There exists overwhelming evidence for mass discrepancies in the Universe from multiple independent
observations. This evidence involves the dynamics of extragalactic systems: the motions of stars and gas in
galaxies and clusters of galaxies. Further evidence is provided by gravitational lensing, the temperature of
hot, X-ray emitting gas in clusters of galaxies, the large scale structure of the Universe, and the gravitating
mass density of the Universe itself (Figure 1). For an exhaustive historical review of the problem, we refer
the reader to [394
].
The data leave no doubt that when the law of gravity as currently known is applied to extragalactic systems, it fails if only the observed stars and gas are included as sources in the stress-energy tensor. This leads to a stark choice: either the Universe is pervaded by some unseen form of mass – dark matter – or the dynamical laws that lead to this inference require revision. Though the mass discrepancy problem is now well established [394, 465], such a dramatic assertion warrants a brief review of the evidence.
Historically, the first indications of the modern missing mass problem came in the 1930s shortly after
galaxies were recognized to be extragalactic in nature. Oort [342] noted that the sum of the observed stars
in the vicinity of the sun fell short of explaining the vertical motions of stars in the disk of the
Milky Way. The luminous matter did not provide a sufficient restoring force for the observed
stellar vertical oscillations. This became known as the Oort discrepancy. Around the same time,
Zwicky [518] reported that the velocity dispersion of galaxies in clusters of galaxies was far too
high for these objects to remain bound for a substantial fraction of cosmic time. The Oort
discrepancy was approximately a factor of two in amplitude, and confined to the Galactic disk – it
required local dark matter, not necessarily the quasi-spherical halo we now envision. It was long
considered a serious problem, but has now largely (though perhaps not fully) gone away [194
, 240].
The discrepancy Zwicky reported was less subtle, as the required dark mass outweighed the
visible stars by a factor of at least 100. This result was apparently not taken seriously at the
time.
One of the first indications of the need for dark matter in modern times came from the stability of
galactic disks. Stars in spiral galaxies like the Milky Way are predominantly on approximately circular
orbits, with relatively few on highly eccentric orbits [132]. The small velocity dispersion of stars relative to
their circular velocities makes galactic disks dynamically cold. Early simulations [343] revealed that cold,
self-gravitating disks were subject to severe instabilities. In order to prevent the rapid, self-destructive
growth of these instabilities, and hence preserve the existence of spiral galaxies over a sizable fraction of a
Hubble time, it was found to be necessary to embed the disk in a quasi-spherical potential well – a
role that could be played by a halo of dark matter, as first proposed in 1973 by Ostriker &
Peebles [343
].
Perhaps the most persuasive piece of evidence was then provided, notably through the seminal works of
Bosma and Rubin, by establishing that the rotation curves of spiral galaxies are approximately
flat [67, 370
]. A system obeying Newton’s law of gravity should have a rotation curve that, like the Solar
system, declines in a Keplerian manner once the bulk of the mass is enclosed:
. Instead,
observations indicated that spiral galaxy rotation curves tended to remain approximately flat with
increasing radius:
constant. This was shown to happen over and over and over again [370] with the
approximate flatness of the rotation curve persisting to the largest radii observable [67], well beyond where
the details of each galaxy’s mass distribution mattered, so that Keplerian behavior should have been
observed. Again, a quasi-spherical halo of dark matter as proposed by Ostriker and Peebles was
implicated.
Other types of galaxies exhibit mass discrepancies as well. Perhaps most notable are the dwarf
spheroidal galaxies that are satellites of the Milky Way [427, 477
] and of Andromeda [217]. These satellites
are tiny by galaxy standards, possessing only millions, or in the case of the ultrafaint dwarfs, thousands, of
individual stars. They are close enough that the line-of-sight velocities of individual stars can be measured,
providing for a precise measurement of the system’s velocity dispersion. The mass inferred from these
motions (roughly,
) greatly exceeds the mass visible in luminous stars. Indeed,
these dim satellite galaxies exhibit some of the largest mass discrepancies observed. In contrast,
bright giant elliptical galaxies (often composed of much more than the
stars of the
Milky Way) exhibit remarkably modest and hard to detect mass discrepancies [367
]. Thus, it is
inferred that fainter galaxies are progressively more dark-matter dominated than bright ones.
However, as we shall expand on in Section 4.3, the primary correlation is not with luminosity,
but with surface brightness: the lower the surface brightness of a system, the larger its mass
discrepancy [279
].
On larger scales, groups and clusters of galaxies also show mass discrepancies, just as individual galaxies
do. One of the earliest lines of evidence comes from the “timing argument” in the Local Group [213].
Presumably the material that was to become the Milky Way and Andromeda (M31) was initially expanding
apart with the general Hubble expansion. Currently they are approaching one another at .
In order for the Milky Way and M31 to have overcome the initial expansion and fallen back
towards one another, there must be a greater-than-average gravitating mass between the two. To
arrive at their present separation with the observed blueshifted line of sight velocity after a
Hubble time requires a dynamical mass-to-light ratio
. This greatly exceeds the
mass-to-light ratio of the stars themselves, which is of order unity in Solar units [42
] (the Sun is a
fairly average star, so averaged over many stars each Solar mass produces roughly one Solar
luminosity).
