The Etudes

Considering the great effort Struve and Bessel expended to measure the distances to only a small number of stars through parallax, they and other astronomers of the mid-nineteenth century could well have given up on charting the relative positions of stars in all directions and uncovering the structure of the sidereal system. Struve did not forget this ultimate objective set by his champion William Herschel, however. In a report Struve wrote in French for the French-speaking Russian Imperial Academy of Sciences in 1847, Etudes d'Astronomie Stellaire, he returned to this important and still elusive goal.

''The preparation of this report has given me an opportunity to return to the study of the Milky Way,'' Struve wrote. ''This entity is so puzzling, at first glance, that one is almost tempted to give up on a satisfactory explanation. However, the man of science must never retreat, neither when faced with the cryptic nature of a phenomenon, nor with the difficulty of an inquiry. Let him procure earlier studies, let him set out to increase knowledge of the phenomenon through new, precise observations; and he can be sure of a measure of success in his studies, if he employs a calm speculation, without giving himself over to the influences of an excited and predisposed imagination.''24

Struve began his Etudes with an historical review of philosophical and astronomical views on the nature of the Milky Way and the distribution of stars in the stellar system. Drawing on the manuscripts he had received from John Herschel on his trip to London, he then examined the evolution of the elder Herschel's thoughts on the construction of the heavens. Struve described in detail Herschel's ''star-gages,'' which explored a section of the stellar system and which suggested that the Milky Way consists of a thin but broad layer of stars.

To bring Herschel's 1785 drawing of the stellar system into a modern framework, Struve derived an approximate scale in light of recent parallax determinations. At the time Struve wrote the Etudes, 35 estimates of stellar distances were available. Assuming that stars all have about the same intrinsic brightness, Struve computed that the average distance to the first magnitude stars in the sample amounted to about 1 million Earth-Sun distances. He noted that Herschel's 1785 system, which Herschel had described in units of the distance to the bright star Sirius, stretched some 817 million Earth-Sun distances at its widest point, or almost 13000 light-years, according to the approximate scale.

Struve reminded his readers that Herschel himself had reconsidered the assumptions on which the 1785 system was based. Herschel had come to recognize that the stars are not distributed uniformly and, more importantly, that his telescopes did not permit him to see to the edge of the stellar system. Still, Struve noted, the outdated drawing retained its status as a standard representation of the Milky Way system. ''As to the explanation of the Milky Way, science has remained approximately at a standstill since the passing of Sir W. Herschel,'' Struve wrote. ''We may ask, why have astronomers generally championed the old doctrine on the Milky Way, articulated in 1785, despite the fact that it was entirely abandoned by the author himself?''25 Struve would probably be surprised to know that many modern textbooks still show Herschel's early drawing as representative of his life's work without mentioning that Herschel became aware of its limitations.

The next sections of Struve's report offered some new thoughts on the stellar system, picking up where Herschel left off. First, Struve insisted that we must consider the Milky Way to be ''fathomless,'' as Herschel had suspected. We cannot see the edge of our system in any direction, Struve asserted. He continued, ''It follows that if we consider all the fixed stars that surround the Sun as forming a large system, that of the Milky Way, we are in perfect ignorance of its extent, and we have not the least idea about the external shape of this immense system.''26 Struve was quite right in that the best telescopes of his day could not penetrate to the edges of our galaxy.

The fact that he thought the stars extended far beyond the limits of available telescopes did not dissuade Struve from trying to glean what information he could from a study of the distribution of stars in different parts of the sky. His approach was statistical — that is, he used samples of data gleaned from different directions in the sky to infer properties of the entire stellar system. He combined Herschel's star-gauges and more recent data to model the density of stars in different directions. The data suggested to him that the Sun is located near the center of the disk of the Milky Way. He envisioned the Milky Way system as a set of thin layers of stars stacked vertically. Within each layer, the stars were distributed uniformly with a particular density. With increasing distance from the central plane—the disk of the Milky Way galaxy—the density of stars decreased in a way that Struve could describe mathematically (see figure 5.8). In other words, Struve could not define the size of the disk in the horizontal direction or vertically, perpendicular to the plane, because he considered it fathomless, but he tried to express quantitatively how the density of stars decreased with distance in the vertical direction.

This model of Struve's stirred up controversy, because not all astronomers agreed that the distribution of stars could be fit to a mathematical function. But the most difficult section of the Etudes, for Struve's peers, was yet to come. In one of the final sections of his report Struve claimed, again based on star counts by Herschel and later researchers, that space is permeated with some absorbing material that diminishes our view of the universe.

