Evidence of the Existence of Dark Matter
Justin P. Skycak
Marian HS
October 9, 2012
Humans are extremely visually-oriented beings: for a great deal of us, seeing is believing.
This might explain why many astronomers were skeptical and disregarded Swiss astronomer
Fritz Zwicky’s findings [2] when he discovered dark matter within the Coma cluster in 1933 [1].
However, the vast majority of scientists have come to accept the existence of dark matter as
more recent studies have backed it with a plethora of evidence. Observations involving mass
discrepancies in galaxies and clusters, cosmic background radiation sources and fluctuations, the
structure of the universe, and big bang nucleosynthesis’s impact on baryon density all support
the existence of dark matter.
Discrepancies between galactic mass calculations using the mass-luminosity relation and
the orbital velocity law have led to the conclusion that galactic matter is mostly dark and does
not add luminosity to the system. A galaxy’s velocity can be calculated by analyzing the Doppler
shift of its light emissions, and it can be used in Hubble’s law to calculate the galaxy’s distance.
The galaxy’s luminosity can then be calculated with the luminosity-distance formula and the
mass-luminosity relation can be used to mass the galaxy. On the other hand, using the orbital
velocity law requires scientists to measure the velocity and orbital radius of the farthest objects
orbiting the galaxy. Although this method is slightly more difficult, Doppler shifts in the
hydrogen gas surrounding most spiral galaxies can be analyzed to determine the gas’s velocity.
Since the orbital velocity law states that the mass of a galaxy is proportional to the product of the
radius and square of the velocity of the orbiting object, the gas’s velocity should decrease as its
orbital radius increases. However, this isn’t the case: even as the radius grows, the velocity of the
gas remains roughly constant. This indicates that the farther an object is from the center of the
galaxy, the greater the amount of mass it orbits. Elliptical galaxies are less organized than spiral
galaxies and usually lack surrounding hydrogen gas, but the diversity of the Doppler shift
spectrum of a region of stars indicates the magnitude of its orbital velocity and allows for the
calculation of the speed of the orbiting objects. Still, the velocity remains constant as the orbital
radius increases. Just as in spiral galaxies, objects in elliptical galaxies are found to orbit an
increasing amount of mass as the radii of their orbits lengthen. In many galaxies, the mass
measured by the orbital velocity law is as much as 50 times the mass inferred by the massluminosity relation, and these large mass-luminosity ratios indicate that there must be matter
surrounding the galaxy which does not contribute to its luminosity. [2]
In clusters of galaxies, too, discrepancies between cluster mass calculations from the
mass-luminosity relation and the orbital velocity law can be found. Standard candles can be used
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to estimate a cluster’s luminosity [14], the luminosity distance formula can be used to calculate
its distance, and the mass-luminosity relation can be used to mass the luminous matter in the
cluster. Doppler shifts in the cluster’s light emissions can be used to calculate the orbital
velocities of the galaxies the orbital velocity law can be used to mass the clusters. Alternatively,
the average speed of the intracluster medium between the galaxies in the clusters is indicated by
its x-ray emissions and can also be paired with the orbital velocity law to calculate the total mass
of the cluster. The results are consistent with those of the Doppler shift analysis. Similar to those
of galaxies, the mass-luminosity ratios of clusters can range from 10 to over 100 solar masses per
solar luminosity [2].
Another method to determine the mass of objects in space is gravitational lensing.
