Star-streams
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Questo testo fa parte della raccolta Scientia - Vol. VIII
STAR-STREAMS
At most of the principal observatories of the world, at least one telescope is devoted continually night after night to the task of measuring the positions of stars on the celestial sphere. At the rate of from ten to twenty stars an hour for each instrument, this work of determining and redetermining the positions of the stars proceeds at stations distributed all over the world. After long reductions, the labour of which far exceeds the labour of the observations themselves, the results are embodied in the star catalogues of the various observatories. Finally from the comparison of observations separated by long intervals of time, data have been collected showing the minute changes of position of the stars among themselves. It is these data, so laboriously obtained, which form the foundation of the theories and deductions here described.
In 1718 it was first shown definitely by Halley that motions and displacements were occurring among the so-called « fixed stars »; and from that time the study of these motions has been one of the principal tasks of sidereal astronomy. I suppose that something like half a million stars are bright enough to be well within the reach of the ordinary meridian instruments. But at present it is only for samples of these that information as to the motions is available. Modern observations are abundant, though by no means exhaustive; but for the majority of stars the changes of position are so minute that it is necessary, before they can be detected, to extend the observations over a very long period. It is well to form some notion of what these displacements amount to. The star which appears to us to move faster than any other is an insignificant object in the southern sky far too faint to be visible without a telescope. This star traverses a space equal to the apparent diameter of the full moon in about two hundred years. If the majority of stars had speeds at all approaching this amount, the detection of their movements would not be difficult; but it is not so. Not one in seventy of the stars visible to the naked eye has so much as one fiftieth part of this speed, and for telescopic stars the proportion is much smaller. An average star might be expected to take say 50.000 years to move over a space in the sky equal to the moon’s diameter. Of course it is on account of the excessive remoteness of the stars that their motions appear so small; judged by terrestrial standards the real speeds are prodigious. The average linear velocity of a star is about 34 kilometres per second.
From the time when the first measures were made of the proper motions, up to near the close of the nineteenth century attention was principally, almost exclusively, devoted to one fascinating problem, the determination of the motion of our own system with respect to the stars. This, and not the study of the relations of the stellar motions to one another, was the main subject of investigation. When the statistics are collected and examined, it is noticed that in the main the stars are moving towards a point of the heavens in or near the constellation Canis Major. The motions of the individuals vary widely, but if the mean of a number of stars is considered, it is practically always possible to detect this tendency. It is as though we were looking at a swarm of gnats, the individuals buzzing in all directions, but the swarm as a whole proceeding steadily in one particular direction. Now in sidereal astronomy we leave behind our ordinary standards of rest; there are no fixed points; the relativity of all motion insists on being recognised. It is immaterial whether, the solar system being at rest, the star-swarm moves towards Canis Major, or whether, the star-swarm being at rest, the solar system moves in the opposite direction towards Lyra; the apparent motion of the stars is the same in either case, and we have no means of testing, or recognising, or even conceiving absolute rest or absolute motion. The second point of view, that the phenomenon is really due to a motion of the sun towards Lyra, is a favourite one; it recognises the insignificance of the solar system in the universe; but it is not necessarily a truer point of view. This « solar motion », as it is called, belongs neither to the sun nor to the stars intrinsically; it is a purely relative motion attributable equally to both.
With the more complete data of recent times, the determination of the solar motion, though still attracting great interest, has come to be regarded as fairly settled. At least it is realized that whatever uncertainties and discordances remain will be best cleared up by studying the peculiarities of the distribution of the individual motions of the stars. For the precision with which the solar motion can be determined depends inter alia on the precision with which we can define the conception of the « mean of the stars », to which the motion is supposed to be referred.
What then are the principles which govern the distribution of stellar motions? In the solar system we see a group of celestial bodies, the planets, strongly under the control of a central body. The clearest evidence of this control is manifested in the shapes of their paths. But an intelligent observer might discover, simply from the instantaneous motions of the planets, that here was not a mere haphazard aggregation, but something of the nature of a system. He would notice, for instance, that each planet moves nearly at right angles to a radius drawn from the sun, and with a smaller velocity the greater the distance? a clear indication of rule and order. Is there anything even remotely analogous in the stellar universe? Anything discoverable in the statistics of the motions, which might lead us to suspect that the universe around us is not a purely haphazard aggregation of independent units? When we realize how vast are the distances which separate one star from another, and how excessively minute must be their mutual attractions, it seems almost useless to look for any such relations. But, as we shall see, relations are found to exist; not the close ties which bind the planets to the sun, but still broad traces of structure which differentiate the universe from an entirely haphazard aggregation.
