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A. From Epicurus to Galileo

Throughout history, natural philosophers have speculated about the nature of matter, and even have contemplated the possibility that there may be forms of matter that are imperceptible – because they were either too far away, too dim, or intrinsically invisible. And although many of the earliest scientific inquiries were less than rigorous, and often inseparable from philosophy and theology, they reveal to us the longevity of our species' desire to understand the world and its contents.

Although many early civilizations imagined their own cosmological systems, it was arguably the ancient Greeks who were the first to attempt the construction of such a model based on reason and experience. The atomists, most famously Leucippus and Democritus who lived in the 5th century BCE, were convinced that all matter was made of the same fundamental and indivisible building blocks, called atoms, and that these atoms were infinite in number, as was the infinite space that contained them. Epicurus (341 BCE – 270 BCE) further suggested in his “Letter to Herodotus” that an infinite number of other worlds existed as well, “some like this world, others unlike it” 1. Others speculated about unobservable matter that might be found within our own Universe. For example, the Pythagorean Philolaus conjectured the existence of the celestial body Antichthon, or counter-earth, which revolves on the opposite side of the “central fire” with respect to the Earth [187].

The cosmological model of Aristotle – which would dominate discourse throughout the Middle Ages – provided an elegant construction, in which the location of the Earth was fixed to the center of an immutable Universe. This model offered what seemed to many to be strong arguments against the existence of invisible or unknown forms of matter. Even the striking appearance of comets, which obviously had no place in Aristotle's highly organized hierarchy of celestial spheres, was dismissed as an atmospheric phenomenon, a belief that continued to be held until Tycho Brahe measured the (absence of) parallax for a comet in 1577.

Although many offered challenges to the orthodoxy of Aristotelian cosmology, these attempts were not met without resistance. The statue of Giordano Bruno in Campo de' Fiori in downtown Rome serves as a reminder of the dangers that were inherent in such departures from the strict Aristotelian worldview embraced by the Catholic Church. It was at the location of that statue that Bruno was burned at the stake in 1600 by the Roman Inquisition, after being convicted on charges that included the holding of a heretical belief in the existence of infinite other worlds.

It was arguably Galileo – who himself had his share of trouble with the inquisition – who did the most to break the hold of Aristotelian cosmology. By pointing his telescope toward the sky, Galileo saw much that had been previously imperceptible. Among his many other discoveries, he learned that the faint glow of the Milky Way is produced by a myriad of individual stars, and that at least four satellites, invisible to the naked eye, are in orbit around Jupiter. Each of these observations encapsulate two lessons that remain relevant to dark matter today. First, the Universe may contain matter that cannot be perceived by ordinary means. And second, the introduction of new technology can reveal to us forms of matter that had previously been invisible.

B. Dark Stars, Dark Planets, Dark Clouds

The course of science, and of astronomy in particular, was transformed in 1687 when Isaac Newton published his treatise Philosophiæ Naturalis Principia Mathematica. Newton's Laws of motion and Universal Gravitation provided scientists with new and formidable tools which, among many other things, enabled them to determine the gravitational mass of astronomical bodies by measuring their dynamical properties.

In 1783, John Michell, also famous for inventing the torsion balance for the measurement of the force of gravity, realized that if light is affected by the laws of gravity – as he reasoned it should, given the universal nature of gravity 2 – then there could potentially exist objects that are so massive that even light would not be able to escape their gravitational pull [213].

This proposal, also famously discussed a decade later by Pierre Simon Laplace, is often considered to be the first mention of what have become known as black holes. We mention it here, however, as an explicit example of a discussion of a class of invisible astrophysical objects, that populate the universe while residing beyond the reach of astronomical observations.

The mathematician Friederich Bessel was perhaps the first to predict the existence of a specific undiscovered astronomical object, based only on its gravitational influence. In a letter published in 1844 [51], he argued that the observed proper motion of the stars Sirius and Procyon could only be explained by the presence of faint companion stars, influencing the observed stars through their gravitational pull:

If we were to regard Procyon and Sirius as double stars, their change of motion would not surprise us.

