by Rene Roy
which consists of the ordinary matter that makes up the stars and planets
and us.
Steven Weinberg 2
As I have shown previously, the probability of the overlapping of images
of nebulae is considerable. The gravitational fields of a number of “fore-
ground” nebulae may therefore be expected to deflect the light coming to
us from certain background nebulae.
Fritz Zwicky 3
How Can We Image the Invisible?
Horace Welcome Babcock (1912–2003) was an American astrophysicist who spent the
greater part of his career at the Mount Wilson Observatory (Fig. 8.1). He was the son
of astronomer Harold Delos Babcock (1882–1965), a spectroscopist and solar physicist,
who joined George Hale at the new Mount Wilson Observatory in 1909, and was the first
to measure the magnetic field of the Sun. Horace was fascinated by instrument building
and invented several new techniques for astronomical observing. In 1953, he pioneered
adaptive optics, a technology now used in almost all large ground-based telescopes, which
corrects atmospheric turbulence and provides images with close to diffraction-limit angu-
lar resolution.4 Babcock also led and carried out the construction of a large observatory
at Las Campanas, Chile, to survey the southern-hemisphere sky and to record images of
1 S. L. Jaki, The Milky Way, An Elusive Road for Science, New York: Science History Publications, 1972, p. 291.
2 S. Weinberg, Physics: What We Do and Don’t Know, The New York Review of Books, 2013, Vol. LX, No. 17, p. 86.
3 F. Zwicky, On the Masses of Nebulae and of Clusters of Nebulae, The Astrophysical Journal, Chicago, 1937, Vol. 86, pp. 237–238.
4 H. Babcock, The possibility of compensating astronomical seeing, Publications of the Astronomical Society of the Pacific, 1953, Vol. 65, pp. 229–236.
173
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Fig. 8.1 Robert Leighton (left) and Horace W. Babcock (right), two of the most creative scientists of
the twentieth century. Credit: Courtesy of the Archives, California Institute of Technology.
galaxies of unprecedented quality. The Chilean site hosts several large optical telescopes,
including the 2.5-m Irénée du Pont telescope, the source of thousands of images of galax-
ies, many used in the splendid atlases of galaxies that are presented in Chapter 10. Allan
Sandage called Babcock the quiet American. “Horace Babcock’s reluctance to advance his
own agenda kept him from achieving the renown he deserves as one of the great minds of
his generation. On the other hand, his inability to indulge in self-aggrandizement made him
an extremely effective director of the joint Mount Wilson and Palomar Observatories.”5
Babcock provided one of the earliest pieces of evidence for the presence of a large amount
of dark matter in spiral galaxies.
Invisible Mass
Astronomers had to swallow an uncomfortable surprise around the middle of the twentieth
century. They found that most matter in the universe might be of a kind that neither absorbs
nor emits radiation. They called the stuff “dark matter,” but it would be more appropriate,
as suggested by the American physicist Steve Weinberg, to describe it as transparent matter
or invisible mass. Despite their extraordinary number and variety of shapes, and the amount
of matter they contain, galaxies constitute only the tip of the iceberg of cosmic mass; they
are islets in a sea of invisible matter. The invisibility is not because the material is very dark
5 A. R. Sandage, Centennial History of the Carnegie Institution of Washington, Volume 1: The Mount Wilson Observatory, Cambridge: Cambridge University Press, 2004, p. 420.
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or extremely cold; it is due to its unusual – and yet unknown – nature. Despite multiple
efforts, we have not yet succeeded in breaking the Gordian knot of what dark matter really
is. Antimatter is not dark matter: it is like ordinary matter; it emits and absorbs light. We
can see and are able to create antimatter in the laboratory.
Nevertheless, we do know a few things about dark matter. First, it exercises a gravi-
tational pull, just like ordinary matter; it creates gravitational potentials giving weight to
objects and accelerating masses that fall into them. We know also that this invisible mass is,
on average, about six times more abundant than ordinary matter, i.e. baryonic matter. The
latter is made of electrons, protons, neutrons and of other exotic well-known species of par-
ticles such as neutrinos, mesons or bosons. Dark matter is none of this stuff. In this chapter,
I will show how observations and images of ordinary matter have revealed the existence of
this perplexing and ubiquitous component of our universe.
A Brief History of Dark Matter
Early in the twentieth century, astronomers used the absolute luminosity of stars and stellar
systems, or the amount of light they emit, to derive the amount of matter contained in
them. They devised clever ways to translate the amount of light coming from stars into the
mass responsible for its emission. They also established how this ratio of “mass to light”
varied for different types of stars. For example, low-mass stars produce relatively little
light compared to massive stars, which emit copious amounts of light. British astrophysicist
Arthur Stanley Eddington (1882–1944) found a simple relation between luminosity and
mass: the luminosity of a star is proportional to approximately the power 3.5 of its mass,
i.e. L M 3.5.6 A star five times as massive as the Sun is 280 times more luminous than
our luminary. The Eddington relation applies to stars on the main sequence, those in the
stable hydrogen-burning phase. To get the overall mass of a galaxy, one also had to estimate
independently the mass of matter that emits very little light: very cool stars, dwarf stars,
black holes, small solid bodies and cold interstellar gases. Applying Newtonian mechanics,
the global kinematics of bodies in a galaxy provided an independent clue about its total
mass and spatial distribution. Most puzzling, the results from the two methods disagreed
very significantly. Something was unbridled.
