RETHINKING THE HISTORY OF SOLAR WIND STUDIES: EDDINGTON'S ANALYSIS OF COMET MOREHOUSE

Introduction

Sir Arthur Eddington's early career differed considerably from his later career in many respects. Most generally, his early years focused quite heavily on dynamical astronomy,1 whereas his later career was devoted to the study of stellar structure and cosmology.2 He was a Smith's prize winner for an essay on the proper motions of stars and for a few years was employed at the Royal Observatory, Greenwich. From 1907 he also held a fellowship at Trinity College, Cambridge, setting the stage for his later career as Plumian Professor of Astronomy and Experimental Philosophy and as Director of the Cambridge Observatory. It was at Greenwich, however, that he analysed the envelopes (outgassing) of Comet Morehouse, a non-periodic comet discovered by the American astronomer Daniel Morehouse at Yerkes Observatory in 1908. Eddington's analysis did not appear in print for another two years,3 perhaps underscoring how truly difficult it was to understand the nature of the motion of the material ejected from the comet.

However, my analysis is concerned with the content of that article with regard to the comet itself and to the solar wind. Eddington's motivation in discerning a mathematical description of the shape of the envelopes was clearly to use it as a method for elucidating the apparent repulsion experienced by comets near the Sun. He was not at all concerned with the source of the outgassing itself, which provided the material that formed the envelope. In particular, he was attempting to verify a theory already developed by Bredichin, Bessel, Bond and others4 in previous years. Because his analysis was primarily a justification for this theory, which Eddington referred to as the ‘fountain-theory’ of envelopes, it was, perhaps, understandably overlooked until much later. However, a reanalysis of both this paper and the text of an earlier presentation of his unfinished work5 provides new evidence that Eddington was tantalizingly close to making a breakthrough that ultimately would not be fully explained for another four decades. In fact, the closest restatement of his conjecture came in 1951 by Ludwig Biermann, though Biermann did not cite Eddington.6 Before introducing this conjecture, however, it is first necessary to take a closer look at Eddington's analysis and the progress that has been made since that time.

Methods of analysis

Eddington was working with photographic plates taken at the Royal Observatory. In an inexplicable move, he never included any of these photographs in the paper, at least in the format in which it appears in Monthly Notices of the Royal Astronomical Society. Other papers in the same issue include photographs, and thus the lack of them in Eddington's paper does not seem to be due to any pre-existing editorial policies at the journal, although it is certainly possible that the lack of photographs represents an ad hoc editorial decision. Eddington's measurement of the photographs was made with a position-micrometer with a low-power eyepiece. This is, essentially, a microscope that allows one to measure minute distances by slowly moving the eyepiece from side to side. Measurements were most often taken in millimetres and thus, when measuring photographs, scaling was required. These devices are still relatively common in educational settings, although they are rarely used for research purposes.

In Eddington's case, the position of the radius vector from the Sun was independently computed (although no indication is given as to the method of computation employed here) and the photographic plate was oriented in the position-micrometer such that it was coincident with (parallel to) the micrometer screw, which was a long screw designed to move the eyepiece laterally in sub-millimetre increments. This was to align the diaphragm in the microscope's eyepiece with the envelopes themselves. The diaphragm was ruled with two fine lines intersecting at right angles in the middle of the eyepiece. These lines were aligned such that each became a tangent to one side of the envelope. In describing this, it is clear that Eddington was working with the pre-existing assumption that the envelopes would be parabolic in two dimensions. Thus, the lines met at the intersection of the axis and directrix of the parabola formed by the envelope. Moving the micrometer from the nucleus of the comet to the vertex of the envelope and then to the directrix would give two independent measurements of the focal length, because the distance from the vertex to both the nucleus and the directrix is equal to the focal length of the parabola. Note that Eddington states that the nucleus of the comet showed quite clearly in each photograph as a star-like point, allowing him to treat the nucleus as the focal point.

Eddington's initial physical assumptions were not necessarily new, because he was attempting to provide an independent verification of the fountain-theory of envelopes that had previously been adopted by Bredichin, Bessel, Bond and several others.7 Thus he stated:

In cometary ejections, the repulsive force of the Sun took the place of gravity because the ejection distances were considerably larger than the nucleus itself, making the comet's own gravity negligible. Because the envelope formed on the side facing the Sun, ejections on the side away from the Sun would not contribute to the formation of the envelopes. In addition, because photographs are inherently two-dimensional and the envelopes that were formed were, of course, three-dimensional paraboloids, some projection had to be employed. As Eddington notes in the diagram he includes in his paper (figure 1), OQ₁, OQ₂ and OQ₃ are all paths of individual particles ejected in three dimensions from the nucleus. However, despite this, all the paths, when projected onto a two-dimensional plot, internally contact the parabola PAP′. This parabola is then a useful model of the envelope in two dimensions.

