Pickering proposed in 1880 the following classification of variable stars, which has been adopted all over the scientific world: Class I., temporary star; Class II., stars undergoing in several months large variations, such as Mira Ceti and U Orionis; Class III., irregular variables, such as Betelgeux and α Herculis; Class IV., short-period variables, such as δ Cephei, ζ Geminorum, and β Lyræ; Class V., “Algol variables,” which undergo variations lasting but a few hours. It is doubtful whether new stars should be included in a classification of variables, although in one case, at least, a new star was found to be a long-period variable. To these a sixth class may now be added. This class, the detection of which is mainly due to the profound investigations of Gore, is composed of what have been termed “secular variables,” which undergo slow fluctuations in periods of many years, and sometimes of centuries. This Class includes δ Ursæ Majoris, Al-Fard, λ Draconis, θ Serpentis, ε Pegasi, 83 Ursæ Majoris, ζ Piscis Australis, β Leonis, α Ophiuchi, η Crateris, and others. The secular variations of some of these stars have been detected by Gore himself during the past thirty years, while in other cases he has detected them by comparison of the most important star-catalogues, from Hipparchus and Al-Sufi down to our own time. In some cases the star in question seems to be slowly gaining in brilliance, in others slowly diminishing.
Thanks to the application of the spectroscope, much is now known of the cause of the light changes in variable stars. Goodricke’s theory of the variations of Algol was theoretically confirmed by the researches of E. C. Pickering in 1880. In 1889 Vogel proved beyond a doubt that the variation in the light of Algol is due to the partial eclipse of its light by a dark satellite. It was obvious to Vogel that, as both Algol and its companion are in revolution round their common centre of gravity, the motion of Algol in the line of sight might be detected by the spectroscopic method of observation. Vogel found that before each eclipse Algol was retreating from our system, while on recovering it gave signs of rapid approach, proving conclusively that both the star and its dark satellite were in revolution round their centre of gravity,—Algol suffering partial eclipse only because the plane of the orbit lies in our line of sight. Algol, therefore, is not inherently a variable star, but merely a binary. Following up his researches, Vogel, assuming that the bright and dark stars are of equal density, arrived at the conclusion that Algol is a globe about one and a half million miles in diameter, the satellite equalling the size of the Sun, and the centres of the stars being separated by about 3,230,000 miles. Thus, variable stars of the Algol type are not variable in the true sense of the word. Even the most irregular of the Algol variables have been explained. Perhaps the most irregular was Y Cygni, discovered by Chandler in 1886. It was soon found, however, that the variations recurred with great irregularity: in less than two years the phases differed by as much as seven hours from the predicted times. At length the subject was taken up by Dunér at Upsala. A series of observations made with the 14-inch refractor at Upsala in 1891 and 1892 convinced him in the latter year that two eclipses take place in the course of one revolution: one star occults the other. Dunér showed that the intervals between minima were thus—1 day 9 hours; 1 day 15 hours; 1 day 9 hours, and so on. Thus, the first, third, fifth, and seventh sets of minima obeyed a different law from the second, fourth, sixth, and eighth. Dunér proved that two stars revolve round their centre of gravity in less than three days, alternately occulting each other, while the ellipticity of the orbit explains the irregularity of the light changes. In April 1900 Dunér gave his final conclusions as follows: “The variable star Y Cygni consists of two stars of equal size and equal brightness, which move about their common centre of gravity in an elliptical orbit, whose major axis is eight times the radius of the stars.” He also stated the exact period of revolution and the eccentricity of the orbit.
In the case of the short-period variables, such as β Lyræ, δ Cephei, ζ Geminorum, and η Aquilæ, the variations do not seem to be due to eclipse. It was discovered by Professor Pickering that β Lyræ is a spectroscopic binary, but Vogel and Keeler showed that the supposed orbit is incompatible with the eclipse theory. Vogel says: “I am convinced that β Lyræ represents a binary or multiple system, the fundamental revolutions of which in 12 days 22 hours in some way control the light change.” The eclipse theory, however, is still maintained by Bélopolsky, who has framed a hypothesis according to which the chief minimum of the star’s light corresponds with the obscuration of the lesser star, the lesser minimum with that of the primary, implying that the primary is much less luminous in proportion to its light than its satellite,—a state of affairs which Miss Clerke concludes to be improbable.