Although it had been usual in researches on the solar motion to make the assumption that the motions of the stars are haphazard and directed with impartiality in all directions, astronomers had long been dissatisfied with this hypothesis. It may seem strange that comparatively little effort was made to examine directly how far the truth differed from it. Insufficient data and other difficulties prevented a satisfactory study of the question; but probably the chief cause of neglect was the not unnatural opinion that any deviations from a haphazard distribution would be found to be complicated and differ from one part of the sky to another. It was not suspected that, over and above the local deviations, there might prevail everywhere a simple law in the distribution of the motions.
Of local irregularities various examples have been pointed out, where evidently associated groups of stars share a common motion more or less exactly. As might be expected the closely congregating stars of the Pleiades move together in this way; in the same constellation Taurus there is another more extensive but similar association of stars. Still more curious is the group formed by five out of the seven stars of the Plough (Ursa Major) together with Sirius, in which there is a remarkable community of motion, although the stars are by no means close together. It would seem that these six stars are in some way associated in their origin, and retain their original common velocity almost undisturbed by the rest of the stars, which not only surround but thoroughly interpenetrate the system. In dealing with statistics of stars, it is necessary to bear in mind the existence of these and other local streams. Any general law of distribution will evidently be subject to deviations due to this cause. If however a sufficiently large number of stars is considered, the disturbing effect of a local stream is generally very slight, and does not mask the more general law of distribution.
The examination of the motions of the stars, which first showed in their distribution an important systematic feature prevailing in all parts of the sky, was made by Prof. J. O. Kapteyn of Groningen. He arrived at the surprising result that the stars form two great streams moving through one another. As the result of his researches and those of subsequent investigators, the motions and characters of these streams are now known with some degree of definiteness. We shall presently indicate how it has been possible to recognise the presence of these streams from a study of the observed stellar motions; but in the first place, it may be well to state the principal results arrived at.1 One of the two streams is moving (relatively to the sun) towards the point E. A. 93° Dec. -7°; this is generally called Stream I. The other, Stream II, is moving towards E. A. 246° Dec. -64°. The velocity of Stream 1 is to that of Stream II in the ratio 3:2; the actual velocities are in fact about 40 and 26 kilometres per second. It will be noticed that the two streams are proceeding in widely diverging directions, being inclined at about 110° to one another; but this angle entirely depends on the point of reference (in this case the sun) to which the relative motions are referred. Looked at from some other star the angle would be altered, so that from the cosmical standpoint the apparent inclination of the two streams has no particular significance. The stars appear to be fairly equally divided between the two streams, a result which holds not only when all the stars are considered together, but for the different parts of the sky separately. Moreover the mean distances of the stars of the two streams from the sun are everywhere nearly equal. This means that the streams completely interpenetrate one another. It is as though two systems of stars were passing through the same part of space entirely ignoring the presence of one another. It is important to grasp this very essential part of the theory because several attempts to explain the phenomenon have broken down at this point. A rotating motion of the stellar universe seen from an eccentric point would perhaps account for two streams, the one passing behind the other; but it does not explain the two streams permeating each other. As regards the number of stars coming within the scope of this theory, we have of course no knowledge of the motions of the many millions of faint stars visible in the great telescopes: but, so far as can be learnt from the samples available, the stars down to the ninth magnitude and even fainter appear to conform to this arrangement. We may estimate that each stream has at least a quarter of a million members.
We may regard the two streams as two independent systems of stars travelling through space, and at the present time passing through one another, perhaps brought together by their mutual attraction; or it may be possible to explain the streaming of the stars in the two favoured directions as due to some other cause which does not postulate a dual origin for the universe. But in either case it is clear that this new presentation differs very markedly from the old idea of a chaos of stars moving at random; and the existence of the two streams is an evidence of structure of a very unexpected kind.