Gravitational lensing occurs when gravity forces light to bend around a massive object, and the
light distortion can be used to calculate the light-bending angle. Since the light-bending angle
depends on the strength of the gravitational force, it can be used to calculate the mass of the
lensing object. There are several types of gravitational lensing that can be used to for this
purpose, such as strong lensing, weak lensing, flexion, and microlensing. Strong lensing occurs
when clusters and galaxies bend light to such an extent that it follows multiple paths around the
lensing object. An “Einstein Ring” forms when the background light comes from directly behind
the gravitational lens, and the radius of the ring is proportional to the square root of the mass of
the lens. If the background light source is slightly off, it can appear in multiple spots and their
locations and distortions can be used to calculate the lensing object’s mass. Weak lensing is
caused by large-scale structures and although the light deflection is minimal, circular galaxies are
often distorted enough that they appear as ellipses. The magnitude of distortion can be used to
determine the mass of the lens. Flexion is caused by substructure and the outer areas of halos,
and the amount of distortion falls between that of strong and weak lensing. Light is not deflected
enough to make use of strong lensing mass calculation techniques, and the area is on too small of
a scale for weak lensing mass calculation techniques. However, there is a known relationship
between mass and flexion distortion that can be used to mass the gravitational lens. Microlensing
occurs when distance causes the lens to appear much smaller than the background light source
and the bent light shows up as a single more luminous object. The duration of microlensing
depends on the mass of the lens—a longer duration indicates a greater mass, while a shorter
duration signifies a smaller mass [3]. Recent studies held the mass-luminosity ratio calculations
in accord with those derived from the orbital velocity law [2], providing more significant
evidence for the existence of dark matter.
A careful analysis of cosmic microwave background radiation can provide evidence for
the existence of dark matter, too. Many dark matter candidates are capable of pair-annihilating
and producing a variety of radiation [6] which can be detected by cosmic ray detectors. The
Pamela telescope has observed more positrons than initially expected in cosmic radiation, and
the Fermi Large Area Telescope found an even larger excess [5]. The Fermi Gamma Ray Space
Telescope detected unique gamma ray emissions coming from the center of the galaxy which
may be attributed to dark matter, and the Wilkinson Microwave Astronomy Probe (WMAP)
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discovered higher levels of microwave radiation near the center of Milky Way as well [7].
WMAP discovered temperature fluctuations of 0.0002 Kelvin in cosmic background radiation
[8], which indicates differences in temperatures [9] and densities [10] of clumps of matter in
early universe. Knowing that various combinations of baryonic (normal) matter and nonbaryonic
(dark) matter would result in unique growth rates of the clumps, scientists were able to conclude
that the ratio of nonbaryonic matter to baryonic matter in the universe is approximately 6 to 1
[9].
Dark matter also plays an indispensable role in the structure of the universe. Although the
universe is expanding, the space within galaxies tends to remain constant [2]. If baryonic matter
had been the only type of matter, it would have been too hot to for these gravitationally bound
systems to form in the time they did [4]. The gravity of dark matter would have been necessary
to bring expanding matter together in this amount of time. It would have collected the first gas
clouds, which would condense to form stars within the dark matter halos, explaining the constant
velocities of objects increasingly farther from the center of galaxies and clusters. The process
would then have repeated with galaxies to form clusters, and it is expected to repeat with clusters
to form super-clusters. This matches what we see in the universe, and scientists have evidence
that super-clusters are already beginning to form [2].
Lastly, dark matter is supported by the well-tested and widely accepted theory of big
bang nucleosynthesis. According to the theory, the big bang produced large amounts of helium-4
and smaller amounts of deuterium, helium-3, and lithium-7. Deuterium was not produced often
after the big bang because it is so weakly bonded and tends to combine to form helium-4, so the
current amount of deuterium must be the lower limit to the amount of deuterium produced by the
big bang. Knowing the cosmic background radiation temperature and that deuterium production
during the big bang depended on baryon density [11], scientists were able to determine that
baryonic matter accounts for 4% of the universe’s critical density [15]. Since then, scientists
have found that the total mass density of the universe is at least 20% of the critical density [12].
This leaves a large amount of mass unaccounted for, which points to the existence of dark
matter.
Everywhere astronomers look, there is evidence for dark matter. Mass discrepancies in
galaxies and clusters, cosmic background radiation, the structure of the universe, and big bang
nucleosynthesis’s impact on baryon density all reveal that although we can’t directly see it, dark
matter exists. Many projects including the COUPP collaboration, PICASSO, CDMS, and others
[13] have embarked on a journey to detect dark matter, learn more about its properties, and prove
its existence once and for all.
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