W. Babcock at the Mt. Wilson and Palomar Observatories, has been responsible for some rather spectacular new developments in the field. A good example of the performance of modern solar spectroscopic equipment is that of the 50 ft vacuum spectrograph of the McMath-Hulbert Observatory, completed in 1955. Measurements by Pierce of the performance of an 8 in., 600 groove/mm Babcock grating show a resolution of 630,000 in the fifth order, the dispersion being about 1 A/cm. The half width of the instrumental profile is about 0.01 A, and the total intensity of ghosts is 1.8 per cent in the fifth order. The half width of the narrowest solar absorption lines is 0"03 A, and therefore the profiles of even very weak lines may be obtained directly by photoelectric scanning, with little or no correction for instrumental distortion. A number of solar observatories in this country and abroad now have equipment with comparable performance. Studies of the solar photosphere are based upon intensity measurements on both continuous and line spectra.
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A. The continuous spectrum Measurements of the intensity of the continuous spectrum can give information on the temperature gradient in the photosphere and on the wavelength dependence of the continuous absorption coefficient at various depths in the atmosphere. The necessary measurements are: (1) the absolute spectral energy distribution of radiation from the center of the sun's disc and (2) measurements of the rate of darkening to the limb at monochromatic wavelengths, spaced so as to give complete coverage of the spectrum. With the assumption of hydrostatic equilibrium, the analysis of such data leads to the derivation both of the temperature and pressure gradients in the photosphere and of the wavelength dependence of the continuous absorption coefficient. Studies of this type have proved that bound-free and free-free transitions in the fields of negative hydrogen ions are the major contributor to the opacity of the photosphere at visible wavelengths. Continuous absorption by neutral hydrogen is also of considerable importance in the deep layers. It is also possible that some of the apparent discrepancy between theory and observation at the shorter wavelengths below ~5000 may be caused by H2 molecules absorbing while in the lowest repulsive electronic state. Empirical models of the photosphere derived from limb darkening observations are uncertain at both the upper and lower boundaries, the upper because of the blurring of the solar limb by the earth's atmosphere and the lower because of uncertainties in estimating the proportion of the energy flux that is transported by convection rather than by radiation. B. The absorption line spectrum The Fraunhofer lines are not a primary source of information on temperature and pressure models of the photosphere, but they may serve to verify or disprove such models. Study of the shapes of Fraunhofer lines also provides a basis on which to decide among alternative mechanisms for the formation of lines, such as coherent or noncoherent scattering, or pure absorption, and to determine the conditions under which local thermodynamic equilibrium is a valid assumption. Currently, the most fruitful investigations of Fraunhofer lines are the chemical composition of the photosphere and the spatial distribution of velocities and magnetic fields. Because of its implications for stellar evolution and element building, the accurate determination of the chemical composition of the sun is one of the central problems of solar physics. Unfortunately, the derivation of solar abundances is not as straightforward a problem as might appear to the non-specialist, who often treats published results with more respect than they deserve. To begin with, only about 60 of the chemical elements have been identified in the sun, although additional ones may soon be discovered in the far ultraviolet. Of the observable sixty, twenty have been insufficiently measured in the laboratory, and ten others show but one or two faint lines, which can hardly be measured with any reasonable degree of accuracy. Even when an element is represented by numerous well-measured lines, the abundance can be derived from the line intensity only by a rather complicated theory involving numerous assumptions as to the structure of the atmosphere, the mechanism of line formation, and the transition probabilities or oscillator strengths. Thus, abundances are a continuing problem. Information on velocity fields in the sun may be inferred from the widths of line
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profiles, which are usually found to be larger than those due to thermal broadening alone and from local Doppler shifts in the positions of the lines. It has been found, for example, that the half widths of faint Fraunhofer lines are about twice as large as would be expected from thermal Doppler broadening at T = 6000°K. This suggests that the photosphere is turbulent, the r.m.s, value increasing with depth from about 0-6 km/sec at the top of the photosphere to about 1.55 km/sec in the deep layers. It should be mentioned in passing that although the chromosphere is completely transparent even at the very centers of most Fraunhofer lines, the central cores of the strongest absorption lines appear to be formed entirely in the chromosphere, and measurements of their shapes suggest that for these lines the turbulent velocity increases from just under 1 km/sec at the top of the photosphere to about 