William Hammond Wright "On a Proposal to use the Extragalactic Nebulae in Measuring the Proper Motions of Stars and in Evaluating the Precessional Constant," Proceedings of the American Philosophical Society 94 1–12 1950

The Galaxies as Anchors for Stellar Proper Motions

By William Hammond Wright

Among the more important problems that invite the attention of the astronomer are those within the field of stellar dynamics; they relate to the structure of the Galaxy as a whole, and to the positions, masses, and velocities of its component stars. When one deals with positions and velocities, it is necessary first to establish a reference system—a system of coordinates if you will—with respect to which these positions and velocities can be measured. In our everyday experience we are, by force of circumstances, obliged to employ a variety of systems of reference for positions and motions: the surface of the earth, the walls of a room, the interior of a vehicle under acceleration and so on.

The astronomer is provided with no ready-made system that enables him to square himself precisely with the millions of stars, the planets, and the rapidly moving comets with which he is confronted, but has managed to use planes and lines that are determined by the stars on the assumption that these apparently slow moving objects, at least, move at random, that is to say as much in one direction as another, and this means that, taken as a whole, the system which in their aggregate they compose may be regarded as without sensible rotation. Coordinate systems based on this assumption have served very well in measuring the comparatively rapid motions of the planets and comets in their travels across the heavens, but how far may they be trusted in measuring the extraordinarily small movements of the stars themselves?

That this is a valid question will be realized when we recall that the revolutions of the planets about the sun are expressible in quantities of the order of degrees per day; the angular motions of the stars, on the other hand, are as a rule less than one second or arc per century. The ratio between these two quantities is, in round numbers, 130 million to one. It is therefore comprehensible that a framework of reference which does very well for planetary motions might not be altogether adequate for the study of the extraordinarily minute motions of the stars themselves.

Consider, for example, one of the more important problems in the field of stellar dynamics: the measurement of the rotation of the galactic system of stars. The most obvious approach to the solution of this problem is through the proper motions of the stars. But the coordinate system with respect to which these proper motions are measured has been determined on the hypothesis that the stars are moving at random, which is but a way of saying that the stellar system is without rotation. Recourse must then be had to special assumptions of one kind or another. Much ingenuity and labor have been directed toward the calculation of the galactic rotation, and there is no desire here to disparage in any way the results that have been achieved in that direction. Nevertheless it would seem desirable to approach the problem by a line of reasoning whose fundamental premise did not deny that the problem exists.

The whole question of stellar proper motions would be much simpler were it not for the precession of the equinoxes which, you will recall, imposes a conical motion of the earth’s axis among the stars. This excursion of the axis has been likened to the motion of the axis of a dying top. The period of the motion is about 26,000 years. Now the unfortunate part of this is that the measurement of stellar positions is necessarily made with reference to the earth’s axis and to the plane at right angles to it; that is to say the measurement is made with respect to a system of coordinates that is continually rotating with respect to the general system of the stars. As a consequence when observations of position are made at two different times, or epochs as they are customarily called, in order to determine the proper motion of a star, it is necessary to allow for the motion of the earth’s axis during the interval between the two observations, especially since the amount of this motion will generally be a thousand or more times as great as the proper motion of the star itself. The amount of the precessional motion is about 50" per annum. The cause of it is well understood, and its amount would be calculable from the figure and content of the earth, the mass of the Moon, and other astronomical data were they known with sufficient accuracy for the purpose. Unfortunately we do not know the shape and structure of the earth, nor the Moon’s mass, well enough to support a calculation of the precessional motion. It has therefore been necessary to determine the precession from the stars themselves. To a logician this would appear to be begging the question, and it is. The saving grace—if in logic there be one—is that there are a great many stars in the sky. If we choose a sufficiently large value of the precession, all of the stars may, on paper, be made to revolve in one direction; too small a value will cause them to go in the opposite direction. For an intermediate value some stars will revolve one way and some the other. What is usually done is to choose a value of the precessional motion which will make as many stars seem to move one way as the other.

The precession was discovered in the year 130 B.C. by the Greek astronomer Hipparchus, who provided the first estimate of its amount; it has been re-evaluated many times since. The value now generally used is that derived by Simon Newcomb in 1898, and I venture to quote the opening paragraph of his discussion, as it closes with a note of prophecy which was soon to be fulfilled:

"In his determination of the elements of the four inner planets and the fundamental constants of astronomy the author was constrained to content himself with a provisional determination of the precessional constant, which be was afterward led to fear might prove too small. One reason for yielding to the pressure of circumstances in this connection was that the constant of precession is of such a nature that a small error in its determination will not seriously affect our general conclusions as to the positions and motions of the stars and planets, such an error being eliminated through the proper motions of the stars and the mean motions of the planets. Indeed, the fact of this elimination is one of the reasons why a satisfactory determination of the constant is difficult. There is, however, a class of researches which must come into prominence in the not distant future, to which the accurate determination of the precessional motion is a necessity. I refer to researches having for their object the determination of absolute and relative motions in the universe at large."

