In Fig. 127 the bright star does not fall anywhere near the focus of the ellipse marked out by the smaller one, and from this we infer that the figure does not show the true shape of the orbit, which is certainly distorted, foreshortened, by the fact that we look obliquely down upon its plane. It is possible, however, by mathematical a.n.a.lysis, to find just how much and in what direction that plane should be turned in order to bring the focus of the ellipse up to the position of the princ.i.p.al star, and thus give the true shape and size of the orbit. See Fig. 128 for a case in which the true orbit is turned exactly edgewise toward the earth, and the small star, which really moves in an ellipse like that shown in the figure, appears to oscillate to and fro along a straight line drawn through the princ.i.p.al star, as shown at the left of the figure.

In the case of a Centauri the true orbit proves to have a major axis 47 times, and a minor axis 40 times, as great as the distance of the earth from the sun. The orbit, in fact, is intermediate in size between the orbits of Ura.n.u.s and Neptune, and the periodic time of the star in this...o...b..t is 81 years, a little less than the period of Ura.n.u.s.

[Ill.u.s.tration: FIG. 128.--Apparent orbit and real orbit of the double star 42 Comae Berenicis.--SEE.]

200. Ma.s.sES OF DOUBLE STARS.--If we apply to this...o...b..t Kepler's Third Law in the form given it at page 179, we shall find--

a^3 / T^2 = (23.5)^3 / (81)^2 = k (M + m),

where _M_ and _m_ represent the ma.s.ses of the two stars. We have already seen that _k_, the gravitation constant, is equal to 1 when the ma.s.ses are measured in terms of the sun's ma.s.s taken as unity, and when _T_ and _a_ are expressed in years and radii of the earth's...o...b..t respectively, and with this value of _k_ we may readily find from the above equation, _M_ + _m_ = 2.5--i. e., the combined ma.s.s of the two components of a Centauri is equal to rather more than twice the ma.s.s of the sun. It is not every double star to which this process of weighing can be applied.

The major axis of the orbit, _a_, is found from the observations in angular measure, 35" in this case, and it is only when the parallax of the star is known that this can be converted into the required linear units, radii of the earth's...o...b..t, by dividing the angular major axis by the parallax; 47 = 35" 0.75".

Our list of distances (-- 189) contains four double stars whose periodic times and major axes have been fairly well determined, and we find in the accompanying table the information which they give about the ma.s.ses of double stars and the size of the orbits in which they move:

---------------------+-------+-------+----------+------- STAR.

Major

Minor

Periodic

Ma.s.s.

axis.

axis.

time.

---------------------+-------+-------+----------+------- a Centauri

47

40

81 y.

2 70 Ophiuchi

56

48

88

3 Procyon

34

31

40

3 Sirius

43

34

52

4 ---------------------+-------+-------+----------+-------

The orbit of Ura.n.u.s, diameter = 38, and Neptune, diameter = 60, are of much the same size as these double-star orbits; but the planetary orbits are nearly circular, while in every case the double stars show a substantial difference between the long and short diameters of their orbits. This is a characteristic feature of most double-star orbits, and seems to stand in some relation to their periodic times, for, on the average, the longer the time required by a star to make its...o...b..tal revolution the more eccentric is its...o...b..t likely to prove.

Another element of the orbits of double stars, which stands in even closer relation to the periodic time, is the major axis; the smaller the long diameter of the orbit the more rapid is the motion and the shorter the periodic time, so that astronomers in search of interesting double-star orbits devote themselves by preference to those stars whose distance apart is so small that they can barely be distinguished one from the other in the telescope.

Although the half-dozen stars contained in the table all have orbits of much the same size and with much the same periodic time as those in which Ura.n.u.s and Neptune move, this is by no means true of all the double stars, many of which have periods running up into the hundreds if not thousands of years, while a few complete their orbital revolutions in periods comparable with, or even shorter than, that of Jupiter.