Rich clusters of galaxies are rare structures containing dozens or even hundreds of bright galaxies. These
objects exhibit mass discrepancies in several distinct ways. Measurements of the redshifts of individual
cluster members give velocity dispersions in the vicinity of typically implying dynamical
mass-to-light ratios in excess of 100 [24
]. The actual mass discrepancy is not this large, as most of the
detected baryonic mass in clusters is in a diffuse intracluster gas rather than in the stars in the galaxies
(something Zwicky was not aware of back in 1933). This gas is heated to the virial temperature and emits
X-rays. Mapping the temperature and emission of this X-ray gas provides another probe of the cluster mass
through the equation of hydrostatic equilibrium. In order to hold the gas in the clusters at the observed
temperatures, the dark matter must outweigh the gas by a factor of
8 [175
]. Furthermore, some
clusters are observed to gravitationally lens background galaxies (Figure 1
). Once again, mass
above and beyond that observed is required to explain this phenomenon [227]. Thus, three
independent methods all imply the need for about the same amount of dark matter in clusters of
galaxies.
In addition to the abundant evidence for mass discrepancies in the dynamics of extragalactic systems,
there are also strong motivations for dark matter in cosmology. Two observations are particularly
important: (i) the small baryonic mass density inferred from Big-Bang nucleosynthesis (BBN)
(and from the measured Hubble parameter), and (ii) the growth of large scale structure by a
factor of
from the surface of last scattering of the cosmic microwave background at
redshift
until present-day
, implying
. Together, these observations
imply not only the need for dark matter, but for some exotic new form of non-baryonic cold
dark matter. Indeed, observational estimates of the gravitating mass density of the Universe
, measured, for instance, from peculiar galaxy (or large-scale) velocity fields, have, for
several decades, persistently returned values in the range
[116
]. While shy of
the value needed for a flat Universe, this mass density is well in excess of the baryon density
inferred from BBN. The observed abundances of the light isotopes deuterium, helium, and
lithium are consistent with having been produced in the first few minutes after the Big Bang if
the baryon density is just a few percent of the critical value:
[480
, 107
]. Thus,
. Consequently, we do not just need dark matter, we need the dark matter to be
non-baryonic.
Another early Universe constraint is provided by the Cosmic Microwave Background (CMB). The small
(microKelvin) amplitude of the temperature fluctuations at the time of baryon-photon decoupling
() indicates that the Universe was initially very homogeneous, roughly to one part in
. The
Universe today (
) is very inhomogeneous, at least on “small” scales of less than
100 Mpc
(
), with huge density contrasts between planets, stars, galaxies, clusters, and empty
intergalactic space. The only attractive long-range force acting on the entire Universe, that
can make such structures, is gravity. In a rich-get-richer while the poor-get-poorer process,
the small initial over-densities attract more mass and grow into structures like galaxies while
under-dense regions become less dense, leading to voids. The catch is that gravity is rather weak, so
this process takes a long time. If the baryon density from BBN is all we have to work with,
we can only obtain a growth factor of
in a Hubble time [424], orders of magnitude
short of the observed
. The solution is to boost the growth rate with extra invisible mass
displaying larger density fluctuations: dark matter. In order not to make the same mark on
the CMB that baryons would, this dark matter must not interact with the photons. So, in
effect, the density fluctuations in the dark matter can already be very large at the epoch of
baryon-photon decoupling, especially if the dark matter is cold (i.e., with effectively zero Jeans
length). The baryons fall into the already deep dark matter potential wells only after that, once
released from their electromagnetic link to the photon bath. Before decoupling, the fluctuations
in the baryon-photon fluid did not grow but were oscillating in the form of acoustic waves,
maintaining the same amplitude as when they entered the horizon; actually they were even slightly
diffusion-damped. In principle, at baryon-photon decoupling, CMB fluctuations on smaller
angular scales, having entered the horizon earlier, would have been damped with respect to
those on larger scales (Silk damping). Nevertheless, the presence of decoupled non-baryonic
dark matter would provide a net forcing term countering the damping of the oscillations at
recombination, meaning that the second and third acoustic peaks of the CMB could then be of equal
amplitude rather than exhibiting a damping tail. The actual observation of a high third-peak in the
CMB angular power spectrum is another piece of compelling evidence for non-baryonic dark
matter (see, e.g., [229
]). Both BBN and the CMB thus drive us to consider a form of mass that
is non-baryonic and which does not interact electromagnetically. Moreover, in order to form
structure (see Section 3.2), the mass must be dynamically cold (i.e., moving much slower than
the speed of light when it decouples from the photon bath), and is known as cold dark matter
(CDM).
Now, in addition to CDM, modern cosmology also requires something even more mysterious, dubbed
dark energy. The fact that the baryon fraction in clusters of galaxies was such that was
implied to be much smaller than 1 – the value needed for a flat Euclidean Universe favored
by inflationary models – , as well as tensions between the measured Hubble parameter and
independent estimates of the age of the Universe, led Ostriker & Steinhardt [344
] to propose in 1995 a
“concordance model of cosmology” or
CDM model, where a cosmological constant
–
supposed to represent vacuum energy or dark energy – provided the major contribution to the
Universe’s energy density. Three years later, the observations of SNIa [351
, 365
] indicating late-time
acceleration of the Universe’s expansion, led most people to accept this model. This concordance
model has since been refined and calibrated through subsequent large-scale observations of the
CMB and of the matter power spectrum, to lead to the favored cosmological model prevailing
today (see Section 3). However, as we shall see, curious coincidences of scales between the
dark matter and dark energy sectors (see Section 4.1) have prompted the question of whether
these two sectors are really physically independent, and the existence of dark energy itself has
led to a renewed interest in modified gravity theories as a possible alternative to this exotic
fluid [100
].
http://www.livingreviews.org/lrr-2012-10 |
Living Rev. Relativity 15, (2012), 10
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