Bessel further argued in favor of the existence of many stars, possibly an infinite number of them, also anticipating the modern concept of the mass-to-light ratio:

But light is no real property of mass. The existence of numberless visible stars can prove nothing against the evidence of numberless invisible ones.

Only two years later, in 1846, the French astronomer Urbain Le Verrier and the English astronomer John Couch Adams, in order to explain some persistent anomalies in the motion of Uranus, proposed the existence of a new planet. Le Verrier's calculations were so precise that the German astronomer John Galle (assisted by Heinrich D'Arrest) identified the new planet at the Berlin observatory the same evening he received the letter from Le Verrier, within 1 degree of the predicted position.

Interestingly, it was Le Verrier himself who also later noticed the anomalous precession of the perihelion of Mercury, and proposed the existence of a perturbing planet to explain it. As it is well known, this “dark planet” – called Vulcan – was never observed, and the solution to this problem would have to await the advent of Einstein's theory of general relativity.

Beside dark stars and planets, astronomers in the 19th century also discussed dark matter in the form of dark clouds, or dark “nebulae”. One of the earliest traces of this discussion can be found in a memoir written in 1877 by father Angelo Secchi, then Director of the Roman College Observatory, describing research on nebulae that had been carried out 20 years earlier [283]:

Among these studies there is the interesting probable discovery of dark masses scattered in space, whose existence was revealed thanks to the bright background on which they are projected. Until now they were classified as black cavities, but this explanation is highly improbable, especially after the discovery of the gaseous nature of the nebular masses.

Around the end of the 19th century, an interesting discussion began to take place within the astronomical community. As soon as astronomical photography was invented, scientists started to notice that stars were not distributed evenly on the sky. Dark regions were observed in dense stellar fields, and the question arose of whether they were dark because of a paucity of stars, or due to the presence of absorbing matter along the line-of-sight. The astronomer Arthur Ranyard, who was among the main proponents of the latter hypothesis, wrote in 1894 [252]:

The dark vacant areas or channels running north and south, in the neighborhood of [θ Ophiuchi] at the center .... seem to me to be undoubtedly dark structures, or absorbing masses in space, which cut out the light from the nebulous or stellar region behind them.

This debate went on for quite some time, and it sparked some interesting ideas. W. H. Wesley, who acted for 47 years as the assistant secretary of the Royal Astronomical Society, proposed a novel way to settle the question, involving a rudimentary simulation of the arrangement of stars in the Milky Way [329]:

It is better to solve the question experimentally. For this purpose [the author] repeated many times the experiment of sprinkling small splashes of Indian ink upon paper with a brush, revolving the paper between each sprinkling, so to avoid the chance of showing any artificial grouping in lines due to the direction in which the spots of ink were thrown from the hairs of the brush.

C. Dynamical Evidence

Lord Kelvin was among the first to attempt a dynamical estimate of the amount of dark matter in the Milky Way. His argument was simple yet powerful: if stars in the Milky Way can be described as a gas of particles, acting under the influence of gravity, then one can establish a relationship between the size of the system and the velocity dispersion of the stars [174]:

It is nevertheless probable that there may be as many as 109 stars [within a sphere of radius 3.09 · 1016 kilometres] but many of them may be extinct and dark, and nine-tenths of them though not all dark may be not bright enough to be seen by us at their actual distances. [...] Many of our stars, perhaps a great majority of them, may be dark bodies.

Kelvin also obtained an upper limit on the density of matter within such a volume, arguing that larger densities would be in conflict with the observed velocities of stars. Henri Poincaré was impressed by Lord Kelvin's idea of applying the “theory of gases” to the stellar system of the Milky Way. In 1906 he explicitly mentioned “dark matter” (“matière obscure” in the original French), and argued that since the velocity dispersion predicted in Kelvin's estimate is of the same order of magnitude as that observed, the amount of dark matter was likely to be less than or similar to that of visible matter [246] (for an English translation, see Ref. [247]. See also Ref. [248] for a more complete discussion):

There are the stars which we see because they shine; but might there not be obscure stars which circulate in the interstellar space and whose existence might long remain unknown? Very well then, that which Lord Kelvin's method would give us would be the total number of stars including the dark ones; since his number is comparable to that which the telescope gives, then there is no dark matter, or at least not so much as there is of shining matter.

