Popular Science Monthly/Volume 66/February 1905/An Address on Astrophysics
|AN ADDRESS ON ASTROPHYSICS.|
DIRECTOR OF THE LICK OBSERVATORY, UNIVERSITY OF CALIFORNIA.
THE investigator in any field of knowledge must, as the price of success, both comprehend the general principles underlying his special problem, and give constant care to its details. Yet it is well, now and then, to leave details behind and consider the bearing of his work upon the science as a whole. Whether our subject is that of determining the accurate positions of the stars, or their radial velocities, the orbits of the planets, or the constitution of the sun, we are making but minor contributions to the solution of the two great problems which at present compose the science of astronomy. These problems, perhaps the most profound in the realm of matter, may be stated thus:
1. A determination of the structure of the sidereal universe; of the form of that portion of limitless space occupied by the universe; of the general arrangement of the sidereal units in space; and of their motions in accordance with the law of gravitation.
2. A determination of the constitution of the nebulæ, stars, planets and other celestial objects; of their physical conditions and relations to each other; of the history of their development, in accordance with the principles of sidereal evolution; and of what the future has in store for them.
The first problem has for its purpose to determine where the stars are and whither they are going. It has been ably treated under the head of astrometry.
The second seeks to determine the nature of the heavenly bodies—what the stars really are. This field of inquiry is well named, astrophysics.
The motives of these problems are distinct and definite; but, judged by the ultimate bearing of his results, nearly every astronomer is working in both fields. The astrophysicist borrows the tools of the astronomer of position, the latter uses the results of the former, and vice versa. Let me give two illustrations. Astrophysics desires to know the relative radiating power of matter in different types of stars—the Sirian and solar types, for example. The meridian circle and the telescope discovered a companion to Sirius; the micrometer determined the form and position of the orbits; the heliometer observed the star's distance; and the photometer measured the quantity of light received from it. Computations determine from these data that Sirius is but two and one half times as massive as our sun, whereas it radiates twenty-one times as much light; from which it follows that a given quantity of matter in Sirius radiates many times as effectively as the same quantity of solar matter—a fact of prime importance in the astrophysical study of all Sirian stars. The parallaxes of the stars are needed by the student of stellar evolution as well as by the student of the structure of the heavens.
Again, the measurement of radial velocities of the stars has been left almost completely to those observers who are especially interested in astrophysical problems and methods, yet it is the student of astrometry who is eager to use their results. The overlapping of the two departments of astronomy is but the symbol of progress.
The term astrophysics is of the present generation, but the beginnings of astrophysical inquiry are somewhat older. Theories of planetary evolution by Kant and Laplace; observations of nebulæ and star clusters by the elder Herschel, and his wonderfully sagacious deductions concerning them; various studies of planetary markings and conditions; systematic investigations of the sun spots, including Schwabe's discovery of their eleven-year period—these constituted the main body of the science in 1859. But the spirit of inquiry as to the nature of the heavenly bodies was latent in many quarters; and Kirchhoff's immortal discovery of the fundamental principles of spectrum analysis opened a gateway which many were eager to enter. The spectroscope became at once, and has remained, the astrophysicist's principal instrument. However, the spectrum is not his only field, nor the spectroscope his only tool. Radiation in all its aspects, and the instruments for determining its quantity and quality, are the means to the ends in view. And the great generalizations of scientific truth, the doctrines of evolution and of the conservation of energy, for example, have been no less helpful here than elsewhere.
The study of our sun forms the principal basis of astrophysical research. The sun is an ordinary star, comparable in size and condition with millions of other stars, but it is the only one near enough to show a disk. The point image of a distant star must be studied as an integrated whole; whereas the sun may be observed in considerable geometrical detail. We can not hope to understand the stars in general until we have first made a thorough study of our own star.
We are unable to study the body of the sun, except by indirect methods. The interior is invisible. The spherical body which we popularly speak of as the sun is hidden from view by the opaque photosphere. This photospheric veil, including the sun spots; the brilliant faculæ and flocculi, projecting upward from the photosphere; the reversing layer, in effect immediately overlying the photosphere; the chromosphere, a stratum associated with and overlying the reversing layer; the prominences, apparently ejected from the chromosphere; and the corona, extending outward from the sun in all directions to enormous distances; these superlatively interesting features of the sun constitute the only portions accessible for direct observation; and they are an insignificant part of its mass. They are literally the sun's outcasts. Our knowledge of the sun is based almost exclusively upon a study of these outcasts. Nevertheless, we are able to formulate a fairly simple and satisfactory theory of its constitution.
The materials composing the sun appear to be the same as those forming the earth's crust. Of the eighty known elements, slightly more than half have been observed in the reversing layer and chromosphere, by means of their spectra. The existence of others remains unproved, but there are no reasons to doubt that they too are present. Our most complete study of the sun's composition was made by Rowland, and he has said that if the earth were heated to the temperature of the sun, the terrestrial and solar spectra would be virtually identical.
The force of gravity at the sun's surface is well known, but the radial pressures at interior points are somewhat uncertain, as they depend upon the unknown law of increasing density with increasing depth. The minimum value of the pressure at the sun's center is thought to be fully ten thousand million times the pressure of our atmosphere at sea-level. The most probable value of the effective temperature of the sun's radiating surface is 6000° Centigrade, and the minimum value for the center is perhaps five million degrees. In view of these high temperatures, and the low average density of the sun, the interior must be largely gaseous, and perhaps entirely so; although, under the stupendous pressures, a great central core is probably of a viscous consistency, but ready to assume the usual properties of a gas when the convection currents carry the viscous masses up into regions of lower pressure.
The surface strata are radiating heat into surrounding space. To maintain the supply, it is imperative that convection currents should carry the cooled masses down into the interior, and bring corresponding hot masses up to the surface. These currents make the sun a very tempestuous body. Further, the outrushing materials must acquire the higher rotational speeds of the surface strata, and the inrushing must lose their tangential momentum; and these can scarcely be ineffective factors in the sun's circulatory system.