Struve used statistical arguments to show that Herschel's telescope did not ''penetrate'' the layers of stars as deeply as one might expect, given its light-collecting power, and argued that the shortfall was due to some absorbing material. Struve made the common and useful—but inaccurate—assumption that all stars are of intrinsically the same brightness. If that were the case, the brightest stars would be the nearest ones, and the apparent brightness of a star would be directly related to the star's distance. Then the number of stars in each magnitude category would increase in a calculable way, e.g., there would be about four times as many second-magnitude stars as first-magnitude stars, and so on. The greater the distance probed, the greater the space corresponding to that distance, and the greater the number of faint stars of the corresponding magnitude limit.

Figure 5.8 Struve's model of the Milky Way, as described verbally in his Etudes d'Astronomie Stellaire (1847). The Milky Way system of stars, in his conception, is thin in one direction but extends to unknown reaches in the other direction. Struve described the distribution of stars mathematically, envisioning them as very densely packed in a thin central layer, surrounded by layers of decreasing density. (Credit: Layne Lundstrom.)

Figure 5.8 Struve's model of the Milky Way, as described verbally in his Etudes d'Astronomie Stellaire (1847). The Milky Way system of stars, in his conception, is thin in one direction but extends to unknown reaches in the other direction. Struve described the distribution of stars mathematically, envisioning them as very densely packed in a thin central layer, surrounded by layers of decreasing density. (Credit: Layne Lundstrom.)

Struve noted that Herschel's star gauges did not reveal as many faint stars as he should have found, if the assumptions about uniform distribution of stars and uniform brightness applied. For example, he calculated that Herschel should have counted about 3000 stars when probing the deepest field of the Milky Way, yet the largest number of stars Herschel found in one of his gauges was 588. The light from the missing faint stars, Struve believed, was too much absorbed en route, and the stars remained essentially invisible.

Struve normally shied away from speculation or bold hypothesis in astronomy, and his suggestion that space is not perfectly transparent marks a departure from his usual style. He was not the first to discuss the possible presence of absorbing material; indeed, he revived arguments for such a phenomenon made by Bessel's mentor, Olbers, and by other astronomers. But he was both correct and ahead of his time in proposing that visible light is partially absorbed in its passage through space. His reasoning, though not strictly correct, even gave him a fair idea of the amount of absorption. He calculated that the light from a first-magnitude star loses about 1/100 of its intensity over the distance it travels. Knowing that Struve believed first-magnitude stars were about 16 light-years away, we can convert his formulation of the amount of absorption into modern terms and compare with our modern value. He got a decrease of about 2 magnitudes per kiloparsec, or 2 magnitudes decrease over a distance of about 3300 light-years; that is a factor of 2 larger than the canonical value quoted today.

Struve sent a copy of Etudes to the main astronomical journal of his day, the Astronomische Nachrichten. He knew that many of his readers would take a stern view of his attempt to gain a broad understanding of the stellar universe and to make simplifying assumptions and statistical arguments for the sake of illuminating the ''big picture.'' He even admitted, at the beginning of the section in which he discussed interstellar absorption, that even the soberest of analysis and speculation sometimes led to ''unexpected'' conclusions.27 As the reviews of his work appeared in subsequent issues of the journal and elsewhere, Struve learned that his apprehensions were well founded. His colleague Johann Encke, director of the Berlin Observatory, wrote in outrage that Struve's authority would ''secure immediate entry'' for his results in all writing on the subject. Encke stressed, ''It appears to me of importance for astronomy that the assumptions and parallaxes of the Etudes do not get into our astronomical and popular writings.''28

The Etudes also received some praise. John Herschel took Struve's conclusions seriously, holding them up for examination in his widely-read textbook, Outlines of Astronomy. George Airy, Astronomer Royal at the Greenwich observatory and a friend of the Struve family, praised the work's importance and the ''ingenuity'' of the mathematical arguments in a carefully-worded review. Privately he told Struve he thought Encke had missed Struve's main points. Still, Encke's criticisms became well known. In condemning Struve's work, he also, perhaps not advisedly, condemned the whole statistical approach.

Struve's methods and conclusions were, in fact, ahead of their time. His statistical approach was particularly important because only a few hundred stellar distances could be found from parallax shifts at the end of the nineteenth century, not enough for astronomers to reconstruct the shape and scale of the Galaxy from direct distance probes. Struve's basic approach, adapted and refined by others, proved to be necessary far into the future. But this final great work of his appeared when he was no longer at the peak of his career, and it did not receive the attention that it probably deserved.

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