Evidence for some dark matter was first inferred in the early 1930s. It came first from the
measurements of velocities of nearby stars and gas clouds in our neighborhood of the Milky
Way. The Dutch astronomer Jan Oort (1900–92) had been analyzing the stellar kinematics
in the solar neighborhood to derive a mean cosmic mass density. In 1932, he found that this
density was twice that deduced from the stars and the gas.7 Compared with the results of
the mass-to-light ratio analysis just discussed, the kinematics led to significantly more mass
than was implied by the stellar light striking our telescopes. The velocities of the stars in
6 A. S. Eddington, On the Relation between the Masses and Luminosities of the Stars, Monthly Notices of the Royal Astronomical Society, 1924, Vol. 84, pp. 308–332.
7 J. H. Oort, The Force Exerted by the Stellar System in the Direction Perpendicular to the Galactic Plane and Some Related Problems, Bulletin of the Astronomical Institute of the Netherlands, 1932, Vol. VI, No. 238, p. 249–287
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our neighborhood of the Milky Way were much higher than could be accounted for solely
from the masses of visible stars, gas and dust clouds, even when all these masses were care-
fully summed up. To explain the discrepancy, Oort suggested the existence of an important
component of invisible mass, or “missing mass.” Studying the edge-on galaxy NGC 3115
in 1940, he also found that “the distribution of mass in this system appears to bear almost
no relation to that of light.”8 Oort’s interpretation of these data was highly debatable.
The puzzle grew when the curious kinematical behavior was found on a much larger
scale, that of clusters of galaxies. Our old friend Fritz Zwicky (1898–1974) of Chapter 3
was an early and astute observer of the extragalactic world (Fig. 3.11). He had taken a
keen interest in the regions of space where galaxies appear to congregate in volumes of
only a few million light-years in diameter. As we have seen, William Herschel and the
Birr Castle observers had noticed such groupings of galaxies in the nineteenth century but
never speculated on the nature of these assemblies of “nebulae” except in describing them
as a “stratum.” We know today that they are galaxy clusters; galaxies group together as
hundreds, sometimes thousands of members, to make up the so-called “rich” clusters. The
American astronomers Harlow Shapley and Adelaide Ames were the first to come up with
the concept of clusters of galaxies, calling them “nebular clouds.”9
By 1933, Zwicky had prefigured the presence of an excess of mass in many clusters.10
Using the newly installed wide-field 18-inch Schmidt telescope of Mount Palomar Obser-
vatory, Zwicky surveyed and catalogued thousands of clusters of galaxies. Employing the
larger Mount Wilson 100-inch telescope for follow-up observations, he obtained the spec-
tra of several of the individual galaxies of clusters, deriving their velocities with respect to
the center of the cluster. Applying Newton’s law of gravitation, Zwicky derived the masses
of the entire cluster by measuring the velocities of the individual member galaxies, just as
we can calculate the mass of the Sun by measuring the orbital speed of the planets and
their distance to the Sun. As Jan Oort had found on a smaller astronomical scale, Zwicky
discovered that the mass from the luminous material of the cluster was clearly insufficient
to account for the high velocities he measured for the galaxies; these should have flown
away. Surmising that they were being held together, he claimed that there was an important
amount of “missing mass.”
Zwicky had also patiently measured the rotational curves of a few clusters of galaxies
to infer their individual mass from Newtonian mechanics. He summed together all their
masses. The “missing mass” did not go away; the masses of the constituent galaxies did
not add up at all to the total mass. The prescient Zwicky wrote, “if this is confirmed, we
would arrive at the astonishing conclusion that dark matter is present with a much greater
density than luminous matter.”11 Soon after, in 1936, the American astronomer and inventor
8 J. H. Oort, Some Problems Concerning the Structure and Dynamics of the Galactic System and the Elliptical Nebulae NGC
3113 and 4494, The Astrophysical Journal, 1940, Vol. 91, pp. 273–306.
9 H. Shapley and A. Ames, A Study of a Cluster of Bright Spiral Nebulae, Harvard College Observatory Circular, 1926, Vol. 294, pp. 1–8.
10 F. Zwicky, Die Rotverschiebung von extragalaktischen Nebeln, Helvetica Physica Acta, 1933, Vol. 6, pp. 110–127.
11 Translated from F. Zwicky and cited by S. van den Bergh, The Early History of Dark Matter, Publications of the Astronomical Society of the Pacific, 1999, Vol. 111, p. 657.