• Download figure
• Open in new tab
• Download PowerPoint

Eddington notes that if one analyses the envelopes at different instants, different particles make up the envelope at different times. This is true of any fountain-like fluid. For instance, a water fountain may maintain its general shape for a very long time and yet, at any given instant, the water particles that form the fountain shape are different. Of course, this implies in Eddington's case some amount of continuous outflow from the comet rather than a single burst. This also implies that any change in the position of the envelope does not correspond to any material displacement within the envelope. Further, Eddington distinguishes here between two different uses of the word ‘envelope’. He notes that it can be either ‘a boundary beyond which little or no material is projected, or … a surface of exceptional density of material.’9 He uses the latter definition for Comet Morehouse. He also points out the uniqueness of this comet in that each envelope can clearly be associated with a single eruption from the nucleus because the eruptions were so irregular. Most other comets known at the time had eruptions that were so numerous that only some general or average effect was observed. In fact, Eddington makes the case that this was the first evidence of the transitory nature of the individual envelopes. Historically, the importance of this point is that it marked the first opportunity to study individual envelopes and may have spurred Eddington's thoughts on the Sun's repulsion.

The lifetime of the average envelope surrounding Comet Morehouse was, according to Eddington's figures, three to four hours. In general, once an envelope had fully formed (which took some time), it immediately began to collapse. Thus there was a short-lived point at which the envelope was at its maximum size. This point of maximum could only be extrapolated, however, because each photographic plate represented 10 minutes of exposure time, which was fully 20% of the time between each plate. Changes clearly occurred during these intervals and, in fact, because of the length of the exposure times it is not clear just how much change is represented in the actual photographs themselves. Of interest is the fact that these exposure times were shorter than originally planned. As Eddington explains in his Royal Institution address:

Considering that the year in which the photographs were taken was 1908, I expect the reason for not further shortening the exposure times was at least partly driven by limitations in technology. Nonetheless, the lifetime of each envelope was long enough that a general pattern could be obtained. Because each photograph might show multiple envelopes at different stages of evolution, one could extrapolate a fairly accurate evolutionary cycle for them. I shall return to this point when I discuss the solar wind and what Eddington observed.

As mentioned above, Eddington modeled the particle eruptions on the comet as if they were vertical and under the effect of gravity where the Sun's repulsion took the place of gravity in the numerical analysis.11 This reduces the problem to one of simple projectile motion. Referring to figure 1, the position of a particle (following, for instance, path OQ₁) at time t and at an angle (180°−α) to Ox is

If one isolates the trigonometric functions, one can use the identity cos²a+sin²a=1 to effectively eliminate a and obtain

(1)

The condition for the roots of this equation to be real and not imaginary is

By setting a=V²/2g, the envelope can be fully described by the parabola

(2)

This is the arc PLAL′P′ in figure 1, and a=OA geometrically. Eddington has used simple projectile motion to describe the shape of the envelope as a parabola. Further, he derives from (1) the time taken by a particle to reach any point on the envelope as

(3)

The significance of (3) is that it can be used to calculate the time it takes for a single particle to move between any two points on the envelope. Because particles are on the envelope at all times after the peak of their trajectory (speaking three-dimensionally), this can be used to calculate the time it takes a particle to move from rest on the directrix (it is at rest here because it is changing direction—like a ball thrown in the air at the peak of its path) to some point considered under the influence of the Sun's repulsive force. Since a in (2) can be found by measurement of the shape of the parabola, because a is also equal to V²/2g on the basis of Eddington's derivation, one can solve for g, where g represents the acceleration produced by the repulsive force of the Sun.

Note that the use of parabolic projections does not necessarily assume that the axis of the three-dimensional paraboloid lies in the plane of the photograph. In reality this axis is inclined to the plane of the photograph by anywhere from 43° to 60°, depending on the photograph. Nevertheless any two-dimensional section of the paraboloid will be a parabola. However, Eddington notes that the comet's path toward the Sun remains roughly in the plane of the photograph. The paraboloids are inclined to the plane because some of the eruptions occur on the sides of the comet. As mentioned above, eruptions technically occur over the entire surface of the comet and so this is not unexpected. Eruptions at more extreme angles or on the side away from the Sun do not contribute to the envelopes or are not visible in the photographs.