Some six years after the publication of Newcomb’s paper, Kapteyn, from a study of proper motions in various parts of the sky, showed that the stellar motions are not, in fact, at random. He found preferential directional trends in various parts of the heavens, which he assumed to be due to the occurrence of two star streams. These preferential trends disappear of course when summed over the whole sky because the precessional constant has been so chosen as to make them do so. There is no occasion here to go into the theory of star streaming as developed by Kapteyn and his followers; the point to be emphasized is that Kapteyn’s observations showed that the stars are not moving at random. If they are arbitrarily constrained to the hypothesis of random motion for the whole sky they break out locally. Is it logical to admit preferential motion in large areas of the sky, and at the same time to accept random motion as the fundamental hypothesis of dynamical astronomy? In any event does it not seem desirable to inquire whether some system of reference might be established which would circumvent the necessity of making any assumption whatever regarding the proper motions of the stars themselves?

In these circumstances one naturally turns to the extragalactic nebulae [galaxies] which lie far beyond the limits of our stellar system, and can probably be counted upon to be uninfluenced by the motions of the

stars that comprise that system. The matter has been the subject of some discussion in the literature, especially in recent years, on the part of astronomers in various parts of the world. This paper constitutes in effect an inquiry into the practicability of using the extragalactic nebulae as the material anchorages of a system of astronomical coordinates. A brief historical sketch of a current undertaking at the Lick Observatory directed toward that end may not be out of order.

I first entertained the idea of using the nebulae for the purpose just indicated in 1916, when it was coming to be realized that the spiral nebulae lie outside the Galaxy, but there was at that time no telescope at the Lick Observatory—nor in fact anywhere else—with which a research in that direction could be undertaken with hope of success. The

observations would require a photographic telescope, or camera, of relatively wide field, so as to include a sufficient number of catalogue stars, as well as a lens of large linear and large angular aperture which would record small faint nebulae in the necessary abundance. Indeed it seemed questionable whether a lens of the requisite quality could actually be made. However, about the year 1920, Dr. Frank E. Ross designed a lens of comparatively large angular aperture which gives a very fine field, and thereafter the problem was much in mind. In 1934 these considerations were brought to the attention of the Carnegie Corporation of New York by Dr. R. G. Aitken, then Director of the Lick Observatory, and that organization very generously made provision for the construction of a 20-inch (50 cm) photographic telescope and a suitable observatory in which to house it. The lens was calculated by Dr. Ross. The construction of the telescope and the development of the project have been greatly hampered by the war, and the disturbed conditions that are following it, but one tube of the telescope has been completed, and satisfactory photographs are now being taken with it. At the present time the full equipment of auxiliary instruments for the measurement of the photographs has not been completed, but enough apparatus has become available to test the various observational procedures at the critical points, and more particularly to check the effects of departures from routine observational practice that have been imposed by the unusual conditions of the problem. These critical checks are vital to the success of the undertaking, and will be referred to later in this paper. For the moment I trust that I may be permitted to pass them with the comments that they seem quite satisfactory, and to proceed with a general account of the observations.

Stated in simplest terms the undertaking includes the following procedures:

A set of photographs is taken which covers, piece by piece, all of the sky that can advantageously be observed from Mount Hamilton. After a suitable lapse of time, which will be many years, another set will be taken for comparison with the first. The future observer will take up a pair of photographs of the same region of the sky, one from the first and one from the second series. These will each show several thousand stars, of which perhaps 15 or 20 will be catalogued stars in whose motion we are especially interested. There will be, let us assume, 50 measurable nebulae on the photographs. In the interval between the taking of the plates the relative positions of the stars with respect to one another and to the nebulae will have changed. It is assumed that the nebulae, because of their enormous distances from our stellar system, will have remained substantially stationary on the celestial sphere. A correction is therefore made to all the measured positions—nebulae and stars alike—such as will cause the displacements of the nebulae to vanish. The resulting discrepancy in the position of each star, corrected where necessary for parallax, will then be regarded as its proper motion during the interval between the taking of the photographs. The question of precession of the equinoxes does not enter. . . .

In the foregoing comments I have tried to indicate the need that has arisen for a system of astronomical coordinates that is free from the assumption of random motion of the stars, and have outlined in a very informal way the theoretical basis for such a system. It is now in order to inquire whether the observations and technics suggested for realizing the proposed system of coordinates are competent; whether the plan will work. That the difficulties are serious is indicated by the fact that the proposed system, or something like it, has not actually become established. I have already taken the liberty of referring to my early interest in the problem some thirty years ago, and to the lack of suitable equipment for undertaking it. So obvious a notion as that of using the extragalactic nebulae to check the proper motions of the stars must have occurred to many persons. . . .

[From the Summary] The instruments and observational procedures employed in the work at the Lick Observatory are described as fully as seems necessary for the purposes of this paper. It appears that there are many thousands of nebulae distributed over approximately three quarters of the sky, whose positions can be measured photographically to the same order of precision as the places of stars are measured with the meridian circle. These nebulae are deemed sufficient to provide reference points for as many stellar proper motions as may be required. . . . It is anticipated that the proper motion stars will be limited to magnitudes 6.2 to 8.2, though material will be available for the calculation of the proper motions of stars between magnitudes 10.2 and 12.2.

The conclusion is drawn that the project is feasible, and will, with the collaboration of meridian astronomers, result in the establishment of a practicable system of coordinates positioned by the extragalactic nebulae.