The mechanical theory of the maintenance of at least a part of the sun's radiation must be considered as a necessary consequence of the law of gravitation—as unavoidably a consequence of that law as precession is. Helmholtz computed that a contraction of the solar diameter of less than 400 feet per year would suffice to maintain the present rate of flow. Whether this is the sole source of supply is uncertain, and very doubtful. The discovery of sub-atomic forces in uranium, thorium and radium is of interest in this connection. These radio-active substances have revealed the existence of intense forces within the atom, long dreamed of by students of physics and chemistry, but never before realized. The energy radiated by an atom of these substances is thousands of times greater than that represented by the ordinary chemical transformations of equal masses of any known element. Whether these forces are working within the sun, prolonging its life many fold, and incidentally diminishing the required rate of Helmholtzian contraction, we do not know; but we are not justified in treating gravitation as the sole regulator of radiation. We are encouraged to this view by the fact that the age of the earth, as interpreted by geology and biology, is many times greater than the superior limit set by the gravitational theory.
The dazzlingly brilliant photospheric veil which limits the depth of our solar view is due, with no room for doubt, to the condensation of those metallic vapors which, by radiation to cold space, have cooled below their critical temperatures. These clouds form and float in a great sea of uncondensed vapors, very much as do our terrestrial clouds; but it seems probable that the process of formation is continuous and rapid; and that they are added to from above, or from the interstices, and melt away from below.
The sun spots are the most extensively studied and the least understood of all solar phenomena. That they are large-scale interruptions in the photosphere, and at the same time the most striking evidence of atmospheric circulation, there can be no doubt. Observations made near the sun's limb, to determine whether the spots are elevations or depressions with reference to the photosphere, seem not to be reliable, perhaps because of abnormal refractions in the strata overlying and surrounding the spots. In the the earth's atmosphere, a high barometer is the indication of descending currents, which generate heat by compression and prevent cloud formation. Is not the umbra of a spot an area of high pressure, which forces the solar atmosphere slowly downward, preventing cloud formation in that area, but favoring the growth of brilliant faculæ and flocculi in the regions of uprush surrounding the spot,—a theory first suggested by Secchi?
The visible spots are not the sole evidences of circulation. The surface is covered with a network of interstices, or vents between clouds, which probably exercise all the functions of the visible spots, but on a smaller scale.
There is no reason to question the truth of Young's discovery that the Fraunhofer lines originate in the absorption of a reversing layer—a thin stratum of uncondensed vapors lying immediately over and between the photospheric clouds.
The chromospheric stratum, several thousand miles in thickness, includes and extends far above the reversing layers, and contains the lighter gases, such as hydrogen and helium, and the vapors of calcium, sodium, magnesium and other elements which do not condense under existing temperatures.
The prominences have in general the same composition as the chromosphere. In some the lighter gases, and in others the heavier metallic vapors, predominate. They are portions of the chromosphere projected beyond its usual level by the more violent ascending currents, or perhaps by eruptions of a volcanic character; and these forces are almost certainly augmented by the pressure of the sun's radiation. It is difficult to account for the quiescent, cloud-like prominences in regions far above the chromosphere on any supposition other than that they are in equilibrium under the opposing influences of gravity and radiation pressure.
The nature of the forces which control the general and detailed coronal forms is but little understood. Motion within the corona has never been directly observed. Yet we can not question that the component particles are driven outward from the sun, and that many of them probably fall back into the sun, either singly or after combining to form larger masses. It is suggested that out-bound particles may be started on their way by the violent solar circulation, continued on their journey by radiation pressure, and arranged in the characteristic streamers under the influence of magnetic forces.
The light received from the corona is of three kinds:
1. A small quantity of bright-line radiations from a gas overlying the chromosphere. This gas is unknown to terrestrial chemistry, and astronomers provisionally call it coronium. It is distributed very irregularly over the solar sphere, and shows a decided preference for the sun-spot zone.
2. The bright-line radiations from coronium are almost a negligible quantity, in comparison with those from the same regions which form a strictly continuous spectrum, and which seem to be due to the incandescence of minute particles heated by the intense thermal radiations from the sun.
3. A small proportion of the inner, and a large proportion of the outer, coronal light are solar rays reflected and diffracted by the coronal particles.
Arrhenius has recently shown that Abbot's observation of an apparent temperature of the corona nearly equal to that of his observing room is in harmony with the spectrographic evidence of an inner corona composed of incandescent particles. Arrhenius finds that one minute dust particle to each 11 cubic meters of space in the coronal region observed by Abbot, raised to the temperature of 4620° absolute required by Stefan's law, would give a corona of the observed brightness, and of the observed temperature. The bolometric strip measured the resultant temperature of the few highly-heated particles and the cold background of space upon which the particles are seen in projection.
Arrhenius further estimates that a corona composed of incandescent dust particles need not have a total mass greater than 25,000,000 tons, to radiate the quantity of light yielded by the brightest corona observed. This is approximately that of a cube of granite only 200 meters on each side; a remarkably small mass for a volume whose linear dimensions are millions of kilometers.
This résumé of solar theory necessarily overlooks many unsettled points of great significance. Most important of all, perhaps, is that of the solar constant: does it vary, and in accordance with what law? Why is there a sun-spot period, and why are the large spots grouped within limited zones? Why does the form of the corona vary in a period equal in length to the spot period? Why does the angular speed of rotation increase from the poles to the equator? What is the origin of the faculæ and the flocculi? Why do the Fraunhofer lines show little evidence of high atmospheric pressure? Why are the radiations from calcium, one of the heavy elements, so prominent in the higher chromospheric strata and in the prominences? A great number of such questions are pressing for solution. Under the stimulus of the brilliant researches of our chairman, the reinventor and the leading developer of the spectroheliograph, cooperative plans for solar work on a large scale are now being organized. We should be vitally interested in promoting these plans; for the study of the sun, as the principal foundation of astrophysical research, has been unduly neglected.