201. DARK STARS.--Procyon, the next to the last star of the preceding table, calls for some special mention, as the determination of its ma.s.s and orbit stands upon a rather different basis from that of the other stars. More than half a century ago it was discovered that its proper motion was not straight and uniform after the fashion of ordinary stars, but presented a series of loops like those marked out by a bright point on the rim of a swiftly running bicycle wheel. The hub may move straight forward with uniform velocity, but the point near the tire goes up and down, and, while sharing in the forward motion of the hub, runs sometimes ahead of it, sometimes behind, and such seemed to be the motion of Procyon and of Sirius as well. Bessel, who discovered it, did not hesitate to apply the laws of motion, and to affirm that this visible change of the star's motion pointed to the presence of an unseen companion, which produced upon the motions of Sirius and Procyon just such effects as the visible companions produce in the motions of double stars. A new kind of star, dark instead of bright, was added to the astronomer's domain, and its discoverer boldly suggested the possible existence of many more. "That countless stars are visible is clearly no argument against the existence of as many more invisible ones." "There is no reason to think radiance a necessary property of celestial bodies." But most astronomers were incredulous, and it was not until 1862 that, in the testing of a new and powerful telescope just built, a dark star was brought to light and the companion of Sirius actually seen. The visual discovery of the dark companion of Procyon is of still more recent date (November, 1896), when it was detected with the great telescope of the Lick Observatory. This discovery is so recent that the orbit is still very uncertain, being based almost wholly upon the variations in the proper motion of the star, and while the periodic time must be very nearly correct, the ma.s.s of the stars and dimensions of the orbit may require considerable correction.

The companion of Sirius is about ten magnitudes and that of Procyon about twelve magnitudes fainter than the star itself. How much more light does the bright star give than its faint companion? Despite the tremendous difference of brightness represented by the answer to this question, the ma.s.s of Sirius is only about twice as great as that of its companion, and for Procyon the ratio does not exceed five or six.

The visual discovery of the companions to Sirius and Procyon removes them from the list of dark stars, but others still remain unseen, although their existence is indicated by variable proper motions or by variable orbital motion, as in the case of ? Cancri, where one of the components of a triple star moves around the other two in a series of loops whose presence indicates a disturbing body which has never yet been seen.

202. MULTIPLE STARS.--Combinations of three, four, or more stars close to each other, like ? Cancri, are called multiple stars, and while they are far from being as common as are double stars, there is a considerable number of them in the sky, 100 or more as against the more than 10,000 double stars that are known. That their relative motions are subject to the law of gravitation admits of no serious doubt, but mathematical a.n.a.lysis breaks down in face of the difficulties here presented, and no astronomer has ever been able to determine what will be the general character of the motions in such a system.

[Ill.u.s.tration: FIG. 129.--Ill.u.s.trating the motion of a spectroscopic binary.]

203. SPECTROSCOPIC BINARIES.--In the year 1890 Professor Pickering, of the Harvard Observatory, announced the discovery of a new cla.s.s of double stars, invisible as such in even the most powerful telescope, and producing no perturbations such as have been considered above, but showing in their spectrum that two or more bodies must be present in the source of light which to the eye is indistinguishable from a single star. In Fig. 129 we suppose _A_ and _B_ to be the two components of a double star, each moving in its own orbit about their common center of gravity, _C_, whose distance from the earth is several million times greater than the distance between the stars themselves. Under such circ.u.mstances no telescope could distinguish between the two stars, which would appear fused into one; but the smaller the orbit the more rapid would be their motion in it, and if this...o...b..t were turned edgewise toward the earth, as is supposed in the figure, whenever the stars were in the relative position there shown, _A_ would be rapidly approaching the earth by reason of its...o...b..tal motion, while _B_ would move away from it, so that in accordance with the Doppler principle the lines composing their respective spectra would be shifted in opposite directions, thus producing a doubling of the lines, each single line breaking up into two, like the double-sodium line _D_, only not s.p.a.ced so far apart. When the stars have moved a quarter way round their orbit to the points _A'_, _B'_, their velocities are turned at right angles to the line of sight and the spectrum returns to the normal type with single lines, only to break up again when after another quarter revolution their velocities are again parallel with the line of sight.

