Robert S. Ball

Sirius Contrasted with the Sun—Stars can be Weighed, but not in general Measured—The Companion of Sirius—Determination of the Weights of Sirius and his Companion—Dark Stars—Variable and Temporary Stars—Enormous Number of Stars.

The splendid pre-eminence of Sirius has caused it to be observed with minute care from the earliest times in the history of astronomy. Each generation of astronomers devoted time and labour to determine the exact places of the brightest stars in the heavens. A vast mass of observations as to the place of Sirius among the stars had thus been accumulated, and it was found that, like many other stars, Sirius had what astronomers call proper motion. Comparing the place of Sirius with regard to the other stars now with the place which it occupied one hundred years ago, there is a difference of two minutes (127´´) in its situation. This is a small quantity: it is so small that the unaided eye could not see it. Could we now see the sky as it appeared one century ago, we should still see this star in its well-known place to the left of Orion. Careful alignment by the eye would hardly detect that Sirius was moving in two, or even in three or in four centuries. But the accuracy of the meridian circle renders these minute quantities evident, and gives to them their true significance. To the eye of the astronomer, Sirius, instead of creeping along with a movement which centuries will not show, is pursuing its majestic course with a velocity appropriate to its dimensions.

Though the velocity of Sirius is about 1,000 miles a minute, yet it is sometimes a little more and sometimes a little less than its mean value. To the astronomer this fact is pregnant with information. Were Sirius an isolated star, attended only by planets of comparative insignificance, there could be no irregularity in its motion. If it were once started with a velocity of 1,000 miles a minute, then it must preserve that velocity. Neither the lapse of centuries nor the mighty length of the journey could alter it. The path of Sirius would be inflexible in its direction; and it would be traversed with unalterable velocity.

The fact that Sirius had not been moving uniformly was of such interest that it arrested the attention of Bessel when he discovered the irregularities in 1844. Believing, as Bessel did, that there must be some adequate cause for these disturbances, it was hardly possible to doubt what the cause must be. When motion is disturbed there must be force in action, and the only force that we recognise in such cases is that known as gravitation. But gravity can only act from one body to another body; so that when we seek for the derangement of Sirius by gravitation, we are obliged to suppose that there must be some mighty and massive body near Sirius. The question was taken up again by Peters and by Auwers, who were able to discover, from the irregularities of Sirius, the nature of the path of the disturbing body. They were able to show that it must revolve around Sirius in a period of about fifty years, and although they could not tell its distance from Sirius, yet they were able to point out the direction in which it must lie. Fig. 92 shows the orbit of Sirius as given by Mr. Burnham, of Yerkes Observatory.

The detection of the attendant of Sirius, and the measures which have been made thereon, enable us to determine the weight of this famous star. Let us attempt to illustrate this subject. It must, no doubt, be admitted that the numerical estimates we employ have to be received with a certain degree of caution. The companion of Sirius is a difficult object to observe, and previous to 1896 it had only been followed through an arc of 90°. We are, therefore, hardly as yet in a position to speak with absolute accuracy as to the periodic time in which the companion completes its revolution. We may, however, take this time to be fifty-two years. We also know the distance from Sirius to his companion, and we may take it to be about twenty-one times the distance from the earth to the sun. It is useful, in the first place, to compare the revolution of the companion around Sirius with the revolution of the planet Uranus around the sun. Taking the earth's distance as unity, the radius of the orbit of Uranus is about nineteen, and Uranus takes eighty-four years to accomplish a complete revolution. We have no planet in the solar system at a distance of twenty-one; but from Kepler's third law it may be shown that, if there were such a planet, its periodic time would be about ninety-nine years. We have now the necessary materials for making the comparison between the mass of Sirius and the mass of the sun. A body revolving around Sirius at a certain distance completes its journey in fifty-two years. To revolve around the sun at the same distance a body should complete its journey in ninety-nine years. The quicker the body is moving the greater must be the centrifugal force, and the greater must be the attractive power of the central body. It can be shown from the principles of dynamics that the attractive power is inversely proportional to the square of the periodic time. Hence, then, the attractive power of Sirius must bear to the attractive power of the sun the proportion which the square of ninety-nine has to the square of fifty-two. As the distances are in each case supposed to be equal, the attractive powers will be proportional to the masses, and hence we conclude that the mass of Sirius, together with that of his companion, is to the mass of the sun, together with that of his planet, in the ratio of three and a half to one. We had already learned that Sirius was much brighter than the sun; now we have learned that it is also much more massive.