The celestial bodies develop under conditions over which we have no control. We must observe the facts as they are, at long range, and interpret them in accordance with those principles of physical science which govern what seem to be closely related terrestrial phenomena. A successful study of the development of matter in distant space, under the influence of heat, pressure, electricity and other forces of nature demands a complete understanding of the action of the same forces upon terrestrial matter. The astrophysicist dwells in the laboratory as well as in the observatory; and laboratory researches must supply the links which connect world life and star life.
It has not been possible for laboratory investigators to reproduce stellar phenomena on a scale approaching that occurring in nature, nor to duplicate conditions of temperature and pressure existing within the stars; and these are unfortunate limitations. Nevertheless, many successes have been achieved in this direction. The low-temperature triumphs of Dewar, Olczewski and others approximate to the conditions of space surrounding the stars. The electric arc and spark appear to reproduce the temperatures of many stellar chromospheres and reversing layers. The electric furnace of Moissan seems to supply temperatures comparable with those of the photosphere, and it promises to throw light upon the processes of cloud formation in the stars. Investigations as to the influence of varying pressures—from almost perfect vacua up to many atmospheres—as to the effects of varying electrical conditions and of other factors have answered many celestial questions, and introduced others equally pressing.
Laboratory observations have established that the spectra of the elements are not the same under all circumstances. We formerly thought it remarkable that nitrogen should have two or three characteristic spectra, or that a metal should have a spark spectrum and an arc spectrum. We are now confronted with the potent fact that an element may have a variety of spectra, depending upon the nature and the intensity of the forces employed in rendering it luminous. But for most cases these involve only moderate variations in the relative intensities of spectral lines. The complications which threaten to result therefrom are more apparent than real. The multiplicity of spectral reactions promises to be a powerful aid to analysis, by supplying a more exact key to the conditions in the celestial light source which produce the observed effects.
For many years following the application of the spectroscope to celestial problems it was supposed that a continuous spectrum must indicate incandescent solid or liquid, matter. The situation is not so simple as this. Some gases radiating under high pressures give spectra apparently continuous.
The effect of increasing temperature conditions on certain spectra has long been well known. Certain lines are enhanced in relative brilliancy when we pass from the temperature of the arc to that of the high-tension spark, and vice versa; but it seems certain that, within measurable limits, the positions of the lines do not change under this influence.
Humphreys and Mohler have proved that the spectral lines are shifted by pressure;—toward the red with increasing pressure in the atmosphere the arc. It is not difficult to see the bearing of this discovery upon astrophysical inquiry. Some subjects are made more complex; but the hope is held out that eventually we may detect these indications of pressure, differentially, in the brighter stars.
It is also known that the spectra of some elements are altered by the presence of other elements, but the extent and character of the induced changes are little understood. As the chemical elements are never found alone in celestial bodies, the serious consequences of this effect must be evident.
The temperature in glowing Plücker tubes is of great interest, from its bearing upon the probable temperatures of nebulæ, the auroræ and other bright-line phenomena of a diffuse nature. It is not certain that direct observation by any thermometric device can deal with the problem. The measures thus far attempted have assigned temperatures but a few degrees higher than that of the environment. These indications are probably correct for the average temperature of the contents of the tube, but hardly so for those molecules which are glowing. It has been suggested that perhaps a very small proportion of the molecules receive and carry the discharge; that while the molecules in action may be very hot, the average for all in the tube is very low. It seems reasonable to suppose, also, that the low-temperature indication is due to the fact that the current is actually passing but a small fraction of the time. The effect upon the eye is that of a continuous glow, whereas the thermometer measures the average effect.
The influence of a magnetic field upon the character of spectral lines, established in the laboratory by Zeeman, has not yet been observed in celestial spectra, but its detection may be merely a question of the dispersive power available on faint spectra.
It will be perceived that the interpretation of celestial spectra must be made with circumspection. We are not always justified in reaching conclusions upon the spectroscopic evidence alone; general conditions must also be taken into account. For example, shall we say that the temperature of the gaseous nebulæ is very high, because they have bright-line spectra? On the contrary, the difficulty of maintaining a high temperature in a mass so attenuated should be given at least equal weight. The radiating molecules or particles may for the instant be quite hot, but the effective temperature of the whole nebula is probably low.
The experimental verification of radiation pressure by Lebedew, and by Nichols and Hull, is far-reaching in its consequences. We must take this force into account, as truly and as constantly as we must consider gravitation. Radiation pressure requires us to reconstruct our theories of comets' tails, of the corona, of the zodiacal light, of the auroræ,—in fact of every phenomenon of nature involving minute particles. And what celestial object does not involve them?
On the other hand, the student of the stars has pointed the way for the laboratory investigator, in many instances. The ultra-violet hydrogen series was photographed by Huggins, in the spectrum of Vega, before it was found in the laboratory; and Pickering has discovered another hydrogen series, in Zeta Puppis, which still awaits terrestrial duplication. The hypothetical element, helium, in the sun, waited a quarter-century for Ramsay's discovery, and the laboratory investigation of its more complete spectrum which followed. Students of the solar corona and of the gaseous nebulæ are discussing the properties of the hypothetical elements coronium and nebulium almost as familiarly as if they had actually handled them. Out of some 20,000 absorption lines mapped by Rowland, more than the half are awaiting laboratory identification.
In this connection, the mathematical relations existing between the positions of lines in the spectra of many of the principal elements, discovered by Balmer, Kayser, Runge and Paschen, have already been of great utility; and they can scarcely fail to illuminate the question of the construction of the atoms involved.