Whilst the statements contained in the foregoing paragraphs are the results of mathematical investigations which could not well be described here, it is possible to indicate in a general way the peculiarity in the distribution of the stars’ motions which led to the detection of the streams. Suppose that in a small region of the sky there are a few hundred stars whose motions have been observed, and that we count how many of these are moving in the various directions. If the group considered consists of stars moving at random, it might at first sight be expected that the observed motions would be in approximately equal numbers in all directions. But this leaves out of account the fact that the group taken as a whole will probably be in motion relatively to the solar system, which is our point of observation. We have already referred to this matter in connection with the solar motion. The fact is that when we speak of a group of stars moving at random, we mean that their motions relative to one another or to the mean of the group are at random; when referred to some independent point such as the sun, the resultant motions cease to be strictly at random for there is, as it were superposed, a systematic motion, namely that of the group as a whole relative to the sun. Let, for example, this motion of the group of stars as a whole be towards the north, each star having in addition its own haphazard motion with respect to the rest; evidently the effect of the group-motion will be that, although stars may be found moving towards all points of the compass, the greatest number will be moving north, the fewest south, the number falling off symmetrically on either side from north to south. But it is possible to advance a stage further. If the motions of the individuals are entirely haphazard (controlled by no law) the tout ensemble will yet be subject to that most paradoxical of laws, the law of chance; and it is possible to predict, at least tentatively, what proportion of stars will be moving in any direction, having given only the direction of the group-motion, and its numerical amount (compared with the average haphazard motions of the individuals). Reversing the process we can test our observed proper motions to see whether they can be accounted for in this way; and if it is found that they do correspond to a haphazard group, we can deduce mathematically the direction and amount of the motion of the group as a whole.
When this test is applied to the observations it becomes plain that there is some very considerable deviation from the haphazard distribution. The differences are fundamental, so that the true law of stellar motions must be something radically different from the law of chance. Even the first condition fails utterly; it is found that the direction in which fewest stars are moving is not by any means opposite to that in which the maximum number move. Moreover there is generally besides the chief maximum a secondary maximum in another direction. We will take as an example the stars of Cassiopeia and parts of neighbouring constellations. Indicating directions by position angles running from 0° to 360°, it is found that the greatest number of stars are moving in the direction 10°. Therefore if the individual motions were governed only by chance, the fewest should be moving in the direction 190°, and the motions should be distributed symmetrically on either side of this direction. Now compare this with the facts; the actual minimum is in the direction 275°, very nearly at right angles to, instead of opposite to, the direction of maximum. The numbers are:
tor 66 stars moving in the direction 10°,
there are 17 stars moving in the direction 190°,
and only 6 stars moving in the direction 275°.
Nor is there any approach to symmetry about the direction of maximum; on the one side there is the rapid decrease from the maximum 66 to the minimum 6 followed by a steady rise to 17; on the other side the number falls more slowly to 19 in the direction 95°, then rises to a secondary maximum of 26 moving in the direction 135°, and falls again to 17 in the direction 190*. These peculiarities can be best seen by reference to Fig. I., in which the distance from the origin to the curve represents the number of stars moving in the corresponding direction.
Other regions of the sky show similar results. The existence in many cases of a secondary maximum hints clearly at the interpretation of the phenomenon, ― the motions of the stars show a preference for two favoured directions. We
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Fig. I
have seen that a preference for one favoured direction merely indicates a motion of the system as a whole with regard to the sun, and is not inconsistent with a haphazard distribution of the motions relative to one another; but a preference for two favoured directions of motion is a very significant peculiarity. We can hardly be wrong in considering it to indicate the coexistence of two streams of stars, using the word stream in a general sense; there is of course an element of hypothesis admitted, when we assume that each stream is a more or less independent stellar system.
Acting on this clue, we now assume that instead of dealing with one system of stars having haphazard motions, there are two such systems, these systems having different motions with respect to the sun. The theoretical distribution of the motions of the stars can be calculated for each system separately and by adding the results together, we arrive at the distribution to be expected from the combination. The success of the hypothesis of the two star-streams in accounting for the observed data becomes very striking when a numerical comparison of observation and theory is made. It is found possible, by choosing suitable directions, velocities and relative proportions of the two streams, to build up from the combination a theoretical distribution of motions agreeing almost precisely with the observed one. This process has been carried out, more or less as here described, for a considerable number of regions of the sky, and from it results our knowledge of the velocities and directions of the streams. It is necessary to remark that what here concerns us is motion projected on the sky, that is transverse motion. As attention is turned from one region of the heavens to another, the stream motions will present themselves in different aspects. For example, there are two points of the sky where the transverse motions of the two streams are identical, and the only difference is in the radial motions, with which we are not here concerned. At these points it would be impossible to detect the presence of two streams, and the individual motions would seem to be haphazard. The full information as to the streams can only be found by comparing results from different parts of the sky.