Before we leave the consideration of Sirius, there is one additional point of very great interest which it is necessary to consider. There is a remarkable contrast between the brilliancy of Sirius and his companion. Sirius is a star far transcending all other stars of the first magnitude, while his companion is extremely faint. Even if it were completely withdrawn from the dazzling proximity of Sirius, the companion would be only a small star of the eighth or ninth magnitude, far below the limits of visibility to the unaided eye. To put the matter in numerical language, Sirius is 5,000 times as bright as its companion, but only about twice as heavy! Here is a very great contrast; and this point will appear even more forcible if we contrast the companion of Sirius with our sun. The companion is slightly heavier than our sun; but in spite of its slightly inferior bulk, our sun is much more powerful as a light-giver. One hundred of the companions of Sirius would not give as much light as our sun! This is a result of very considerable significance. It teaches us that besides the great bodies in the universe which attract attention by their brilliancy, there are also other bodies of stupendous mass which have but little brilliancy—probably some of them possess none at all. This suggests a greatly enhanced conception of the majestic scale of the universe. It also invites us to the belief that the universe which we behold bears but a small ratio to the far larger part which is invisible in the sombre shades of night. In the wide extent of the material universe we have here or there a star or a mass of gaseous matter sufficiently heated to be luminous, and thus to become visible from the earth; but our observation of these luminous points can tell us little of the remaining contents of the universe.

The most celebrated of all the variable stars is that known as Algol, whose position in the constellation of Perseus is shown in Fig. 83. This star is conveniently placed for observation, being visible every night in our latitude, and its interesting changes can be observed without any telescopic aid. Everyone who desires to become acquainted with the great truths of astronomy should be able to recognise this star, and should have also followed it during one of its periods of change. Algol is usually a star of the second magnitude; but in a period between two and three days, or, more accurately, in an interval of 2 days 20 hours 48 minutes and 55 seconds, its brilliancy goes through a most remarkable cycle of variations. The series commences with a gradual decline of the star's brightness, which in the course of four and a half hours falls from the second magnitude down to the fourth. At this lowest stage of brightness Algol remains for about twenty minutes, and then begins to increase, until in three and a half hours it regains the second magnitude, at which it continues for about 2 days 12 hours, when the same series commences anew. It seems that the period required by Algol to go through its changes is itself subject to a slow but certain variation. We shall see in a following chapter how it has been proved that the variability of Algol is due to the occasional interposition of a dark companion which cuts off a part of the lustre of the star. All the circumstances can thus be accounted for, and even the weight and the size of Algol and its dark companion be determined.

There are, however, other classes of variable stars, the fluctuation of whose light can hardly be due to occasional obscuration by dark bodies. This is particularly the case with those variables which are generally faint, but now and then flare up for a short time, after which temporary exaltation they again sink down to their original condition. The periods of such changes are usually from six months to two years. The best known example of a star of this class was discovered more than three hundred years ago. It is situated in the constellation Cetus, a little south of the equator. This object was the earliest known case of a variable star, except the so-called temporary stars, to which we shall presently refer. The variable in Cetus received the name of Mira, or the wonderful. The period of the fluctuations of Mira Ceti is about eleven months, during the greater part of which time the star is of the ninth magnitude, and consequently invisible to the naked eye. When the proper time has arrived, its brightness begins to increase rather suddenly. It soon becomes a conspicuous object of the second or third magnitude. In this condition it remains for eight or ten days, and then declines more slowly than it rose until it is reduced to its original faintness, about three hundred days after the rise commenced.

More striking to the general observer than the ordinary variable stars are the temporary stars which on rare occasions suddenly make their appearance in the heavens. The most famous object of this kind was that which blazed out in the beginning of November, 1572, and which when first seen was as bright as Venus at its maximum brightness. It could, indeed, be seen in full daylight by sharp-sighted people. As far as history can tell us, no other temporary star has ever been as bright as this one. It is specially associated with the name of Tycho Brahe, for although he was not the discoverer, he made the best observations of the object, and he proved that it was at a distance comparable with that of the ordinary fixed stars. Tycho described carefully the gradual decline of the wonderful star until it disappeared from his view about the end of March, 1574, for the telescope, by which it could doubtless have been followed further, had not yet been invented. During the decline the colour of the object gradually changed; at first it was white, and by degrees became yellow, and in the spring of 1573 reddish, like Aldebaran. About May, 1573, we are told somewhat enigmatically that it "became like lead, or somewhat like Saturn," and so it remained as long as it was visible. What a fund of information our modern spectroscopes and other instruments would supply us with if so magnificent a star were to burst out in these modern days!