A new era of physical science was inaugurated about eight years ago by the discovery of argon on the one hand, and of the X-rays on the other. The former was followed by the discovery, in quick succession, of several other constituents of the earth's atmosphere which at present demand our attention as to their presence in chromospheric and auroral phenomena. It would be most surprising if the many forms of radiation, including those of the radio-active substances, discovered in the train of the X-rays, should not throw strong light upon the constitution of matter. And how shall we deal intelligently with the forms of matter in other worlds before we understand the constitution of matter upon the earth? The modern theory of electrons, in which material atoms play the subordinate part, and electric charges the principal part, promises to have a wide application to celestial phenomena. Further, the actual transport and interchange of matter in the form of small particles, from one star to another, as urged with great learning and skill by Arrhenius, seems to be a plain and unavoidable consequence of recently established physical facts. Should this theory stand the test of time, its far-reaching consequences would accord it a position of the first rank.
The photographic program inaugurated with the Crossley Reflector by Keeler comprised 104 negatives of the regions containing the principal nebulæ and star clusters. These photographs, covering but one six-hundredth part of the entire sky, record 850 nebulæ, of which 746 are new. If this proportion should hold good over the whole sphere, the number discoverable with this instrument, with exposures of ordinary length, would be half a million. This estimate would be too large, in case the smaller nebulæ have a tendency to cluster around the prominent nebulæ, which to some extent is probably true. The number of stars visible in our great telescopes is of the order of one hundred millions. The dark or invisible bodies indicated by several considerations—the planets in the solar system, the spectroscopic binaries, the eclipsing variable stars, and the gravitational power of the universe—should outnumber the bright ones several fold. It is the thesis of astrophysics that all these objects—the nebulæ, the bright stars and the invisible bodies—are related products of a system of sidereal evolution. The general course of the evolutionary process, as applied to the principal classes of celestial objects, is already known. We are able to group these classes, with little chance of serious error, in the order of their effective ages.
The earliest form of material life known to us is that of the gaseous nebulæ. In accordance with the simplest of physical laws, a nebula must radiate its heat to surrounding space. In accordance with another law, equally simple, it must contract in volume—toward a center, or toward several nuclei—and generate additional heat in the process. Eventually a form of considerable regularity will result. Whether this form is that of a typical planetary nebula, of a spiral nebula, or of some other type, is a matter of detail. It is quite possible that nature uses several molds in shaping the contracting masses, according as they lie on one side or the other of critical conditions. The variety of existing forms is extensive. One can see very little resemblance in the Trifid Nebula, which is apparently breaking up into irregular masses; the Dumb Bell Nebula, from whose nearly circular form rings of matter seem to be separating; the great spiral nebulæ; the Ring Nebula in Lyra, with a central star; the compact planetary nebula G. C. 4390, containing a dense, well-defined nucleus; and many others of distinct types.
The condensed globular forms occupying the positions of nebular nuclei have almost reached the first stage of stellar life.
It is not difficult to select a long list of well-known stars which can not be far removed from nebular conditions. These are the stars containing both the Huggins and the Pickering series of bright hydrogen lines, the bright lines of helium, and a few others not yet identified. Gamma Argus and Zeta Puppis are of this class. Another is DM. + 30.° 3639, which is actually surrounded with a spherical atmosphere of hydrogen, some five seconds of arc in diameter. A little further removed from the nebular state are the stars containing both bright and dark hydrogen lines;—caught, so to speak, in the act of changing from bright-line to dark-line stars. Gamma Cassiopeiae, Pleione and Mu Centauri are examples. Closely related to the foregoing are the helium stars. Their absorption lines include the Huggins hydrogen series complete, a score or more of the conspicuous helium lines, frequently a few of the Pickering hydrogen series, and usually some inconspicuous metallic lines. Calcium absorption is absent, or scarcely noticeable. The white stars in Orion and the Pleiades are typical of this age.
The causes which produce bright lines in stars are not thoroughly understood; but atmospheres of higher temperatures than their underlying strata, or very extensive simple atmospheres, seem to be demanded. The former condition, on the large scale required, involves some difficulties, and mildly suggests the possibility that external influences may be acting upon the radiating strata of bright-line stars.
The assignment of the foregoing types to an early place in stellar life was first made upon the evidence of the spectroscope. The photographic discovery of nebulous masses in the regions of a large proportion of the bright-line and helium stars affords extremely strong confirmation of their youth. Who that has seen the nebulous background of Orion, or the remnants of nebulosity in which the individual stars of the Pleiades are immersed, can doubt that the stars in these groups are of recent formation?
With the lapse of time, stellar heat radiates into space; and, so far as the individual star is concerned, is lost. On the other hand, the force of gravity in the surface strata increases. The inevitable contraction in volume is accompanied by increasing average temperature. Changes in the spectrum are the necessary consequence. The second hydrogen series vanishes, the ordinary hydrogen absorption is intensified, the helium lines become indistinct, and calcium and iron absorptions begin to assert themselves. Vega and Sirius are conspicuous examples of this period. Increasing age gradually robs the hydrogen lines of their importance, the H and K lines broaden, the metallic lines develop, the bluish-white color fades in the direction of the yellow, and, after passing through types exemplified by many well-known stars, the solar stage is reached. The reversing layer in solar stars represents but four or five hydrogen absorption lines of moderate intensity; the calcium lines are commandingly prominent; and some 20,000 metallic lines are observable. The solar type seems to lie near the summit of stellar life. The average temperature of the mass must be nearly a maximum, for the low density indicates a constitution that is still gaseous.
Passing time brings a lowering of average temperature. The color passes from yellow to the red, in consequence of lower radiating temperatures and increasing general absorption by the atmosphere. The hydrogen lines become indistinct, metallic absorption remains prominent, and broad absorption bands are introduced. In one type, of which Alpha Herculis is an example, these bands are of unknown origin; in another, illustrated by 19 Piscium, they have been definitely identified as of carbon origin. The relation between the two types is not clear. It has even been advocated that the evolutionary process divides shortly after passing the solar stage; that the reddish stars with absorption bands sharply terminated on the violet edges are on one branch, and that the very red stars with absorption bands sharply defined on the red edges are on the other branch. This plan of overcoming a difficulty seems to me to introduce a greater difficulty; and I do not doubt that systematic investigation will supply the connections now missing. That the denser edges of the bands in Type IV (Secchi) should occupy the same positions as the denser edges of absorption bands in Type III, can hardly be without significance; and Keeler's view that the carbon absorption bands in Type IV are matched by carbon radiation in some stars, at least, of Type III suggests a most promising line of investigation for powerful instruments.