Along similar lines, in 1915, the Estonian astronomer Ernst Öpik built a model (published in Russian) of the motion of stars in the Galaxy, also concluding that the presence of large amounts of unseen matter was unlikely [103].

An important step forward in the understanding of the structure of the Milky Way was made by the Dutch astronomer Jacobus Kapteyn. In his most important publication, which appeared shortly before his death in 1922, Kapteyn attempted “a general theory of the distribution of masses, forces and velocities in the sidereal system” – that is, in the Milky Way.

Kapteyn was among the first to offer a quantitative model for the shape and size of the Galaxy, describing it as a flattened distribution of stars, rotating around an axis that points towards the Galactic Pole. He argued that the Sun was located close to the center of the Galaxy, and that the motion of stars could be described as that of a gas in a quiescent atmosphere. He then proceeded to establish a relationship between the motion of stars and their velocity dispersion, similar to what Öpik had done a few years earlier.

Kapteyn expressed the local density in terms of an effective stellar mass, by dividing the total gravitational mass by the number of observed stars – including faint ones, through an extrapolation of the luminosity function – and he explicitly addressed the possible existence of dark matter in the Galaxy:

We therefore have the means of estimating the mass of the dark matter in the universe. As matters stand at present, it appears at once that this mass cannot be excessive. If it were otherwise, the average mass as derived from binary stars would have been very much lower than what has been found for the effective mass.

In 1932, Kapteyn's pupil, Jan Oort, published an analysis of the vertical kinematics of stars in the solar neighborhood [226]. In this work, Oort added to the list of estimates for the local dark matter density, including those by James Jeans (1922) [168] and by Bertil Lindblad (1926) [197]. In his analysis, Oort made a number of improvements on Kapteyn's seminal work, relaxing for instance the assumption of the “isothermality” of the gas of stars.

Oort derived a most probable value for the total density of matter near the Sun of 0.092 M / pc3, corresponding to 6.3 × 10−24 g/cm3. He compared this number to the value obtained by Kapteyn, 0.099 M / pc3, and noticed that the agreement was “unexpectedly good”, given the differences in treatment and the data used. The numbers obtained by Jeans and Lindblad were each somewhat higher, 0.143 M / pc3 and 0.217 M / pc3, respectively.

In order to estimate the amount of dark matter, Oort then proceeded with an estimate for the contribution from stars to the local density, arguing that an extrapolation of the stellar mass function based on the observed stars seemed to be able to account for a substantial fraction of the inferred total density. It is interesting to recall the words used by Oort to illustrate the constraint on the amount of dark matter:

We may conclude that the total mass of nebulous or meteoric matter near the sun is less than 0.05 M pc−3, or 3 · 10−24 g cm−3; it is probably less than the total mass of visible stars, possibly much less.

We learn from this quote not only that the maximum allowed amount of dark matter was about half of the total local density, but also that astronomers thought that the dark matter was likely to consist of faint stars, that could be accounted for through a suitable extrapolation of the stellar mass function, along with “nebulous” and “meteoric” matter.

As we shall see in Chapter IV , the pioneering work of Kapteyn, Jeans, Lindblad, Öpik and Oort opened the path toward modern determinations of the local dark matter density, a subject that remains of importance today, especially for experiments that seek to detect dark matter particles through their scattering with nuclei.

1 Epicurus, Letter to Herodotus (c. 305 BCE), Extracted from Diogenes Laertius, Lives of Eminent Philosophers, trans. R. D. Hicks, vol. 2 (1925). Back.

2 This is already implicit in Query 1 of Newton's Opticks: “Do not Bodies act upon Light at a distance, and by their action bend its Rays; and is not this action (cteris paribus) strongest at the least distance?” Back.

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