The interval of time between consecutive doublings of the lines in the spectrum thus furnishes half the time of a revolution in the orbit. The distance between the components of a double line shows by means of the Doppler principle how fast the stars are traveling, and this in connection with the periodic times fixes the size of the orbit, provided we a.s.sume that it is turned exactly edgewise to the earth. This a.s.sumption may not be quite true, but even though the orbit should deviate considerably from this position, it will still present the phenomenon of the double lines whose displacement will now show something less than the true velocities of the stars in their orbits, since the spectroscope measures only that component of the whole velocity which is directed toward the earth, and it is important to note that the real orbits and ma.s.ses of these _spectroscopic binaries_, as they are called, will usually be somewhat larger than those indicated by the spectroscope, since it is only in exceptional cases that the orbit will be turned exactly edgewise to us.

The bright star Capella is an excellent ill.u.s.tration of these spectroscopic binaries. At intervals of a little less than a month the lines of its spectrum are alternately single and double, their maximum separation corresponding to a velocity in the line of sight amounting to 37 miles per second. Each component of a doubled line appears to be shifted an equal amount from the position occupied by the line when it is single, thus indicating equal velocities and equal ma.s.ses for the two component stars whose periodic time in their orbit is 104 days. From this periodic time, together with the velocity of the star's motion, let the student show that the diameter of the orbit--i. e., the distance of the stars from each other--is approximately 53,000,000 miles, and that their combined ma.s.s is a little less than that of a Centauri, provided that their orbit plane is turned exactly edgewise toward the earth.

There are at the present time (1901) 34 spectroscopic binaries known, including among them such stars as Polaris, Capella, Algol, Spica, Aurigae, ? Ursae Majoris, etc., and their number is rapidly increasing, about one star out of every seven whose motion in the line of sight is determined proving to be a binary or, as in the case of Polaris, possibly triple. On account of smaller distance apart their periodic times are much shorter than those of the ordinary double stars, and range from a few days up to several months--more than two years in the case of ? Pegasi, which has the longest known period of any star of this cla.s.s.

Spectroscopic binaries agree with ordinary double stars in having ma.s.ses rather greater than that of the sun, but there is as yet no a.s.sured case of a ma.s.s ten times as great as that of the sun.

204. VARIABLE STARS.--Attention has already been drawn (-- 23) to the fact that some stars shine with a changing brightness--e. g., Algol, the most famous of these _variable stars_, at its maximum of brightness furnishes three times as much light as when at its minimum, and other variable stars show an even greater range. The star ? Ceti has been named Mira (Latin, _the wonderful_), from its extraordinary range of brightness, more than six-hundred-fold. For the greater part of the time this star is invisible to the naked eye, but during some three months in every year it brightens up sufficiently to be seen, rising quite rapidly to its maximum brilliancy, which is sometimes that of a second-magnitude star, but more frequently only third or even fourth magnitude, and, after shining for a few weeks with nearly maximum brilliancy, falling off to become invisible for a time and then return to its maximum brightness after an interval of eleven months from the preceding maximum. In 1901 it should reach its greatest brilliancy about midsummer, and a month earlier than this for each succeeding year. Find it by means of the star map, and by comparing its brightness from night to night with neighboring stars of about the same magnitude see how it changes with respect to them.

The interval of time from maximum to maximum of brightness--331.6 days for Mira--is called the star's period, and within its period a star regularly variable runs through all its changes of brilliancy, much as the weather runs through its cycle of changes in the period of a year.

But, as there are wet years and dry ones, hot years and cold, so also with variable stars, many of them show differences more or less p.r.o.nounced between different periods, and one such difference has already been noted in the case of Mira; its maximum brilliancy is different in different years. So, too, the length of the period fluctuates in many cases, as does every other circ.u.mstance connected with it, and predictions of what such a variable star will do are notoriously unreliable.

205. THE ALGOL VARIABLES.--On the other hand, some variable stars present an almost perfect regularity, repeating their changes time after time with a precision like that of clockwork. Algol is one type of these regular variables, having a period of 68.8154 hours, during six sevenths of which time it shines with unchanging l.u.s.ter as a star of the 2.3 magnitude, but during the remaining 9 hours of each period it runs down to the 3.5 magnitude, and comes back again, as is shown by a curve in Fig. 130. The horizontal scale here represents hours, reckoned from the time of the star's minimum brightness, and the vertical scale shows stellar magnitudes. Such a diagram is called the star's light curve, and we may read from it that at any time between 5h. and 32h. after the time of minimum the star's magnitude is 2.32; at 2h. after a minimum the magnitude is 2.88, etc. What is the magnitude an hour and a half before the time of minimum? What is the magnitude 43 days after a minimum?