There is scarcely room for doubt that these types of stars are approaching the last stages of stellar development. Surface temperatures have lowered to the point of permitting more complex chemical combinations than those in the sun. The development of 'sun spots' on a large scale is quite probable, and the first struggles to form a crust may be enacted. Type III includes the several hundred longperiod variable stars of the Omicron Ceti class, whose spectra at maximum brilliancy show several bright lines of hydrogen and other elements. The hot gases and vapors seem to be alternately imprisoned and released. It is significant that the dull red stars are all very faint;—there are none brighter than the 51⁄2 magnitude. Their effective radiating power is undoubtedly very low.
The period of development succeeding the red-star age of Type IV has illustrations near at hand, in the planets Jupiter and the earth; invisible save by borrowed light. When the interior heat of a body shall have become impotent, the future promises nothing save the slow leveling influence of its own gravitation and meteorological elements. It is true that a collision may occur to transform a dark body's energy of motion into heat, sufficient to convert it into a glowing nebula, and start it once more over the long path of evolution. This is a beautiful theory, but the facts of observation do not give it satisfactory support. There is little doubt that the principal novas of recent years have been the results of collisions, either between two massive dark bodies, or between a massive body and an invisible nebula. The suddenness with which intense brilliancy is generated would seem to call for the former, but the latter is much more probable, in view of many facts. The nebular spectra of the novas are generated in a few months; but in every case thus far observed the bright nebular bands grow faint very rapidly, and in the course of a few years leave a continuous spectrum, apparently that of an ordinary star. Either the masses involved in the phenomena are extremely small, or the disturbances are but skin-deep. In any case, the novas afford little evidence as to the complete re-nebularization of dark bodies.
I spoke of the average temperature of a developing star as reaching a maximum near the solar stage, when the border-line between gaseous and liquid constitution is reached. This refers to the entire mass. The law of surface temperatures is quite a different one. The bright-line and helium stars seem to have hotter surfaces than the solar and red stars. The spectra which we observe are surface phenomena which indicate the temperatures of the radiating and absorbing strata. The maximum intensity of continuous radiations is higher up in the spectrum for the white stars than for the yellow and red, a safe indication of higher temperatures. The lines in white-star spectra are distinctly the enhanced lines thought to be produced by high temperatures. These facts are not inharmonious. Surface temperature is a function of the rapidity with which convection currents can carry heat from the interior to the surface. The comparatively low internal heat of white stars, delivered quickly at the surface by rapidly moving gases, may readily maintain higher atmospheric temperatures than the much hotter interiors of solar stars, whose circulation has the sluggishness of viscosity.
Sir William and Lady Huggins are inclined to assign greater importance to mass and density, as factors in evolution, than to temperatures. Their view is that under the influence of great surface gravity, the generation and radiation of heat is accelerated, and the life of the star is lived more rapidly. They have been led to this view, in part, by the apparent anomaly of double stars, in which the more massive primary is generally yellower than the less massive companion. The subject is one of great difficulty and importance, and, unfortunately, laboratory methods are on too small a scale of mass and pressure to solve the problem.
Up to the year 1800 only twelve variable stars were known. Chandler's catalogue dated 1888 contains 225 entries. The remarkable progress made by astronomical science in the past fifteen years is fairly indicated by the fact that in this interval the number of known variable stars increased from 225 to more than 1400. To Harvard College Observatory belongs the great credit of discovering nearly 900 of these objects.
In many respects variable stars constitute the most interesting class of objects in the heavens. The tens of millions of ordinary stars are undoubtedly growing older; and the tens of thousands of nebulas, from which stars will eventually be formed by processes of condensation, are undergoing transformation; but appreciable changes in the ordinary stars and in the nebulas proceed with extreme deliberation, and no permanent changes have yet been noted. Variable stars, on the contrary, are changing before our eyes; and they repeat their fluctuations continually. They present opportunities for discoveries of the greatest interest in themselves, and of remarkable utility in the study of the problem of stellar evolution.
It is a conservative statement that in nineteen variable stars out of twenty we have little idea as to the causes of variability. The causes of the variations have been determined in the case of Algol and a few others of that class: large dark companions revolve around these stars, and once in every revolution the companions pass between us and the principal stars, thus preventing a portion of their light from reaching us. In Zeta Geminorum and three or four others of its class the spectroscope has shown that massive dark companions are close to, and rapidly revolving around, the principal stars. These invisible companions produce disturbances in the extensive atmospheres of the stars, and cause the observed variations in brightness; but the nature of the disturbances is still a matter of conjecture. Omicron Ceti and other stars of its class have given no evidence of companions. Brightness variations in them seem to be due to internal causes. Perhaps they have reached the age when solid crusts attempt to form on their surfaces, just as one day a crust struggled to form on the liquid earth. A crust formed one month may be melted or sink to a lower level a few months later. Perhaps there are 'sun-spots' on these stars, in scale vastly more extensive and in period shorter than those on our sun; but these suggested explanations may be far from the truth.
For more than half a century a great many astronomers have devoted themselves assiduously to making photometric observations of variable stars. There are a dozen observatories, both large and small, which are systematically devoting some of their resources to this work. By common consent of the profession, or by appointment from learned societies, there have for some fifty years been individual astronomers, or committees of astronomers, who systematize results, call attention to the need for observations of certain neglected objects, and in many other ways encourage the photometric study of variable stars. Photometers are inexpensive, the methods are simple, and results have rapidly accumulated.