Eddington also modified his calculation for certain envelopes in which careful measurement found that, in (2), the focal length a gradually increases with x, giving a more hyperbolic shape. In a much more recent work, Chen and Zheng12 showed that cometary envelopes are in fact closer in shape to a catenary, which is given by the equation y²=a cosh(x/a).

Nature of the solar repulsion

The importance of describing Eddington's analysis in detail is the understanding it provides when reviewing his actual data. Considering how well the envelopes observed in the photographic plates matched a parabola, Eddington's model seems reasonable, particularly considering that the repulsive force of the Sun would be acting in the same general direction as gravity for a particle forming the two-dimensional parabola that outlines the paraboloid. Eddington's calculated values for g were not wholly unexpected, either. They well exceeded the value of the Sun's gravitational attraction, which is expected considering the direction of the particles after they are ejected from the comet's nucleus. However, the extent to which the repulsion exceeded the attraction was surprising to Eddington, and his values are still cited as being some of the highest ever recorded13. Specifically, he found that the repulsion ranged from 180 to 19 000 times the attraction. At that time the acceleration due to the solar gravitational attraction was known to be 34.6 km h⁻², whereas Eddington's numbers put the repulsion at no less than 81 500 km h⁻². Yet these numbers were not entirely unheard of: Eddington makes the point that they agree with values obtained from studies of cometary tails. In fact, according to his own Royal Institution address, he began this work, the ultimate goal of which was to elucidate the nature of the solar repulsion, by studying the tail of the comet and mentions the envelopes only later in the address.14 Incidentally, these numbers also indicate an initial velocity, V, for erupted particles ranging from 10 to 100 km s⁻¹, a fact that should have merited further investigation of the source of the eruptions themselves (as opposed to a study of the shape they produced). However, Eddington only speculates on the source of these eruptions, saying:

Eddington's true interest, as I have noted, lies in the determination of the ultimate nature of the repulsive force provided by the Sun, foreshadowing his later interest in stellar structure. It is therefore surprising that he did not follow up one of the most important implications of his work. The implication is evident from two passages that are rather striking in a historical context. The first refers to a previously published suggestion by Nichols and Hull16 concerning condensation that occurs as a result of the expansion and cooling of emitted vapors. He asks:

The presence of a ubiquitous outflow of gas from the Sun seems, in retrospect, like an obvious solution to this problem. But one must remember that little was then known about stellar structure or stellar processes. In fact it was Eddington himself who arguably contributed the most to the foundation of that field of study.

But this statement is even more striking when taken in the context of his second striking passage, which was actually a mere footnote in the original paper. The footnote states:

In these two passages Eddington has seemingly suggested the possible existence of the solar wind without actually saying as much. Although the tone of his remarks indicates that he personally felt the concept to be highly speculative, the matter seems to have been given an even greater sense of urgency in his Royal Institution address of the previous year. The origin of the above footnote in that address appears in the following passage, where he attempts to explain bright patches in the comet's tail that apparently lack any acceleration. He supposes that

Note that in this passage he assumes that it is electrons that are flowing outwards from the Sun rather than the ions suggested in the footnote of his final paper. It is unclear how or why he made the change but it should be remembered that ions can be either positively or negatively charged and so the only change in his thinking may have been the masses of the outflowing particles. Note also that the source of his solution to the condensation problem can also be seen in this passage, particularly in the final line.

Before jumping to any conclusions about what Eddington did or did not discover, some historical facts must be put into order. Historically, solar–terrestrial interaction was noticed as early as 1859,20 although this was still in the age of the æther and the nature of the interaction was very poorly understood. By the time of Eddington's Royal Institution address, numerous theories had been put forward to account for the repulsion of comets' tails. In addition to what Eddington refers to as the ‘electrical’ theory described in the above passage, radiation pressure from the Sun's light was widely considered to be a potential explanation. In fact it was in an effort to test this theory that Nichols and Hull created their artificial comet only to find that the repulsive force was not, in their case, due to any radiation pressure. Eddington mentions this point in his Royal Institution address and proceeds to show that radiation pressure would have little effect on extraordinarily small particles, thus dismissing it as a possibility for an overall explanation of the repulsion.21 In addition, he closes this address with the following evaluation of George Hale's work on solar vortices (and further foreshadowing his later work in stellar structure), calling it

Eddington's presentation to the Royal Institution occurred on Friday, 26 March 1909. Hale made a presentation of his work on solar vortices to the Royal Institution on Friday, 14 May 1909, and the transcript appears immediately after Eddington's in Lovell's compilation.23 Oddly, Eddington's final published version of his work does not mention Hale's research.24