[Ill.u.s.tration: FIG. 130.--The light curve of Algol.]

The arrows shown in Fig. 130 are a feature not usually found with light curves, but in this case each one represents a spectroscopic determination of the motion of Algol in the line of sight. These observations extended over a period of more than two years, but they are plotted in the figure with reference to the number of hours each one preceded or followed a minimum of the star's light, and each arrow shows not only the direction of the star's motion along the line of sight, the arrows pointing down denoting approach of the star toward the earth, but also its velocity, each square of the ruling corresponding to 10 kilometers (6.2 miles per second). The differences of velocity shown by adjacent arrows come mainly from errors of observation and furnish some idea of how consistent among themselves such observations are, but there can be no doubt that before minimum the star is moving away from the earth, and after minimum is approaching it. It is evident from these observations that in Algol we have to do with a spectroscopic binary, one of whose components is a dark star which, once in each revolution, partially eclipses the bright star and produces thus the variations in its light. By combining the spectroscopic observations with the variations in the star's light, Vogel finds that the bright star, Algol, itself has a diameter somewhat greater than that of the sun, but is of low density, so that its ma.s.s is less than half that of the sun, while the dark star is a very little smaller than the sun and has about a quarter of its ma.s.s. The distance between the two stars, dark and bright, is 3,200,000 miles. Fig. 129, which is drawn to scale, shows the relative positions and sizes of these stars as well as the orbits in which they move.

The mere fact already noted that close binary systems exist in considerable numbers is sufficient to make it probable that a certain proportion of these stars would have their orbit planes turned so nearly edgewise toward the earth as to produce eclipses, and corresponding to this probability there are already known no less than 15 stars of the Algol type of eclipse variables, and only a beginning has been made in the search for them.

[Ill.u.s.tration: FIG. 131.--The light curve of Lyrae.]

206. VARIABLES OF THE LYRae TYPE.--In addition to these there is a certain further number of binary variables in which both components are bright and where the variation of brightness follows a very different course. Capella would be such a variable if its...o...b..t plane were directed exactly toward the earth, and the fact that its light is not variable shows conclusively that such is not the position of the orbit. Fig. 131 represents the light curve of one of the best-known variable systems of this second type, that of Lyrae, whose period is 12 days 21.8 hours, and the student should read from the curve the magnitude of the star for different times during this interval.

According to Myers, this light curve and the spectroscopic observations of the star point to the existence of a binary star of very remarkable character, such as is shown, together with its...o...b..t and a scale of miles, in Fig. 132. Note the tide which each of these stars raises in the other, thus changing their shapes from spheres into ellipsoids. The astonishing dimensions of these stars are in part compensated by their very low density, which is less than that of air, so that their ma.s.ses are respectively only 10 times and 21 times that of the sun! But these dimensions and ma.s.ses perhaps require confirmation, since they depend upon spectroscopic observations of doubtful interpretation. In Fig. 132 what relative positions must the stars occupy in their orbit in order that their combined light should give Lyrae its maximum brightness? What position will furnish a minimum brightness?

[Ill.u.s.tration: FIG. 132.--The system of Lyrae.--MYERS.]

207. VARIABLES OF LONG AND SHORT PERIODS.--It must not be supposed that all variable stars are binaries which eclipse each other. By far the larger part of them, like Mira, are not to be accounted for in this way, and a distinction which is pretty well marked in the length of their periods is significant in this connection. There is a considerable number of variable stars with periods shorter than a month, and there are many having periods longer than 6 months, but there are very few having periods longer than 18 months, or intermediate between 1 month and 6 months, so that it is quite customary to divide variable stars into two cla.s.ses--those of long period, 6 months or more, and those of short period less than 6 months, and that this distinction corresponds to some real difference in the stars themselves is further marked by the fact that the long-period variables are prevailingly red in color, while the short-period stars are almost without exception white or very pale yellow. In fact, the longer the period the redder the star, although it is not to be inferred that all red stars are variable; a considerable percentage of them shine with constant light. The eclipse explanation of variability holds good only for short-period variables, and possibly not for all of them, while for the long-period variables there is no explanation which commands the general a.s.sent of astronomers, although unverified hypotheses are plenty.