Observations of variable stars with slit-spectrographs, on the contrary, are surprisingly meager and fragmentary. Not a single institution, not a single telescope, not a single observer, is working continuously or even extensively on the subject. Yet the method is a very powerful one: the few isolated studies made on variable stars have led to results of remarkable richness. The subject is one of great difficulty. Photographic spectra require much time for accurate measurement and reduction. And, finally, powerful and expensive instruments are demanded.
Harvard College Observatory has been remarkably successful in discovering variable stars by means of peculiarities in their spectra, as well as in classifying them, and in qualitative studies of many spectral details, using objective-prism spectrographs; but it is hoped that slit spectrographs, attached to powerful telescopes, may soon be devoted systematically to this subject, as it constitutes one of the richest fields now awaiting development.
A century and a half of meridian-circle observations has given to the world, as one of many priceless contributions, a knowledge of the proper motions of several thousand stars. Some of the ablest astronomers have used these results as a basis for determining the most probable elements of the sun's motion, and in studies upon the distribution of the stars in space. Unfortunately, these investigations necessarily involve assumptions as to the unknown distances of the stars.
A few years following the application of the spectroscope to the study of celestial objects, Huggins recognized that the Doppler-Fizeau principle supplied, in theory at least, the long hoped-for method of measuring the components of stellar motions in the line of sight—their radial velocities; and that the application of this method would enable us to determine both the direction and the speed of the solar motion, entirely independently of the distances of the stars. Efforts to apply this method met with signal failure for twenty years, and doubts even as to ultimate success were quite generally felt and freely expressed. The beginnings of success were made by Huggins and Pickering, in showing that photography reveals, with great clearness, the delicate spectral lines which the eye in purely visual observations is unable to see at all. In 1888, Vogel applied this knowledge in the first photographic attempt to measure radial velocities, and his work inaugurated a new era. His observations, obtained with a small telescope and imperfect spectrograph, were not sufficiently accurate to meet the needs of the principal sidereal problems, but they led to several brilliant discoveries at Potsdam, and were invaluable in marking out the path of progress. It was not until 1896 that the use of a powerful telescope, equipped with an efficient spectrograph, gave results accurate enough to satisfy present requirements. In fact, the accuracy obtained exceeded our most hopeful expectations.
It is not surprising that thirty years were required to develop successful methods. The work is so delicate that, unless suitable precautions are taken at every point in the process, the errors introduced may readily be larger than the quantities sought for. With the Mills spectrograph, for example, a speed of nine kilometers per second displaces the lines only 0.01 mm. The probable error of a velocity determination for the best stars, such as Polaris, is but one fourth of a kilometer per second, corresponding to a linear displacement of 0.0003 mm., or 0.00001 inch. In view of the newness of the subject, the richness of the field, and the fact that the more active great telescopes are now nearly all applied to this work, I append a list of the improvements which have contributed most powerfully to recent progress:
1. A realization of the fact that a spectrograph is an instrument complete in itself. The telescope to which it is attached serves only to collect the light and to deliver it properly upon the slit.
2. The development of a method of reduction which permits the use of all good stellar lines, irrespective of whether they correspond to, or lie between, the comparison lines.
3. The use of a longer collimator, permitting a wider slit, and requiring larger prisms, with greater resolving power.
4. The use of simple prisms, of better glass, with better optical surfaces.
5. Care in collimating, to insure that the star light and comparison light traverse identically the same part of the collimator lens.
6. The adoption of a compact and rigid form of spectrograph mounting, designed in accordance with good engineering practise.
7. The elimination of flexure effects by supporting the spectrograph, in connection with the telescope, in accordance with engineering principles. The conventional spectrograph had been supported entirely at its extreme upper end; the instrument projected out into space, unsupported, boldly inviting flexure under the varying component of gravity.
8. The use of a constant temperature case around the instrument.
9. Precautions taken to eliminate many sources of error from the measures of the spectrograms.
Up to December, 1900—the last month of the departing century—the speeds of 325 stars had been determined with the Mills Spectrograph in the northern two thirds of the sky. Omitting several stars whose lines could not be measured accurately, and some thirty spectrograph and visual binaries for whose centers of mass the velocities were still unknown, 280 stars remained available for deducing the relative motion of our solar system. The observational data were distributed symmetrically in right ascension, and the result for this coordinate of the apex agreed with Newcomb's proper-motion result within a small fraction of a minute of arc. The data were extremely unsymmetrical in declination, as there were few observations between −15° and −30° declination, and none whatever south of −30°. The solution placed the apex 15° south of Newcomb's position. The deduced speed, 20 km. per second, is no doubt close to its true value.
There is a question whether the direction of the solar motion can be determined more accurately from proper motions or from radial velocities, an equal number of stars being available in the two cases; but as to the speed, no doubt of the very marked superiority of the spectrographic method can exist. This, however, is but incidental, for the two methods are in fact mutually helpful and mutually dependent: the motion of every star involves both components.
In this connection two points call for appreciation: First, the motion of the solar system is a purely relative quantity. It refers to the group of stars used in the solution. We could easily select twenty or thirty of these stars whose velocities were such that the deduced motion would be reversed 180° from that given by the entire list of stars. We want to know the solar motion with reference to the entire sidereal system. A satisfactory solution of the problem demands that we use enough stars to be considered as representative of the whole system. Second, the great sidereal problems require that observational data for their solution should cover the whole sky. Until one year ago radial velocity measures were confined to the northern two thirds of the celestial sphere. Further attempts to deduce the solar motion from northern observation alone would not be justified. Observations in the southern third of the sky were needed, not only to represent that large region in the solution, but in order that the unknown systematic errors which affect the northern observations, as well as the southern, might be eliminated, through the symmetrical balancing of the material. Fortunately the energetic and wise policy of the Cape Observatory and the generosity of Mr. D. O. Mills have provided two complete equipments, which are now busily engaged in supplying the southern data required. The Mills spectrograph in the northern hemisphere has secured about three thousand spectrograms of approximately five hundred stars, and the Mills spectrograph in the southern hemisphere has secured four hundred spectrograms of one hundred and twenty-five stars. The number of stars not on the Mills list, and accurately observed with other high-dispersion spectrographs, is not known, but it is probably between one hundred and two hundred. We may reasonably expect that, in two or three years, as many as eight hundred well-determined radial velocities may be brought to bear upon pressing sidereal problems.