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Fig. 8.2 Transformational Image: Zwicky’s Map of the Distribution of Galaxies in the Coma
Cluster of Galaxies. From Zwicky (1937), The Astrophysical Journal. C
AAS. Reproduced with
permission.
Sinclair Smith (1899–1938) also found the presence of large amounts of invisible mass in
another nearby large galaxy cluster, the Virgo cluster of galaxies at about 54 million light-
years.
In a fascinating paper in 1937, Zwicky summarized the extensive set of observations he
had conducted of the Coma cluster of galaxies hosting hundreds of galaxies and located at
about 333 million light-years (Fig. 1.4). While mapping the distribution of galaxies in the
cluster, Zwicky had been struck by its apparent spherical symmetry (Fig. 8.2). He demon-
strated that the galaxies in the Coma cluster were evenly distributed and that individual
galaxies had much higher velocities than expected, based solely on the gravitational mass
inferred from the stellar light of the galaxies.12 Repeating Oort’s remark about the solar
12 F. Zwicky, On the Masses of Nebulae and of Clusters of Nebulae, The Astrophysical Journal, Chicago, 1937, Vol. 86, pp. 217–246.
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neighborhood in our Milky Way, Zwicky concluded that light was not a good tracer of
mass. Highly intrigued, he explored alternative approaches to calculate the total mass of
clusters of galaxies in order to put his unexpected finding on solid ground and to find pos-
sible inconsistencies. In order to do this, Zwicky used an extraordinarily powerful tool, the
virial theorem.
The Virial Theorem
The virial theorem is based on Newton’s gravitational theory, and is a simple mathematical
relation between the mass of a system, its size and the velocities of its components. It can
be employed to infer the mass of a system of particles in hydrostatic equilibrium. Zwicky
made the assumption that galaxies of a large cluster were particles of such a system. Tak-
ing the mean velocity of all the individual galaxies, σ , and the size of the cluster, R, the
total mass, M, derived from the virial is written in its simple form as M
5 Rσ 2/ G,
v irial
where G is the gravitational constant. The basic assumption is simple: the system, in this
case the galaxy cluster, has had the time to settle dynamically. The members are neither in
free fall, nor escaping from the gravitational potential of the cluster. The beautiful morpho-
logical symmetry of the many galaxy clusters Zwicky had photographed indicated that the
hydrostatic state assumption was reasonable, at least in the case of the Coma cluster.
Applying the virial equation, Zwicky arrived again at an astounding value for the total
mass of the cluster. Combining the results of his several approaches, Zwicky announced the
presence of a “missing mass” that was 100 times greater than that of the luminous matter.
Zwicky was adamant: a kind of matter other than the luminous one was necessary to keep
the cluster gravitationally bound, and to explain the smooth distribution of galaxies around
its center.
Unsatisfied, Zwicky explored the possibility that clusters of galaxies were dynamically
unstable or had not had time to settle. The galaxy ve
locities would then be unreliable tracers
of the total mass and the virial theorem could not then be applied. He rejected this hypoth-
esis, stating that clusters of galaxies would be so short-lived that there would be very few
clusters in existence. This was not the case as clusters of galaxies peppered the deep sky.
Zwicky was finding clusters all over, above and below the plane of the Milky Way, direc-
tions where he could probe deep into the universe. Most galaxy clusters must have had the
time to relax gravitationally, making the use of the virial theorem justifiable and its results
reliable, he re-affirmed.
Zwicky could not escape the stunning conclusion that clusters of galaxies were big pock-
ets of dark matter, loci with huge concentrations of this matter that create deep depressions
in the membrane of spacetime. Ordinary matter just falls and assembles into these deep
“valleys.” We know today that dark matter stretches across space as large-scale cosmic
filaments; the filaments form a web of structures that crisscross each other; clusters of galax-
ies are found at the junctions of these large-scale filaments. The visible structures, i.e. the
galaxies, groups of galaxies and clusters of galaxies, trace the dark matter as streetlights
outline the patterns of our cities seen at night.
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The Secret of Symmetry of Galaxy Clusters and X-Rays
When later observed from space, the clusters of galaxies revealed another surprise: they
contain colossal quantities of X-ray-emitting gas. X-ray-emitting plasma from the Coma
cluster, so well studied by Zwicky, was discovered during a balloon flight in 1966; this
finding of hot intracluster gas was one of the major breakthroughs of X-ray astronomy
(Chapter 7). Because of their deep gravitational potential, clusters of galaxies are able to
retain and heat their intracluster gas to very high temperatures (Plate 8.1). In Coma, X-rays
indicated a binding mass of about 7 x 1014 solar masses, with its intracluster gas heated
to 100 million kelvin.13 These high temperatures meant that the speeds of the ions were
the same as those of the galaxies moving within the cluster’s gravitational potential. There-