6 kin/see at a height of about 3000 km. Thus the turbulent velocity appears to pass through a minimum and to increase both inward and outward from the top of the photosphere. Furthermore, the turbulent velocity field in the photosphere appears to be anisotropic; from observations made at points near the limb, the ratio of horizontal to vertical velocities is found to be just under two. The scale of the microturbulence is probably smaller than the thickness of the photosphere, and therefore cannot be resolved no matter how high the angular resolution of the image. There is a second type of motion, on a size scale ranging from 1000 to 5000 km (1 sec of arc = .750 km), which manifests itself as local Doppler shifts in the positions of Fraunhofer lines, the r.m.s, value of the velocity being a few tenths of a kilometer per second. The detection and measurement of such tiny ~/elocities implies the measurement of wavelength shifts on the order of one part in a million. Actually, the performance of modern grating solar spectrographs is such that velocity shifts as small as one part in five million can be detected with relative ease. Although local Doppler shifts have been systematically measured in the solar spectrum since 1950, their real nature was not understood until 1960 when Leighton and his associates at the California Institute of Technology discovered that the local velocity field is periodic in the form of a damped oscillation with a period of about five minutes, which happens to correspond to the characteristic frequency of the atmosphere. Similar results have also been obtained independently by Evans and Michard at the Sacramento Peak Observatory. The oscillations appear to be excited by convective motions originating in an unstable layer below the photosphere. These oscillatory velocities seem to be largely radial in direction. Leighton has also called attention to a second flow pattern, the scale of which is about 15,000 km. This large scale motion is predominantly horizontal with a mean lifetime of about 10 hr. The distribution of velocities over the surface of the sun strongly suggests that the flow pattern of the large scale motion is shaped by the lines of force of the sun's magnetic field. There are also many other lines of evidence which show that praetieaUy all solar phenomena--sunspots, faculae, prominences, flares, etc.--are either caused or influenced in a major way by solar magnetic fields. Thus, solar phenomena must be interpreted'in the framework of magnetohydrodynamics, and clearly the measurement of magnetic fields with high accuracy is essential in this context. The measurement of magnetic fields on the sun is based upon the splitting of spectral lines by the Zeeman effect. For the sake of simplicity, simple Zeeman triplets with large g-factors are selected for measurement and usually only the longitudinal component of the field is measured. Thus the
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problem reduces to measuring the separation of two Zeeman components circularly polarized in opposite directions. The classical method of observation, as first applied to the sun by George Ellery Hale in 1908, makes use of a Nicol prism and compound quarter wave plate in front of the slit of a spectrograph. The spectrum then consists of a series of parallel strips in which circular polarization of a given sign is alternately transmitted and extinguished. The direct method is well suited to the measurements o f the relatively intense fields, from a few hundred to a few thousand gauss, found in sunspots. But even a field Of 100 gauss causes a shift of only 0.004 A in the magnetically sensitive line Fe I A5250. Since the half width of this line is in the neighborhood of 0.10 A, it is obvious that direct measurement of line shifts is impractical for solar fields as small as tens of gauss, to say nothing of a few tenths of a gauss, for which the Zeeman shifts are as small as 0.0005 of the half width. Solar magnetographs, which are capable of measuring fields as small as a few tenths of a gauss, with automatic recording of the sign and intensity of the field over the entire solar image, were first perfected by H. D. and H. W. Babcock at the Mr. Wilson and Palomar Observatories about 1952. When a pair of exit slits is placed on opposite sides of a line profile and when the circular polarization in the line profile is modulated at a fixed frequency by an optical analyzer, the profile will appear to shift back and forth, and the light passing through the slits will fluctuate slightly in intensity. Magnetographs are now in operation at a number of solar observatories here and abroad. The systematic mapping of the entire sun by the Babcocks has led to the definite detection of a general or poloidal field with an intensity of I to 2 gauss, and to new insights into the origin and development of the solar cycle. The fine scanning of magneticallyactive regions, which has been intensively pursued at the Crimean Astrophysical Observatory, seems destined to throw light on the origin of solar flares. The future development of magnetographs should be in the direction of still higher angular resolution, in the near future on the order of 1 see of arc, and ultimately from a balloon or satellite on the order of 0.1 sec of arc. The scientific goal of such high resolution would be the measurement of magnetic fields associated with the so-called granulation, the bright-dark pattern caused by convection, which has a scale as small as half a second of arc and less.