It is a frequent question: Is the solar system moving in a simple orbit, and will it eventually return to the part of its orbit where it is now? The idea of an affirmative answer to this question is very prevalent in the human mind. It is natural to think that we must be moving on a great curve, perhaps closed like an ellipse, or open like a parabola, the center of mass of the universe being at the curve's principal focus. The attraction which any individual star is exerting upon us is certainly very slight, owing to its enormous distance; and the combined attractions of all the stars may not be very much greater; for since we are somewhere near the center of our stellar system, the attractions of the stars in the various directions should nearly neutralize one another. Even though we may be following a definite curve at the present time, there is, in my opinion, little doubt that we should be prevented from continuing upon it indefinitely. In the course of our travels we should be carried, sooner or later, quite close to some individual star whose attraction would be vastly more powerful than that of all the other stars combined. This would draw us from our present curve and cause us to follow a different one. At a later date, our travels would carry us into the sphere of attraction of some other great sun which would send us away in a still different direction. Thus our path should in time be made up of a succession of unrelated curves.
Spectroscopic binary systems, as by-products of radial velocity measurements, are of exceedingly great interest, from the light which they cast upon the construction of other systems than ours. When we look at the sky on a clear night, we may be sure that at least one star in six or seven is attended by an invisible companion, comparable in mass with the primary body, the two revolving around their common center in periods varying from two or three days in many cases, up to three or more years in others. For the triple system of Polaris the long period perhaps exceeds fifteen or twenty years. As the shortest-period visual binary now known, that of δ Equulei, is only 5.8 years, the gap between visual and spectroscopic binaries has been definitely closed.
The companions of binaries discovered by means of the spectrograph have not been observed visually in our powerful telescopes, although they have been carefully searched for. They may be so close to the principal star that, viewed from our distance, the two images can not be resolved. The separation of the components is probably less than one hundredth of a second of arc for most of the binaries thus far announced. Again, for very few of the systems are the spectra of both components recorded. This does not establish that the companion is a dark body, but only that it is at least one or two photographic magnitudes fainter than the primary. The fourth-magnitude companion of a second-magnitude star would scarcely be able to impress its lines upon the primary's spectrum. The invisible components in many spectroscopic binaries might be conspicuous stars, if they stood alone.
Only those systems have been detected whose periods are relatively short, and for which the variations of radial speed are considerable. The smallest observed variation is that of Polaris—six kilometers per second. Had the variation for Polaris been only one kilometer, it would no doubt have escaped detection. Such a variation could be measured by present instruments and methods; but this range would not have excited the observer's suspicion, and the discovery would have remained for the future. It is probable that there are more systems with variations of speed under six kilometers than there are with larger ones; and all such are awaiting discovery. The velocity of our sun through space varies slightly, because it is attended by companions—very minute ones compared with the invisible bodies discovered in spectroscopic binaries. It is revolving around the center of mass of itself and its planets and their moons. Its orbit around this center is small, and the orbital speed very slight. The total range of speed is but three one hundredths of a kilometer per second. An observer favorably situated in another system, provided with instruments enabling him to measure speeds with absolute accuracy, could detect this variation, and in time say that our sun is attended by planets. At present, terrestrial observers have not the power to measure such minute variations. As the accuracy attainable improves with experience, the proportional number of spectroscopic binaries discovered will undoubtedly be enormously increased. In fact, the star which seems not to be attended by dark companions may be the rare exception. There is the further possibility that the stars attended by massive companions, rather than by small planets, are in a decided majority; suggesting, at least, that our solar system may prove to be an extreme type of system, rather than a common or average type.
Observations of stellar motions in the line of sight enable us to solve many other important auxiliary problems. Only one will be referred to here. The determination of stellar distances is exceedingly important, and correspondingly difficult. We know the fairly accurate distances of a dozen stars, and the roughly approximate distances of two or three dozen others. Radial velocity observations, in combination with proper motions, will enable us to determine the average distances of entire classes of stars. Let us consider the stars of the fifth magnitude, of which there are a thousand or more. They travel in practically all directions. A definite relation will exist between their average proper motion and their average radial motion, within a small limit of error. If meridian observations ascertain that the average annual proper motion of these fifth-magnitude stars is 0.03 seconds of arc, and spectrographic observations determine that their average speed in the line of sight is thirty-five kilometers per second, it is a simple matter to compute what their average distance must be in order to harmonize the two components.
A study of 280 observed stars as to the relation existing between visual magnitude and velocity in space led to interesting results. The average speed of 47 stars brighter than the third magnitude is 26 km.; of 112 stars between the third and fourth magnitude, 32 km.; and of 121 stars fainter than the fourth magnitude, 39 km. The progression in these results is very pronounced, and I think we are justified in drawing the important conclusion that, on the average, the faint stars of the system are moving more rapidly than the bright stars. This interesting indication should be confirmed or disproved by the use of a much greater number of stars.
The proper method of combining radial velocities for statistical purposes is a question of great importance. The method of least-squares is based upon the assumption that the accidental errors of observation follow a certain law, found by experience to be substantially true. This method is not applicable to the combination of radial velocities, unless radial velocities are distributed in accordance with the law of accidental errors. Do stellar velocities whose values are near zero exist in greatest numbers? Or does some moderate speed predominate? The average speed in space of the 280 stars observed spectrographically is 34 km. When a much greater number of radial velocities is available, the law of distribution must be investigated, and a safe method of combination be developed.