The number of stars known to be variable is about 400, while a considerable number of others are "suspected," and it would not be surprising if a large fraction of all the stars should be found to fluctuate a little in brightness. The sun's spots may suffice to make it a variable star with a period of 11 years.

The discovery of new variables is of frequent occurrence, and may be expected to become more frequent when the sky is systematically explored for them by the ingenious device suggested by Pickering and ill.u.s.trated in Fig. 133. A given region of the sky--e. g., the Northern Crown--is photographed repeatedly upon the same plate, which is shifted a little at each new exposure, so that the stars shall fall at new places upon it. The finally developed plate shows a row of images corresponding to each star, and if the star's light is constant the images in any given row will all be of the same size, as are most of those in Fig. 133; but a variable star such as is shown by the arrowhead reveals its presence by the broken aspect of its row of dots, a minimum brilliancy being shown by smaller and a maximum by larger ones. In this particular case, at two exposures the star was too faint to print its image upon the plate.

[Ill.u.s.tration: FIG. 133.--Discovery of a variable star by means of photography.--PICKERING.]

208. NEW STARS.--Next to the variable stars of very long or very irregular period stand the so-called _new_ or _temporary stars_, which appear for the most part suddenly, and after a brief time either vanish altogether or sink to comparative insignificance. These were formerly thought to be very remarkable and unusual occurrences--"the birth of a new world"--and it is noteworthy that no new star is recorded to have been seen from 1670 to 1848 A. D., for since that time there have been no less than five of them visible to the naked eye and others telescopic. In so far as these new stars are not ordinary variables (Mira, first seen in 1596, was long counted as a new star), they are commonly supposed due to chance encounters between stars or other cosmic bodies moving with considerable velocities along orbits which approach very close to each other. The actual collision of two dark bodies moving with high velocities is clearly sufficient to produce a luminous star--e. g., meteors--and even the close approach of two cooled-off stars, might result in tidal actions which would rend open their crusts and pour out the glowing matter from within so as to produce temporarily a very great accession of brightness.

The most famous of all new stars is that which, according to Tycho Brahe's report, appeared in the year 1572, and was so bright when at its best as to be seen with the naked eye in broad daylight. It continued visible, though with fading light, for about 16 months, and finally disappeared to the naked eye, although there is some reason to suppose that it can be identified with a ruddy star of the eleventh magnitude in the constellation Ca.s.siopeia, whose light still shows traces of variability.

No modern temporary star approaches that of Tycho in splendor, but in some respects the recent ones surpa.s.s it in interest, since it has been possible to apply the spectroscope to the a.n.a.lysis of their light and to find thereby a much more complex set of conditions in the star than would have been suspected from its light changes alone.

One of the most extraordinary of new stars, and the most brilliant one since that of Tycho, appeared suddenly in the constellation Perseus in February, 1901, and for a short time equaled Capella in brightness. But its light rapidly waned, with periodic fluctuations of brightness like those of a variable star, and at the present time (September, 1902) it is lost to the naked eye, although in the telescope it still shines like a star of the ninth or tenth magnitude.

By the aid of powerful photographic apparatus, during the period of its waning brilliancy a ring of faint nebulous matter was detected surrounding the star and drifting around and away from it much as if a series of nebulae had been thrown off by the star at the time of its sudden outburst of light. But the extraordinary velocity of this nebular motion, nearly a billion miles per hour, makes such an explanation almost incredible, and astronomers are more inclined to believe that the ring was merely a reflection of the star's own light from a cloud of meteoric matter, into which a rapidly moving dark star plunged and, after the fashion of terrestrial meteors, was raised to brilliant incandescence by the collision. If we a.s.sume this to be the true explanation of these extraordinary phenomena, it is possible to show from the known velocity with which light travels through s.p.a.ce and from the rate at which the nebula spread, that the distance of Nova Persei, as the new star is called, corresponds to a parallax of about one one-hundredth of a second, a result that is, in substance, confirmed by direct telescopic measurements of its parallax.