Despite all of these comments that seem, in hindsight, to be agonizingly close to the idea of the solar wind, it is Eugene Parker who is officially acknowledged as having first suggested the concept of a solar wind in 1958,25 an idea that won him a Kyoto Prize in 2003. Parker did not cite Eddington's paper, nor did he cite Ludwig Biermann or Cuno Hoffmeister, both of whom suggested nearly the same exact thing as Eddington in 1951 and 1943 respectively.26 Biermann, despite not being mentioned in Parker's paper, is usually duly credited with this point. But Biermann does not cite Eddington's paper either. In fact, of all the citations to Eddington's article in major journals (the first of which appeared in 1942), only two even mention the solar wind, and both of these refer only to Eddington's work on the parabolic shape of the envelopes.

How original, then, was Biermann's work? Did he cite anyone else who can be connected to Eddington's paper? He did cite Bredichin and Jägermann's 1903 presentation,27 which was also apparently a source for Eddington, but this paper deals mainly with the fountain-theory of envelopes which Eddington was trying to verify and has nothing to do with the specific suggestion of an outflow of charged particles that is under discussion here. However, although Biermann and sometimes Hoffmeister are credited with this suggestion, the basic idea that charged particles could be ejected from the Sun is credited to Frederick Lindemann in 1919.28 The difference between these two ideas is the notion of a continuous outflow. Lindemann had suggested that protons and electrons were ejected from the Sun during periods of solar activity, particularly from solar flares, an idea probably made possible by Hale's research on solar vortices. Three years before Lindemann's idea, Kristian Berkelund suggested that positive and negative ions could be ejected from the Sun and were probably ubiquitous in space,29 although, again, the idea is not treated historically as being one involving a continuous outflow. Simply being ubiquitous in space is not enough to produce the tremendous repulsion measured by Eddington. Of course, in hindsight, a related discovery was that of cosmic rays by Viktor Hess in 1912 (a discovery worthy of the 1936 Nobel Prize in Physics). In the 1930s, Lindemann's idea was revisited as a result of studies performed at various cosmic-ray observatories that suggested a link between solar activity and cosmic-ray counts.

It is my opinion that the appearance of the Lindemann paper represents the point at which Eddington's name drops from the history of the discovery of the solar wind. Eddington himself seems to have played a part in this by not mentioning Hale or representing the same excitement or urgency in his final paper that he demonstrated in his Royal Institution address. Though Hess's discovery of cosmic rays could have led to a much earlier version of Parker's ideas, I suspect that the political climate of Europe in 1912 played a role in distracting people from their usual lines of thought. Eddington himself was only a few years away from his battle with the government over his pacifism (rooted in his Quakerism).30 By the time that Lindemann produced his paper in 1919 (which, like many of these early works, contained no citations), the war had ended and Eddington was too ensconced in relativity and internal stellar structure to have probably taken much interest. Because Lindemann's paper contained no citations it is no wonder that, if he had been inspired by Eddington's work, those ideas were probably lost to history by the time that Lindemann's ideas were resurrected in the 1930s. Although Eddington never followed through on this idea, he should at least be credited with its formation alongside Lindemann, Biermann and others. It is perhaps surprising that Eddington did not follow through on this idea, in view of his engrossing work in stellar structure and the seeming relation between these ideas. Considering how many pieces of the puzzle were in place in 1910, I am equally surprised that it took nearly four decades for the unified idea of a solar wind to appear, not to mention how poorly it was initially received in the years after Parker's work. A complete history of solar science was fairly recently produced by Hufbauer (who also fails to mention Eddington) and discusses some of these issues.31

Eddington has certainly begun to receive his due with regard to the mathematical study of the shapes of the envelopes: there are no less than 34 citations (all since 1942) of his article on Comet Morehouse, 30 of which have appeared since 1970. In addition, his conclusion that the envelopes were parabolic stood as the standard for more than eight decades until the recent modification by Chen and Zheng.32 However, Eddington should also be rightly acknowledged for his suggestion that a continuous outflow of ions from the Sun—the first suggestion of its kind and thus worthy of recognition in its own right—would serve to explain not only the shape of the envelopes but also the distribution and mere existence of condensation. Whether or not Eddington himself realized the significance of this idea, or even if he was dismissive toward his own concept, the fact remains that he published it. The history of science is littered with instances of similar circumstances. An additional measure of recognition should be given him considering how far ahead of Biermann he was.