In order to form a clearer view of the significance of the phenomena now revealed, let us abandon the solar system, which has hitherto served as the reference point, and transfer ourselves to the centre of gravity of the stars here considered. Looked at from this point the streams must be moving in directions exactly opposite to one another. It is perhaps not easy to realise that the inclination of the two star-streams is a purely relative phenomenon depending entirely on the point of reference chosen; but this is the case. If we divest our minds of all standards of rest, and contemplate simply two objects in space, the two star-streams, all that can be said is that they are moving towards or away from or through one another along a certain line. This line, the direction of relative motion of the two streams, is a very important and fundamental axis; for it is an axis of symmetry of distribution of stellar motions. The points in which it meets the celestial sphere are called the Vertices. If, as seems to be the case, the number of stars belonging to the two streams is the same, the velocities of the two streams referred to the mean of the stars must be equal. The results, regarded from this new standpoint, can be given numerically. Each star has a streamvelocity of about 26 kilometres per second directed towards R. A. 5h 44m, Dec. 24°, or towards the opposite point according as it belongs to Stream I or to Stream II: in addition it has its own peculiar motion, equally likely to be in any direction, and averaging about 28 kilometres per second. This is the fact that emerges when we have abstracted from the results and thrown aside whatever has peculiar reference to the Sun, and has not a general cosmical importance.
A somewhat different conception of the distribution of stellar motions has been put forward by Professor Schwarzschild. His theory is rather difficult to describe in non-mathematical language and we have therefore preferred to keep to the older point of view of the « two-drift theory » in this article; but it is clear from his researches that it is the existence of the axis of symmetry of the stellar motions, mentioned in the last paragraph, rather than the division into two distinct systems, that is the fact directly indicated by the observations. Professor Schwarzschild showed that a « spheroidal distribution of velocities » (a kind of haphazard distribution modified by the assumption of greater mobility in the direction of the axis of symmetry) would agree very satisfactorily with the observed results. Although his theory contemplates the universe as single, instead of as composed of two distinct systems, there is really but little difference between the actual distributions of the motions, which the two theories formulate, They express nearly the same law, but by the aid of different mathematical functions. Their relation has been well summed up by Professor Dyson. « The dual character of Kapteyn’s system should not be unduly emphasized. Division of the stars into two groups was incidental to the analysis employed, but the essential result was the increase in the peculiar velocities of stars towards one special direction and its opposite. It is this same feature and not the spheroidal character of the distribution, which is the essential of Schwarzschild’s representation. »
The position in the sky of the line of relative motion of the two streams is not without a deep significance, for it lies accurately in the plane of the Milky Way. The course of the Milky Way in the heavens marks out a plane towards which the stars show a strong tendency to crowd. It seems a little curious that, whereas the principal feature in the distribution of the stars themselves is the existence of this plane of symmetry, the principal feature in the distribution of their motions is the existence of an axis of symmetry. That the axis should lie in the plane might perhaps have been anticipated, but it is none the less important to have discovered this relation between the two phenomena.
In a description of a branch of investigation which is yet barely five years old, there may well be much that future researches will revise, or at least present in a different light. In certain details discrepancies occur between the results of different investigations, which may be due to defective data, but which may on the other hand point to complications in the phenomena, which have not yet been grasped But at least we may believe that a first approximation has been reached; and the recognition that the stars distributed throughout vast regions show common tendencies and associations is a remarkable advance in knowledge. We recognise organisation beyond the limits of the single star and beyond the clusters of associated stars. A tie which points to some community of origin or experience prevails to the farthest limits discoverable. The new theory may indeed divide the universe in two, but it unites the individual stars in a way hardly dreamed of hitherto.
Greenwich, Royal Observatory.
A. Stanley Eddington
Note
- ↑ The numerical results adopted in this paragraph have generally been taken from Prof. Dyson’s papers.