The variable stars, δ Cephei and η Aquilæ, were both found in 1894 by Bélopolsky to be binaries; but as the times of minimum light do not correspond with those of eclipses in the hypothetical orbits, he concludes that the variations cannot be explained on the eclipsing satellite theory. Miss Clerke is inclined to the theory that the increase of luminosity in short-period variables is due to tidal action, so that while the revolutions of the stars control their variability, they are inherently unstable in light. A large number of these stars are known, and it is a remarkable fact that the majority of these variables lie on or near the Galaxy, so that their variations have probably something to do with their vicinity.
We now come to the long-period variables of which Mira Ceti, χ Cygni, and U Orionis are examples. Although varying in regular periods, generally of about a year, they are subject to remarkable irregularities, so that an exact period cannot be assigned even to Mira Ceti, of which the maxima are at times retarded and at others accelerated with no apparent law. The spectroscopic investigations of Campbell in 1898 have shown that Mira Ceti is a solitary star, while bright lines of hydrogen appear in its spectrum at maximum, showing that the variations are due to periodical conflagrations in its atmospheres. In many other long-period variables bright lines have been observed.
A remarkable fact regarding these stars is the amount of their light change. Mira Ceti, for instance, varies from the first to the ninth magnitude, and U Orionis from the sixth to the twelfth. As M. Flammarion says, “the longer the period the greater the variation.” Another remarkable fact is that their light curves show a curious resemblance to the curves of the solar spots, only on a vastly greater scale, which indicates that, relatively, these long-period variables are much older than our Sun, the small variations in the light of which are imperceptible. “Here, if anywhere,” says Miss Clerke, “will be found the secret of stellar variability.”
To the irregular variables no period can be assigned. Betelgeux, in Orion, the variation of which was noted by Sir John Herschel in 1840, is a typically irregular variable. But the most extraordinary of all variables is η Argus, in the southern hemisphere, which is probably a connecting link between variable and temporary stars. The traveller Burchell, from 1811 to 1815, observed the star as of the second magnitude, but in 1827 he noted it to be of the first magnitude. In the following year it fell to the second magnitude. In 1834 Sir John Herschel noted the star to be between the first and second magnitude, and in 1838 it rose to the first, being equal to α Centauri. After a decline, it became in 1843 equal to Canopus, and not much inferior to Sirius. Then it began to fade, and in 1868 it was only of the sixth magnitude. In 1899 Innes estimated it as 7·71. Rudolf Wolf suggested a period of 46 years, and Loomis 67 years; but astronomers generally agree with Schönfeld that the star has no regular period.
The first temporary star of the nineteenth century was discovered by Hind, in London, April 28, 1848. It was of the fifth magnitude at maximum, and soon after began to fade, falling to the tenth magnitude. In 1860 a new star appeared in the cluster Messier 80 in Scorpio, and was discovered by Auwers at Königsberg. It reached only the seventh magnitude.
On the night of May 12, 1866, a new star of the second magnitude blazed out in the constellation Corona Borealis. It was first observed at Tuam, in Ireland, by the Irish astronomer, John Birmingham. Four hours earlier Schmidt had been observing that part of the heavens, and it was not then visible. Birmingham at once communicated the discovery to Huggins, at Tulse Hill, who had commenced his spectroscopic observations. On May 16 Huggins observed its spectrum. In the words of Miss Clerke, “The star showed what was described as a double spectrum. To the dusky flutings of Secchi’s third type, four brilliant rays were added. The chief of these agreed in position with lines of hydrogen; so that the immediate cause of the outburst was plainly perceived to have been the eruption, or ignition, of vast masses of that subtle kind of matter.” Nine days after the appearance of the new star it was invisible to the naked eye, and afterwards fell to the tenth magnitude. In 1856 Schönfeld had observed it at Bonn as a telescopic star, so that it was not a “new star” in the true sense of the word.
The next temporary star observed was discovered by Schmidt, at Athens, November 24, 1876. It was of the third magnitude, situated in the constellation Cygnus. On December 2 its spectrum was examined at Paris by Alfred Cornu (1841-1902), and some days later at Potsdam by Vogel and Lohse. It was closely similar to that of the new star of 1866, bright lines of hydrogen and other elements standing out in front of an “absorption” spectrum. By the end of 1876 the star was of the seventh magnitude. On September 2, 1877, Nova Cygni was observed at Dunecht, and its spectrum was found to have been transformed into that of a planetary nebula. Three years later, however, the ordinary stellar spectrum reappeared.