But though we have not in our own times been favoured with a view of a temporary star as splendid as the one seen by Tycho Brahe and his contemporaries, it has been our privilege to witness several minor outbursts of this kind. It seems likely that we should possess more records of temporary stars from former times if a better watch had been kept for them. That is at any rate the impression we get when we see how several of the modern stars of this kind have nearly escaped us altogether, notwithstanding the great number of telescopes which are now pointed to the sky on every clear night.

In 1866 a star of the second magnitude suddenly appeared in the constellation of the crown (Corona Borealis). It was first seen on the 12th May, and a few days afterwards it began to fade away. Argelander's maps of the northern heavens had been published some years previously, and when the position of the new star had been accurately determined, it was found that it was identical with an insignificant looking star marked on one of the maps as of the 9-1/2 magnitude. The star exists in the same spot to this day, and it is of the same magnitude as it was prior to its spasmodic outburst in 1866. This was the first new star which was spectroscopically examined. We shall give in Chapter XXIII. a short account of the features of its spectrum.

The next of these temporary bright stars, Nova Cygni, was first seen by Julius Schmidt at Athens on the 24th November, 1876, when it was between the third and fourth magnitudes, and he maintains that it cannot have been conspicuous four days earlier, when he was looking at the same constellation. By some inadvertence the news of the discovery was not properly circulated, and the star was not observed elsewhere for about ten days, when it had already become considerably fainter. The decrease of brightness went on very slowly; in October, 1877, the star was only of the tenth magnitude, and it continued getting fainter until it reached the fifteenth magnitude; in other words, it became a minute telescopic star, and it is so still in the very same spot. As this star did not reach the first or second magnitude it would probably have escaped notice altogether if Schmidt had not happened to look at the Swan on that particular evening.

We are not so likely to miss seeing a new star since astronomers have pressed the photographic camera into their service. This became evident in 1892, when the last conspicuous temporary star appeared in Auriga. On the 24th January, Dr. Anderson, an astronomer in Edinburgh, noticed a yellowish star of the fifth magnitude in the constellation Auriga, and a week later, when he had compared a star-map with the heavens and made sure that the object was really a new star, he made his discovery public. In the case of this star we are able to fix fairly closely the moment when it first blazed out. In the course of the regular photographic survey of the heavens undertaken at the Harvard College Observatory (Cambridge, Massachusetts) the region of the sky where the new star appeared had been photographed on thirteen nights from October 21st to December 1st, 1891, and on twelve nights from December 10th to January 20th, 1892. On the first series of plates there was no trace of the Nova, while it was visible on the very first plate of the second series as a star of the fifth magnitude. Fortunately it turned out that Professor Max Wolf of Heidelberg, a most successful celestial photographer, had photographed the same region on the 8th December, and this photograph does not show the star, so that it cannot on that night have been as bright as the ninth magnitude. Nova Auriga must therefore have flared up suddenly between the 8th and the 10th of December. According to the Harvard photographs, the first maximum of brightness occurred about the 20th of December, when the magnitude was 4-1/2. The decrease of the brightness was very irregular; the star fluctuated for the five weeks following the first of February between the fourth and the sixth magnitude, but after the beginning of March, 1892, the brightness declined very rapidly, and at the end of April the star was seen as an exceedingly faint one (sixteenth magnitude) with the great Lick Refractor. When this mighty instrument was again pointed to the Nova in the following August, it had risen nearly to the tenth magnitude, after which it gradually became extremely faint again, and is so still.

The temporary and the variable stars form but a very small section of the vast number of stars with which the vault of the heavens is studded. That the sun is no more than a star, and the stars are no less than suns, is a cardinal doctrine of astronomy. The imposing magnificence of this truth is only realised when we attempt to estimate the countless myriads of stars. This is a problem on which our calculations are necessarily vain. Let us, therefore, invoke the aid of the poet to attempt to express the innumerable, and conclude this chapter with the following lines of Mr. Allingham:—