Another modern temporary star is Nova Aurigae, which appeared suddenly in December, 1891, waned, and in the following April vanished, only to reappear three months later for another season of renewed brightness.

The spectra of both these modern Novae contain both dark and bright lines displaced toward opposite ends of the spectrum, and suggesting the Doppler effect that would be produced by two or more glowing bodies having rapid and opposite motions in the line of sight. But the most recent investigations cast discredit on this explanation and leave the spectra of temporary stars still a subject of debate among astronomers, with respect both to the motion they indicate and the intrinsic nature of the stars themselves. The varying aspect of the spectra suggested at one time the sun's chromosphere, at another time the conditions that are present in nebulae, etc.

CHAPTER XIV

STARS AND NEBULae

209. STELLAR COLORS.--We have already seen that one star differs from another in respect of color as well as brightness, and the diligent student of the sky will not fail to observe for himself how the l.u.s.ter of Sirius and Rigel is more nearly a pure white than is that of any other stars in the heavens, while at the other end of the scale a Orionis and Aldebaran are strongly ruddy, and Antares presents an even deeper tone of red. Between these extremes the light of every star shows a mixture of the rainbow hues, in which a very pale yellow is the predominant color, shading off, as we have seen, to white at one end of the scale and red at the other. There are no green stars, or blue stars, or violet stars, save in one exceptional cla.s.s of cases--viz., where the two components of a double star are of very different brightness, it is quite the usual thing for them to have different colors, and then, almost without exception, the color of the fainter star lies nearer to the violet end of the spectrum than does the color of the bright one, and sometimes shows a distinctly blue or green hue. A fine type of such double star is Cygni, in which the components are respectively yellow and blue, and the yellow star furnishes eight times as much light as the blue one.

The exception which double stars thus make to the general rule of stellar colors, yellow and red, but no color of shorter wave length, has never been satisfactorily explained, but the rule itself presents no difficulties. Each star is an incandescent body, giving off radiant energy of every wave length within the limits of the visible spectrum, and, indeed, far beyond these limits. If this radiant energy could come unhindered to our eyes every star would appear white, but they are all surrounded by atmospheres--a.n.a.logous to the chromosphere and reversing layer of the sun--which absorb a portion of their radiant energy and, like the earth's atmosphere, take a heavier toll from the violet than from the red end of the spectrum. The greater the absorption in the star's atmosphere, therefore, the feebler and the ruddier will be its light, and corresponding to this the red stars are as a cla.s.s fainter than the white ones.

210. CHEMISTRY OF THE STARS.--The spectroscope is pre-eminently the instrument to deal with this absorption of light in the stellar atmospheres, just as it deals with that absorption in the sun's atmosphere to which are due the dark lines of the solar spectrum, although the faintness of starlight, compared with that of the sun, presents a serious obstacle to its use. Despite this difficulty most of the lucid stars and many of the telescopic ones have been studied with the spectroscope and found to be similar to the sun and the earth as respects the material of which they are made. Such familiar chemical elements as hydrogen and iron, carbon, sodium, and calcium are scattered broadcast throughout the visible universe, and while it would be unwarranted by the present state of knowledge to say that the stars contain nothing not found in the earth and the sun, it is evident that in a broad way their substance is like rather than unlike that composing the solar system, and is subject to the same physical and chemical laws which obtain here. Galileo and Newton extended to the heavens the terrestrial sciences of mathematics and mechanics, but it remained to the nineteenth century to show that the physics and chemistry of the sky are like the physics and chemistry of the earth.

211. STELLAR SPECTRA.--When the spectra of great numbers of stars are compared one with another, it is found that they bear some relation to the colors of the stars, as, indeed, we should expect, since spectrum and color are both produced by the stellar atmospheres, and it is found useful to cla.s.sify these spectra into three types, as follows: