Art. VII.—On Temporary and Variable Stars.
[Read before the Philosophical Institute of Canterbury, 4th July, 1878.]
The sudden appearances of stars in various regions of the sky have been recorded from very early dates. Some of these stars have had an intensity of light greater than any of the fixed stars, and in some cases have remained visible for a year or more, the intensity of light all the while gradually diminishing.
Two considerable stars of this kind have appeared within the last twelve years, and in both cases they have been examined with the spectroscope. Unfortunately the results have not been so satisfactory as could be desired. The spectrum of the star of 1866 appears to have been continuous, with bright lines. The lines diminished in number and intensity until they finally disappeared, leaving only a feeble continuous spectrum. The light of the star of 1877 at first appeared yellowish, and when five or six days afterwards it was examined with the spectroscope, a line spectrum was seen. The number of lines gradually lessened until only one was left, and that the same line as is seen in some nebulæ.
A few considerations will show the stupendous nature of these phenomena. Temporary stars have all appeared to be fixed in the heavens, this fact showing them to be at true stellar distances, and consequently, like the fixed stars, their luminosity is comparable to that of our sun. The sun may be roughly classed as a star of the second magnitude; its intensity is approximately one four-hundredth that of Sirius, which is a very short distance from us relatively to the size of the universe, therefore it is not improbable that these temporary stars should be, on an average, at least as far away as he is.
We may therefore safely assume that most of the temporary stars whose appearance has been recorded, have had an intensity of light as great as the sun, and probably in some cases many times greater. The amount of heat
radiated from each square yard of our sun's surface is estimated to be equal to the combustion of ten cubic yards of coal in every hour, while the sun's disc has four times the area enclosed by the orbit of the moon. The star of 1866 when first seen was of the second magnitude, and its spectrum shows that it consisted of a nucleus of compressed gas, or of liquid or of solid matter. This was surrounded by an atmosphere of heated gas, having a greater monochromatic light than the nucleus; or it might have been simply a small permanent star in the same line of vision as the gaseous temporary star. I cannot say if this suggestion agrees with the present condition of the star. This star diminished from a star of the second magnitude to the tenth in about a fortnight. The spectroscope showed the star of 1877 to be ignited gas only, and from the number of the lines diminishing the temperature and pressure probably did so likewise. The intensity diminished in four months from the third magnitude to the ninth.
Many hypotheses have been formed to account for the nature of these stars, of which the following appear to be the most noteworthy:—
1. Zoolner imagines a sun in which spots have covered the whole surface, the temporary stars being produced by the breaking of such a surface.
2. Vogel assumes a volcanic bursting-out on a dead sun.
In both of these hypotheses a decomposition and combustion of hydrogen and other elements is also assumed to account for the great intensity.
3. Meyer and Klein suppose that a similar dark body is suddenly raised to incandescence by the projection of a planet or other body upon its surface.
4. Proctor supposes that the atmosphere of a dead sun is suddenly brought to a high degree of luminosity by the passage of a meteoric train through it.
In examining these hypotheses, we find that there is one thing in common, namely, the assumption of the existence of large dark bodies in space. The first two of them also depend on the existence of internal commotion, attended with combustion. The last two depend upon the energy developed by gravitation.
A little consideration will be sufficient to show that, on grounds of intensity alone, Zoolner's and Vogel's—in fact, any hypothesis not dependent upon gravitation—is improbable. Is it conceivable that a dark body should suddenly change its surface by volcanic or other internal action in such a manner as to heat gases to a pitch of luminosity as high as our sun's, especially when it is considered that if a gas and solid be at the same temperature, the solid is much the more luminous of the two; nor would combustion or decomposition help it; generally the latter would take
place, but would tend to diminish rather than increase the intensity. How inadequate combustion would be is shown by the fact that a pound weight would develope about forty million units of heat in falling upon the sun, and the combustion of a pound of mixed oxygen and hydrogen would only develope about 4000 units. And again, in either case the chief luminosity must be from the fused material; a continuous spectrum would then result, which in the last star at least is altogether contrary to observation. The precipitation of a body upon the surface of a dead sun is much more probable; so likewise is the meteoric theory; but in the former case if sufficient heat could be developed a fused mass would almost certainly result, and in the latter case nothing short of a marvellous combination would prevent its resulting. The latter hypothesis Proctor bases on the bright momentary light once observed on the face of the sun; he assumes that the gaseous photosphere was temporarily raised to a high luminosity by meteors. I think this of itself is very improbable. I cannot conceive how it is possible that if the atmosphere were raised to incandescence it could cool again in so short a time as two minutes. I think it far more probable that that most wonderful phenomenon (affecting as it did the entire earth) was due to the collision of two bodies revolving in approximately opposite directions around the sun. Such a pair of bodies would have their temperature raised to about one hundred million degrees Centigrade. I need not say that such a temperature would quickly volatilize such small bodies and produce an intense light, the phenomenon is in this way explained without any assumption other than known laws. The basis of the meteoric hypothesis is thus shown to be in the highest degree improbable, and even if it were admitted it would require an inconceivable number of meteors to raise the atmosphere of a dark body to such a temperature as to produce a luminosity as great as our sun's and of some months' duration. Still more inconceivable does it appear that the body upon which they impinge should only have its atmosphere raised to such a luminosity, whilst the body itself remained non-luminous. Altogether the theory of Meyer and Klein appears the only possible one, but it is only when both bodies are of such stupendous dimensions as to produce complete volatilization that the hypothesis agrees with spectroscopic observation; and such a case does not appear to be contemplated by the authors or they would scarcely have suggested a planet. Complete dissipation into space could not take place by the entire coalescence of two bodies however large, unless they had a higher initial velocity than observations of the proper motion of stars render probable. No one of these hypotheses, therefore, appears to be a satisfactory explanation of the phenomenon.
An hypothesis that agrees better with observation would be one of partial impact. If two immense bodies moving in space come well within
the influence of each other's gravitation, they would be attracted out of their path with a constantly increasing velocity. Three possibilities present themselves: the first, the most general one, of passing each other and ultimately attaining their original velocity in space; the second would be that of imperfect impact; and third, as an extreme case, we should have complete impact when the centre of each mass would have, except for the collision, occupied the same point at the same time. It is reasonable to assume that in impact the case of partial collision would be more probable than complete impact. And it is this imperfect impact that is the basis of the present hypothesis. In this case a piece will be struck off each colliding body; these two pieces would to a greater or less degree coalesce, developing at the same time a high degree of heat, whilst the remainder of the two bodies would pass on in space. What would finally happen to the two retreating bodies depends on the original proper motion and the masses of the coalesced piece. If the original proper motions were large and the piece cut off small, one or both of the two bodies would most likely pass entirely away from the other bodies and travel on independently in space. If, on the other hand, the original proper motion were small and the piece struck off large, then it would be most probable that they would be once more attracted back and collide again and again until complete coalescence took place; or, as I shall show further, it is possible that they may form a system similar to our solar system. The size of the bodies will also have an influence in the escape or otherwise of the pieces. Other things being equal, the larger the body the greater the probability of escape, as the distance between the centres will be greater and consequently the attraction will be less.
Partial impact appears competent to explain the occurrence of temporary, double, and variable stars, nebulæ of various kinds (the kind depending on the nature of the impact), comets, and finally stars or suns accompanied by bodies of smaller size. The third case, that of complete coalescence, is probable only in the collision of very large bodies, and offers an explanation of the existence of large spherical nebulæ with a general condensation towards the centre. (We will consider the hypotheses somewhat in detail.) In order to render the conception of the hypothesis as simple as possible, I shall all through keep as far as I can to a direct conception of energy, as in this way most questions may be reduced to ordinary arithmetical series. Thus, if the two approaching bodies be equal to each other (at the same distance), the attracting force acting on each unit of mass will be proportional to the total mass of either; now in a force acting through space, the work equals the force multiplied by the space through which it acts, and the work is equal to the heat.
The sun, by attracting a body from infinite space, would give it a velocity of 378 miles a second, or each unit of mass would develope about forty million units of heat. If we suppose two bodies, each half the size of the sun, to come together by mutual attraction alone, then each unit of mass would develope about twenty million units of heat. If, on the other hand, two bodies twice the mass of the sun come together, each unit of mass would have four times the force acting upon it through equal spaces, and each unit of mass would consequently develops four times as much heat. If the impact of such bodies were imperfect, as we have seen the general case would be, a piece of each would be cut off, and these two pieces would coalesce. Suppose a quarter of each be struck off, a body of the mass of the sun would be produced, but it would have four times the temperature the sun would have, assuming the sun to have been formed by direct impact and complete coalescence. Each unit of mass in this case would have approximately eighty million units of heat; and the temperature will depend upon the specific heat of the material, and may be much higher than this.
I will now show, in the case of partial collision, how small relatively the work of cutting off the piece is compared to the energy available. It appears to me that in all cases the energy needed for shearing force has its superior limit in the latent heat of fusion. This, in the case of ice, is about one-fiftieth that of combustion, and combustion is about one twenty-thousandth part that of percussion, in the case we have been considering. The work of shearing would consequently not be greater than one millionth that of the energy of velocity, and so it appears it may safely be disregarded. Thus in the case of such a partial collision it may certainly be accepted that those parts not in the line of motion of the other body will not coalesce with the other body, but will pass on in space. In the piece struck off we shall have partial destruction of motion in space, with development of heat; many pieces will fly off, and a rotary motion of the whole will ensue. There will be a slight pause from inertia, then the powerful outward pressure due to the expansion by heat will overcome all resistance, and will expand the whole into gas, much of it certainly passing beyond the limits of effective attraction, and away into distant space. Let us pause for an instant to examine a little more fully what has happened.
Two pieces of different bodies, each with a velocity of about 500 miles a second, have coalesced, but although the motion of translation is destroyed the larger part of each side of the mass is made up chiefly of one of the two different bodies: as these are moving in opposite directions, there is consequently a couple acting on the mass, and this couple spins the mass on its centre. Consequently many pieces fly off, and are followed by the mass of gas, being impelled outward by the energy of heat and centrifugal force;
whilst, on the other hand, we have inertia and gravity tending to keep the mass together. The centrifugal force acts only in one plane, whilst the repellent force of heat acts in every plane; a bun-shaped mass must result, with a number of distinct pieces, which at first at least are in advance of the general mass. Follow it on in time and we get the ring nebulæ, with or without a luminous centre; in the latter case, with a dark circle dividing those parts whose velocity has carried them beyond the powers of the attractive force, from those parts held prisoner by it. These parts, as they gradually radiate heat into space, are once more slowly attracted to the centre by gravitation. If the piece struck off from each body were very small, then complete dissipation of the whole into space would result. Clearly such collisions as I have described would be competent to produce every variety of temporary stars that has appeared. Applying the spectroscope to such a star, we get at first a continuous spectrum; then black lines, quickly followed by bright lines and spectrum; then bright lines alone. Again, if the colliding bodies were of very different size, or if the heat were not great enough to entirely volatilize the star, we should have lines and spectrum. Lastly, as heat and pressure diminish by the dissipation of the body into space, we get fewer and fewer lines, until only those substances in greatest quantity, or of greatest power in giving lines at lowest temperature and pressure, remain luminous, and we have a nebulæ left; or in the case of total dissipation of the gaseous mass all evidence of its existence will disappear. It will be seen how exactly the above hypothesis agrees with the spectroscopic observation of temporary stars; and I have shown as fully as perhaps it is wise to do in this paper, that the hypothesis of partial impact is competent to account for every variety of these bodies, and also for their intensity and short duration.
We must now return to the parent bodies which we left travelling on in space. A cylindrical or curved slice has been cut out of each; sometimes that is the chief thing that will happen. But on the other hand we may have the molten interior of the body exposed to view. If there were atmospheres on the two colliding bodies, a very great heating of the surface of the section would result, and when both causes are acting in unison a stupendous lake of fire must be formed. Let such a body rotate on its axis, alternately the light and dark sides are shown, and we get a variable star. May not Mira in this way be attempting to tell us her autobiography; how she is a dark body, with a molten lake of fire, 30 degrees of arc, a lake as big as our sun, and how she rotates about an axis in a little less than a year? If it be so, she tells us of a dark body almost as large as Sirius, or how would 30 degrees of arc produce a star of the first magnitude? Algol appears to tell us that it is a dark and gloomy parent, with a brilliant son who periodically passes
partly behind his dusky parent's body, and in this way suffers partial eclipse.
But the autobiographies of these bodies must not detain us; we must discuss the existence of such gigantic feebly-luminous or non-luminous bodies as our hypothesis demands. The existence of variable stars seems sufficient to prove there are such bodies, and, as I have shown, all the hypotheses offered in explanation of temporary stars assume their existence. The high temperature and small relative light of celestial radiation points to the same conclusion, or to non-luminous gas. It might be asked, if there are dark bodies, why not stellar eclipse. I do not know if such have been observed; it would be wonderful if any had been, for they must be very rare, probably as rare as temporary stars; for, although we have all the depths of space in which eclipses are possible, on the other hand with temporary stars we have attraction bringing very distant bodies together. Further, the points of light of the fixed stars form but a small area in space, and, lastly, if eclipses occurred they would probably not be recorded, as small black patches of cloud so often obscure a portion of the sky that such an occurrence would scarcely attract attention. But why should there not be large dark bodies? Laplace's theory of a universal nebulæ may be assumed to be against it; but did Laplace assume that it was contemporaneous? if not, then even that theory does not interfere. All our conceptions seem to agree more with a rhythmic cycle than with any definite beginning or end. If we assume this hypothesis, then the period of dissipation of energy seems indefinitely projected into futurity; for all radiation falling on the matter in space, must prevent its temperature from falling so low as without this radiation, and when at a subsequent date a collision occurs, this heat must exalt the final temperature. Nor does it appear that we need look forward to a gigantic dead sun as the final condition of this universe; for doubtless our universe has its own proper motion in space, which may bring us into collision with other universes. This shows that gravitation may be as competent to multiply worlds as to absorb them one into another. But after all our hypothesis only takes us a step back in time, and our imaginations a step forward into the future, thus removing further than ever from our conceptions every trace of a beginning or promise of an end.