C. Solar rotation The observation of details on the surface of the sun shows that the sun is rotating and furthermore that the angular velocity decreases with latitude as follows: = 14.°38-2.°77 s i n ~
(1)
This unusual relationship has been confirmed by the measurement of Doppler shifts at the east and west limbs where the line of sight velocity arising from the rotation at the equator is about 2 km/sec. It may be possible to explain most of the observed features of the sunspot cycle as a consequence of the action of the differential rotation in amplifying an initially weak dipole field.
D. The infrared solar spectrum Observations of the infrared solar spectrum are generally inferior in quality to those in the visible owing to the relative insensitivity of detecting systems and to absorption
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by the earth's atmosphere, which is total in many large regions of the spectrum and partial in others. The photographic plate is not an efficient detector for infrared wavelengths longer than about 9000 A, although it may be useful for some purposes up to 13,500 A. Photoconductive cells have given good results up to about 5 p, and thermocouples out to the infrared cutoff of the atmosphere at about 23.7/~. The spectroscopic resolving power attained so far decreases more or less regularly from about 200,000 at 1 /~ to about 2000 at 20 /z. The time seems ripe to undertake new observations, especially in the region 8 to 13/z, with some of the recently developed detectors such as the superconducting bolometer. The continuous absorption coefficient of the negative hydrogen ion increases toward wavelengths longer than 1-6/~. Consequently, observations of the infrared continuous radiation from the sun can give important information on the temperature distribution of the highest layers of the photosphere. In the vicinity of 1.6/~, the wavelength dependence of the opacity of the photosphere passes through a minimum, and consequently intensities are relatively high for many of the high excitation lines that occur in this portion Of the spectrum. At longer wavelengths, the increasing opacity coupled with the tendency of infrared atomic lines to arise from highly excited levels causes the solar Fraunhofer spectrum, at least the atomic component, to fade out rapidly from 2.0/~ to longer wavelengths. On the other hand, the infrared solar spectrum should be rich in vibration-rotation bands of a number of molecules known to be abundant on the sun. To date only the fundamental and first overtone bands of CO have been studied in detail; the detection of the vibration-rotation bands of other molecules such as CH, CN, NH, NO, OH is impeded by insufficient spectroscopic resolving power and by atmospheric absorption. The spectra of sunspots should be rich in infrared bands and may offer the best possibility for the detection of the rare isotopes of C, N, and O. THE CHROMOSPHERE The spectrum of the chromosphere may be viewed in three different ways. First, although the chromosphere is completely transparent to visible radiation at nearly all wavelengths, its lowest layers are opaque to radiation at the centers of a number of strong Fraunhofer lines. The cores of these lines therefore originate in the low chromosphere, mostly at heights on the order of a few hundred kilometers and in the case of the very strongest lines, at heights up to five or six thousand kilometers. Second, the emission spectrum of the chromosphere may be observed when the radiation from the photosphere is occulted--most effectively by the moon during a total eclipse but also by an occulting disc under good seeing conditions. Third, the far ultraviolet emission spectrum of the chromosphere may be observed from high altitudes in rockets or satellites. A. The spectrum of the chromosphere on the disc One of the most interesting and puzzling phenomena connected with the spectrum of the chromosphere on the disc is the so-called double reversal in the cores of the H and K lines of Ca II. The emission reversals are also observed in other cool stars in which a remarkable correlation--the Wilson-Bappu effect--has been found between the width of the emission feature and the intrinsic luminosity of the star, a correlation that holds
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over a range of over a factor of a million in luminosity. There is no satisfactory explanation as yet either for the origin of the double reversal or for the correlation between the width of the emission and stellar luminosity. It is not unlikely that the effect will ultimately be explained as a magnetohydrodynamic phenomenon. We have referred already to the broadening of the cores of strong Fraunhofer lines by thermal or non, thermal motions in the chromosphere. Although the r.m.s, velocity of the motion clearly increases with height, we are still not able to specify the exact heights to which the measurements refer. Solar spectrographs are also frequently used to make spectroheliograms, or photographs of the sun in a very narrow band of wavelengths, say 0.1 A. Ordinarily, the wavelength selected is at or close to the center of a very strong Fraunhofer line, e.g. the H~ line of H and the H and K lines of Ca +. This is a powerful technique for studying solar activity at different heights in the chromosphere, even though the heights themselves are not well known. Solar flares are almost always detected and studied on spectroheliograms, usually in H~, since only a small number of the very brightest flares have been known to emit detectable amounts of continuous radiation. Aside from the spectacular forms of solar activity such as the flares, and the dark filaments, spectroheliograms of the so-caUed quiet chromosphere also show a wealth of detail, both in the form of apparently random bright and dark mottling and a kind of coarse network that seems to delineate a celJular structure. Some interesting variants of the spectroheliogram have recently been designed by Leighton. One is a so-caUed velocity map of the sun, in which the bright and dark regions represent matter with velocities of approach and recession respectively. The second is a magnetic map in which the field intensity is measured by the degree of blackness or whiteness, one denoting negative polarity and the other positive. The brightness fluctuations of spectroheliograms seem to be intimately related to the distribution of magnetic and velocity fields in the chromosphere.
