In 1933 Fritz Zwicky observed that the velocity distribution of galaxies in the Coma cluster cannot be explained solely by the luminous matter [2]. This was one of the first indications for the existence of dark matter. Since then, numerous observations were made that provide overwhelming evidence for dark matter.
1.1.1 Rotation Curves of Galaxies
The smallest length scales where direct evidence for dark matter can be observed are individual galaxies. The measurement of rotation curves which describe the orbital velocity of stars around the galactic center as a function of their distance r from the galactic center, gives hints about the presence of a mass component in addition to the luminous matter. The measured rotation curves show discrepancies with respect to the
Figure 1.1: Rotation curve of the spiral galaxy M33. The observed velocity distribution of the stars is shown by black data points [3]. The expected contribution from the observed luminous matter is shown in purple for the inner stellar component, red for the the outer stellar component, and dark blue for the gas contribution. The best fit to the data points is shown in light blue and results in contribution of dark matter (green) that is needed to explain to the measured rotation curve. Image taken from [4].
expectations based on the observations of luminous matter. In spiral galaxies most of the luminous mass is clustered in the central bulge of the galaxy. Outside of it the velocities of stars are expected to fall off with v ∼ 1/√
r, which is in contrast to the observations.
As an example, the rotation curve of the spiral galaxy M33 is shown in figure 1.1.
The measurement of the rotation curves (e.g. performed by measuring the Doppler shift of the 21 cm line of hydrogen) is shown by black data points [3]. It can be seen that the rotation curve remains flat also for large radii. Consequently, the rotation curve can only be explained by an additional contribution from dark matter in form of a large halo around the galaxy. From a fit of the data the distributions of the different mass components can be extracted. This shows that dark matter has the largest contribution to the velocities for large radii, which allows to deduce the mass distribution of dark matter. The measured rotation curve can only be explained with dark matter forming a large halo around the luminous matter.
1.1.2 Galaxy Clusters
Observations of galaxy clusters also hint to the existence of an additional dark matter component. A direct observational evidence for dark matter was found in the Bullet Cluster, which actually consists of two galaxy clusters that collided∼100 Myr ago [5].
In a collision of galaxy clusters the stars in the galaxies pass through each other col-lisionless, while the intracluster plasma is slowed down due to friction. Thereby, the plasma was heated up which allows to measure its distribution via X-ray emission. A typical galaxy cluster contains much more mass in the form of gas than stars. Thus,
Figure 1.2:An optical image of the Bullet Cluster is shown in the left picture, with the white bar indicating a length of 200 kpc at the distance of the cluster. The right image shows the X-rays emitted by the intracluster plasma. The gravitational potential is shown as overlaid green contours in both images. It can can be seen that the gravitational potential is spatially coincident with the galaxies, but not with the plasma. Image taken from [5].
it is expected that the location of the center of mass is coincident with the location of the gas.
In figure 1.2 an optical picture of the Bullet Cluster (left image) and an image of the X-rays emitted by the plasma (right image) are shown. As expected, the plasma spatially decoupled from the galaxies and was left behind during the collision. Addition-ally, the gravitational potential was measured with weak gravitational lensing, which measures the distortions of images of background galaxies caused by the gravitational deflection of light due to the cluster’s mass. The gravitational potential is visualized by green contours overlaid in both images. It can be seen that it is overlapping with the distribution of visible galaxies but not with the plasma.
Since the gravitational potential is spatially coincident with the galaxies but not with the plasma, an even more massive component must be present in the cluster, that cannot be seen and is hardly interacting. This is another evidence for dark matter and was observed in several other merging galaxy clusters [6].
1.1.3 Cosmic Microwave Background
About 380,000 years after the Big Bang electrons and protons combined to form neutral hydrogen and the Universe became transparent for photons. The photons from this time are still observable today as the cosmic microwave background (CMB) and form a perfect black body spectrum with today’s temperature ofT = (2.72548±0.00057) K [8].
The spectrum of the CMB is uniform over the whole sky with only tiny fluctuations of the level of 10−5 (see figure 1.3). Due to gravitational redshifting of the photons occurring at the surface of the last scattering, the observed structure in the CMB appears. This makes the CMB a probe of the matter distribution at that time.
From the angular variations of the temperature, among other parameters, the dis-tribution of the gravitating matter in the Universe can be determined. The latest and most precise measurement of the CMB was done by the Planck satellite. In figure 1.3 a sky map of the CMB temperature fluctuations observed between 2009 and 2013 is shown [1].
Figure 1.3:Sky map of the CMB temperature fluctuations observed by the Planck satellite with foregrounds subtracted. Color-coded are the variations of the mean temperature ofT ≈2.7 K on the level of±300µK. Image taken from [7].
The measurement can be well fitted by the ΛCDM model which describes the Universe to be dominated by dark energy (Λ) and non-relativistic cold dark matter (CDM) [9].
Within the standard model of cosmology the total energy content of the Universe can be described by Ωtot = ΩM + ΩΛ with the energy density of dark energy ΩΛ and the matter density ΩM being the sum of contributions from all matter species, in particular baryonic matter, neutrinos, and dark matter. The data of Planck is consistent with Ωtot = 1 which shows that the Universe is spatially flat [9].
Among many other results, from the data of the Planck satellite the contents of the Universe were determined [10]:
The major component of the Universe is the completely unknown dark energy with ΩΛ= 0.692.
The largest part of the matter content is non-baryonic cold dark matter with ΩCDM= 0.259.
Only a small fraction of the Universe is baryonic matter: ΩB = 0.049.
The CMB, being a snapshot of the early Universe, shows evidence for dark matter on a cosmic scale. Only about one fifth of the matter in the Universe is baryonic matter.
1.1.4 Structure Formation
While the CMB shows a picture of the early near-uniform Universe, todays cosmic structure and the distribution of galaxies can be observed in great detail with powerful telescopes like the Sloan Digital Sky Survey (SDSS) [11]. The large scale structure, that is observed today, evolved from the tiny density fluctuations in the early Universe
visible in the CMB. This evolution can be modeled with large computer simulations (like e.g. the Millennium Simulation [12]).
From these simulations, it is not possible to reproduce today’s large scale matter distribution when only baryonic matter is included. Instead, there needs to be a signifi-cant amount of non-baryonic matter, that clumps together earlier than baryonic matter, which is driven apart by electromagnetic radiation and, thus, cannot form large struc-tures. Dark matter fulfills this requirement as it is able to clump together early. Then, Baryonic matter will follow the gravitational potential of dark matter and can create the observed structure.
With an amount of dark matter that is similar to the fraction of dark matter deter-mined by the CMB, the simulated large-scale structure of the Universe matches the one observed today [13]. This implies that the density of dark matter observed at different time scales of the Universe is consistent.