Other practical questions exist as to the proper weights to assign to results of different degrees of accuracy, when it is desired to combine them statistically. The speeds of the brighter second-and third-type stars can be determined well within a kilometer per second, whereas the speeds of first-type stars, containing only broad and hazy lines, may be in error from five to fifteen kilometers. Again, low dispersion spectrography is developing so rapidly that in a few years the speeds of hundreds of the fainter stars will be known within two kilometers. Shall the weights assigned to individual results be proportional to the inverse squares of their probable errors? I think not. The deduced solar motion, for example, should refer to an observed program of stars which shall be representative of the entire sidereal system. It must refer to a star with hazy lines, or to a faint star, as truly as to a bright solar-type star. One poorly determined result for velocity, used alone, should have small weight, but a large number of such determinations should be given considerable weight; proper care being taken to avoid systematic error. Prudence would suggest that separate solutions be made, first for the stars whose spectra admit of accurate measurement, and later for those whose spectra contain hazy lines, or which have been observed with low dispersion. From these a guide as to the relative weights to be assigned to the three or more classes of stars in combination may be found.
Redial velocity observers are concerned as to the part played in the results by pressure in the reversing layers of the stars. The differential effects of pressure are too small to detect in stellar spectra by present means, and there is no known method of eliminating them. We have no recourse but to assume that the stellar lines, neglecting the effect of radial motion, are in identically the same position as the solar lines and the laboratory lines of the elements. Whether the lines in the blue stars are produced under lower pressure than those in the sun, and the lines in the red stars under greater pressure than those in the sun, remains unknown, but this is not impossible. The effect of systematic errors in observed speeds from this source, as well as from other sources, would be eliminated from many statistical inquiries by having all parts of the sky represented in the solution.
Errors in the tables of absolute wave-lengths do not enter into radial-velocity results, provided the relative values are correct. In fact we scarcely need to know the wave-lengths at all, for the determinations of velocity may be put upon a strictly differential basis, and I incline strongly to the belief that this should be done. Let us consider the case very briefly. Rowland's wave-lengths are based upon spectrograms taken with high dispersion and resolving power. Radial-velocity spectrograms are secured with instruments of much lower power. Close solar and laboratory lines, of different intensities, clearly separated on Rowland's plates, are blended on stellar plates. For this and other reasons, the effective wave-lengths on the two classes of plates are different. The difficulty of assigning correct wave-lengths in the case of plates taken with a single-prism spectrograph is even greater: whole groups of separate lines are blended into one apparent line, and lines actually single are very few indeed. It is necessary to use blends, both in the stellar and comparison spectra. Two methods at least are available to eliminate errors in velocity due to errors in assumed wave-lengths. First: At the conclusion of a long series of observations of stars of the same spectral type, the velocity yielded by each line for each star should be tabulated. If one line gives velocities consistently large or consistently small, the conclusion is that its effective wave-length has been wrongly assumed, and we should be justified in changing it arbitrarily. And so on, for each line employed. This involves the assumption that the comparison bright-lines and the corresponding stellar lines have the same wave-lengths; and all the wave-lengths are reduced to one system, true for the particular spectrograph employed. The method is not entirely free from objection. Second: If the solar spectrum and the comparison spectra are photographed on one and the same plate, under precisely the usual observing conditions, measures of this plate, corrected for the observer's very slight radial velocity with reference to the sun, will form a reduction curve of zero velocity, expressed in terms of micrometer readings. If a spectrogram of star and comparison, made with the same instrument and measured in the same manner, is compared with this reduction curve, measure for measure, the speed of the star will be obtained directly, and irrespective of wave-length values; and many other fruitful sources of systematic error will be eliminated at the same time. Mr. R. H. Curtiss, of Mount Hamilton, formulated a method on this basis last year, and he has applied it to a specroscopic-binary variable star. The observations were made with a spectrograph whose dispersion is but one fifth, and whose exposure time for a given star is but one tenth that of the Mills spectrograph. The probable error for a faint star seems to be not more than twice as great as that for a bright star with the Mills spectrograph. The method promises to be of great utility, capable of application to several thousand stars between the fifth and eighth magnitudes.
On account of the large proportion of spectroscopic binaries, stars should not be used statistically until observations covering several years have established the constancy of their motions. To determine the orbits and the speeds of the centers of mass of the binary systems, from twenty-five or more spectrograms each, is a task several fold more extensive than that of measuring the constant speeds of the non-binary stars.
There remains the question of cooperation, on the part of radial-velocity observers, to avoid useless duplication, and to increase the output of results. Seven leading observatories in the northern hemisphere, and one in the southern, are in this field, presumably with the intention of remaining indefinitely. A second observatory in the southern hemisphere, devoted exclusively to this work, is of an expeditionary character, and its long continuance is problematical. It is fair to the participating observatories to say, judging by results thus far published, that some are still in the period of experiment and development; and, in fact, that all observers are introducing frequent improvements, which lead to greater accuracy. As long as the development of instruments and methods is in rapid progress, formal cooperation is unwise. Premature cooperation leads to confusion. Duplication of observations for the principal stars is as valuable and desirable in radial-velocity measurements as in meridian determinations of stellar positions. But just as soon as the methods assume a reasonably stable form, the entire sky should be apportioned amongst the interested observatories, in accordance with carefully considered plans which shall permit and encourage individual initiative. I have little doubt that this point will be reached, by a sufficient number of observatories, within two years, and that it would be well to conclude the preliminary organization of cooperative plans within the coming year. Such plans should be formed with severe deliberation, as the labor involved would be commensurate with that devoted to the construction of the Astronomische Gesellschaft Zones for the entire sky.
The problems immediately confronting the astrophysicists of the twentieth century are serious ones. They call for our best efforts. The volume of work demanded is stupendous, and the difficulties to be overcome are correspondingly great. Nevertheless, the men and the means will be forthcoming. The mass of solid fact brought within the realm of knowledge by astronomers now living, many of whom are happily with us this week, is sufficient indication that the general solution of the problems of to-day is but a question of time. And we should be equally hopeful as to the problems of the future, for the desire to know the truth about the universe which surrounds us is an enduring element in human nature.
- Delivered at the St. Louis International Congress of Arts and Science.