B. The flash spectrum The intensity of the visible emission of the chromosphere is only about one tenthousandth that of the photosphere. Therefore, if the chromosphere is to be observed at the solar limb, both instrumental and atmospheric scattering present very severe problems. Although the chromospheric spectrum may be photographed on any clear day when seeing conditions are good, by far the best results are obtained when the sun's disc is occulated by the moon at a total solar eclipse. Known as the flash spectrum because it is observable for just a few seconds immediately before and after totality, this type of observation has yielded most of the information we now have about the physical state of the chromosphere. At visible wavelengths, the flash spectrum is in most respects an emission-line reversal of the Fraunhofer spectrum. A striking exception is the presence of fairly strong lines of both neutral and ionized He, which are not present in the spectrum of the photosphere. There are also relatively faint continua comprising the free-free and capture continua of both H and H - as well as photospheric radiation scattered by free electrons. Eclipse sPectrographs may be used in both slit and slitless forms. When accurate line profiles are desired, it is better to use slit spectra, b u t it is then difficult to determine the height at which the observation was made. In the slitless form, which is most commonly used, the edge of the moon defines the slit, and each line contains all chromospheric
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radiation above the moon's limb. Since the position of the moon at any instant is known with high accuracy, a series of spectra taken in rapid succession can in principle lead to a determination of the variation with height of densities, temperatures, pressures, and other conditions in the atmosphere. Unfortunately, such analyses are not entirely unambiguous and therefore the structure of the chromosphere is still highly controversial. First, the observations do not give the volume emission straight away but its double integral over the radial and tangential directions. The volume emission can only be extracted unambiguously if the atmosphere is spherically symmetric whereas in fact inhomogeneities in density and temperature appear to be the rule rather than the exception. Second, the chromosphere deviates strongly from thermal equilibrium, and therefore the usual ionization and excitation equations are invalid. Thus, although it may be possible to derive the height distribution of the number density of atoms in a given excited state and in a given stage of ionization, there is no obvious way of translating this number into the total density of atoms in all stages of excitation and ionization. A third complication is that the chromosphere appears to be in a state of violent hydrodynamic motion in which magnetic fields may also play a role, and it is not an easy matter to incorporate such motion into a theory of line formation. C. The corona
The visible radiation of the corona is still fainter than that of the chromosphere, by about two orders of magnitude. Thus, while important observations of the corona can be carried out from mountain stations with coronagraphs, the corona is best studied during total eclipses. About 97 per cent of the visible radiation of the corona is in a continuous spectrum, the remainder being in the form of bright emission lines which result from magnetic dipole and quadrupole transitions in very highly ionized atoms, typical of which are Ca XII, Fe XIV, Ni XVI, etc. Obviously, the occurrence of such high stages of ionization signifies temperatures in the neighborhood of one or two million degrees. In the inner parts of the corona, the continuous spectrum is simply radiation from the photosphere scattered by the free electrons in the highly-ionized corona. The outer parts of the corona also show a contribution arising from the scattering of solar light by the dust in interplanetary space. The relative contributions of dust and electrons may be assessed by taking account of the fact that the electron scattered radiation is polarized while the dust scattered component is not. Although there is no doubt that 106 degrees is the correct order of magnitude for the coronal temperature, the exact value, or even whether the corona is in fact spatially uniform in temperature remains both unknown and controversial. There are many different ways of deducing the temperature of the corona, among which are: (1) the widths of coronal emission lines, assumed to be thermally widened; (2) the distribution of electron density, assuming hydrostatic equilibrium; (3) the intensity of radio-frequency radiation interpreted as black body emission; and (4) the relative intensities of lines from different stages of ionization together with an appropriate theory of ionization equilibrium. Values of the temperature derived by these different methods show a spread of between 500,000 ° and 4,000,000 °. The temperatures derived from the shapes and intensities of emission lines show two systematic trends. First, the temperature increases with ionization potential, and second, for the same stage of ionization, the
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temperature derived from the line width is about 1.3 million degrees greater than that derived from ionization theory. These apparent discrepancies may be reconciled if it is assumed (1) that the different emissions come f r o m regions of different temperature, as was first suggested by Shklovsky; and (2) that the abnormally high widths of the line profiles are due in part to large scale motions. The required r.m.s, velocity of turbulent motion is about 35 km/sec. The Doppler spectrum of radar echoes from the sun reported by the Lincoln Laboratory at 38 Mc has a total width of 18 kc, which seems to confirm the presence of large scale motions of about the same size suggested by the optical line widths.
D. The far ultraviolet solar spectrum The high temperature of the upper chromosphere and corona was not discovered until 20 years ago, despite the fact that excellent spectra of both the chromosphere and the corona were taken as early as the beginning of the century. There were many reasons why the high temperature was overlooked for so long, but one of them is that the visible spectrum of the chromosphere is in most respects that of a gas of a temperature of 5000 ° to 6000 °. Aside from the anomalous intensities of the He lines, the existence of a temperature that increases outwards can be inferred only after rather intricate and sophisticated analysis of eclipse spectra. At first sight, it may seem strange that the visible spectrum of the chromosphere should not show any lines of more than once-ionized elements. The reason seems to be that the temperature of the chromosphere at first increases only very slowly with height and rises very steeply in a region of relatively low density. The steepness of the temperature gradient is such that the abundance of any one ionization stage is too small for it to radiate any but the resonance lines, which fall in the far ultraviolet. After all, the transition probability depends on the cube of the frequency, and this fact alone explains why the permitted lines of highly-ionized atoms are not observed at visible wavelengths. This suggests that the low chromosphere can best be studied through the medium of its visible spectrum, but that the zone of transition to the corona, the region of steep temperature gradient, should be investigated by its far ultraviolet spectrum. Thanks to the pioneering work of groups at the Naval Research Laboratory, the University of Colorado, the Air Force Cambridge Research Laboratories, and the Goddard Space Flight Center of NASA, the far ultraviolet spectrum has been observed in its entirety to a short wave limit somewhat below 100 A. Most investigations to date have been carried out from rockets, but the G o d d a r d group has obtained more than 10,000 scans of the solar spectrum between 100 and 400 A in the first Orbiting Solar Observatory. The spectra obtained with the first OSO refer to integrated solar radiation. The second OSO, to be launched in the Fall of 1963, will record spectra in the region 5001500 A of solar radiation from a small region of the disc and will also make time-lapse spectroheliograms in a number of far ultraviolet wavelengths. An up-to-date review of developments in far ultraviolet solar spectroscopy will be found in the review by H. Friedman cited below. This review has been necessarily brief and incomplete and has either omitted many important subjects or mentioned them only briefly. For example, the spectroscopy of solar activity is a special field by itself, requiring rather specialized instruments and techniques, as is the investigation of the far ultraviolet spectrum f r o m high altitudes. 9
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T h e r e a d e r wishing to p u r s u e these subjects a n d others m a y do so with the aid o f the references below. GENERAL REFERENCES 1. Articles by C. DE JAGERand by L. GOLDBERGand A. K. PIERCEin Encyclopaedia of Physics, vol. LII (Ed. H. FLOGCE), Springer, Berlin (1959). 2. Annual Review of Astronomy and,4strophysics, vol. I (Ed. L. GOLDBERG).Articles by H. W. BAaCOCK, R. B. LEI~ITON, and H. FRIEDMAN,Annual Reviews, Inc., Palo Alto (1963) 3. R. N. THOMASand R. G. ATHAY,Physics of the Solar Chromosphere, Interscience, New York (1961).