The Complexity of dark matter

The Complexity of dark matter

Dr. TJ Gunn Ph.D. Applied Physics, Ph.M. Masters Philosophy

Published: 5 February, 2017

What we do know is that dark matter does not interact with light and therefore
cannot be seen. It prefers to clump into massive clouds and unlike protons and
neutrons, does not collapse to form dark galaxies and dark planets (i.e. if we put
on dark matter glasses we would not see a copy-cat dark Universe). Fortunately
this amount of dark matter does not go unnoticed and effects the way the Universe
The existence of a mysterious non-baryonic particle that interacts primarily via
gravity and dominates the Universe can seem somewhat perverse. However,
several independent lines of evidence for the existence of dark matter have been
accumulating now for nearly 100 years and are beyond contention.
It was initially proposed by Zwicky (1933) as a means to explain the
discrepancies between the extreme velocity dispersions of galaxies in the Coma
cluster and the observed mass. Since this study in the early part of the 20th
Century, evidence has continued to grow including independent studies of the
velocity of gas rotating in galaxies, which were found to be anonymously high in
the outer regions of the galaxy where the light appeared to dissipate. According
to Keplerian laws, the velocity of gas is expected to drop off v ∝ r
−1/2, assumingthat matter follows light, however studies reported a flat rotation curve,
a M ∝ r relation. Such problems were initially expressed by Oort (1932), yet did
not postulate the presence of missing material. Later studies noted similar effects,
saying that this could only be explained by either a modification to gravity or
the existence of unobserved dark matter (Rubin et al., 1980; Bosma, 1978).
More recently there have been other probes that have independently supported
the existence of dark matter. As mentioned, Table 2.1 shows how Planck predicts
that the total matter density in the Universe is of order ∼ 0.3. However, it is
possible to estimate the the baryonic matter density from the CMB using the
relative heights of the peaks in the CMB power spectrum, since this is related to
the baryon oscillations in the early Universe (Planck Collaboration et al., 2013a),
and BBN. BBN refers to the production of the light elements in the early Universe.
Since it is impossible to make elements above a certain mass through fusion, it
is possible to theoretically estimate the abundance of baryons at the end of the
early Universe and hence compare with places where little stellar nulceosynthesis
has occurred, for example in dwarf galaxies (e.g Bania et al., 2002; Burles et al.,
2001). From these different lines of evidence, baryons only contributes ∼ 13%
of this, meaning that there must be another contribution from a non-baryonic
component. It seems that dark matter is a necessity in order for structure to
grow in the Universe, a fact that is heavily supported by N-body simulations.

Astronomical particle colliders
Its shear mass heavily bends the space around it, like a large weight
bending a sheet of rubber. The effect is to cause any object that comes too close
to follow the curvature of space, as if rolling a ball near the crest of a hill and
seeing it follow the curvature of the hill and fall down.
Similarly, should that ball be rolled fast enough, it wouldn’t fall down, but
shoot past the hill. However, its path would not be completely unaffected as it
will have had its direction slightly altered. If we consider the ball as a photon,
then if it travels too close to a large cloud of dark matter, such that it slightly
falls down into it, then the path of the photon will be altered. Although we can’t
see or detect dark matter, we can capitalise on the fact that billions of photons
are passing through clouds of dark matter like this all the time and feel the
gravitational attraction causing the objects from which they were emitted to be
distorted. This is known as gravitational lensing. Since dark matter is dominating
the Universe we can use gravitational lensing to trace where the clouds of dark
matter are, as if constructing an Ordnance Survey map of the sky. Figure 1.1
shows a diagram of the effect of dark matter with the background galaxy’s light
being bent by the foreground dark matter.
These clouds of dark matter that prefer to clump can grow to become thousands of
times more massive than a single galaxy. This attracts a lot of close by galaxies
(as well as forming some of its own) and very hot gas. The result is a huge
mixing pot of dark matter, with a sea of hot X-ray emitting gas interspersed with
thousands of galaxies, all orbiting the centre of mass. This is known as a galaxy
cluster and is the largest known structure in the Universe.
In rare events galaxy clusters can be attracted to other galaxy clusters,
resulting in a car crash on an astronomical scale. In the event that two galaxy
clusters do collide, their gas, dark matter and galaxies will all behave differently.
The galaxies will behave like small bullets that pass by each other completely
unaffected. The gas will behave like a liquid such that if the two collide haloes of
gas will splash together and either form a single halo, or they will decelerate and
become misshapen. What the dark matter does will depend on what dark matter
is. If dark matter is collisionless, then it will pass through, like the stars and be

Dark matter Gas
Colliding galaxy clusters are ideal laboratories to study the subtle
properties of dark matter. Here, two galaxy clusters have passed through one
another, causing the gas to separate from its associated dark matter cloud. The
dark matter still remains coincident with the collisionless galaxies. By measuring
the three different components of a galaxy cluster, I shall study the properties of
dark matter in this thesis.
completely unaffected, however if it interacts it will behave differently. We can use
gravitational lensing to trace dark matter in these collisions of galaxies clusters
and compare this with the distribution of gas and galaxies to make statements on
the nature of dark matter in galaxy clusters. It is only this way, in these clouds
of dark matter that we test these properties. In this thesis I shall compare the
positions of gas, dark matter and galaxies in various clusters in a bid to make
further inroads in to the unknown nature of dark matter. Figure 1.2 shows the
‘Bullet Cluster’, an example of a colliding cluster where the gas (red) as detected
in the X-ray, originally associated with the clouds of darks matter (blue), have
been stripped and separated during the collision. We observe it here post merger,
after they have passed one another. In this thesis I will use these events to directly
probe the properties of dark matter.

Cosmology and the large scale structure
The Universe is statistically homogeneous and isotropic, that is on large enough
scales the Universe is of constant density and the same in all directions. At first
this would seem implausible if not impossible as if different parts of the Universe
are separated by distances greater than the distance light could have travelled
since the beginning of the Universe and could thus not be in causal contact.
However, as observed by Layzer (1957) and Shane et al. (1959), the Universe did
indeed appear to be homogeneous on large scales. In addition to this cosmological
puzzle, in the early 1920’s Vesto Slipher observed that galaxies were all apparently
redder than they should be, proposing that they were all receding. It was not long
after that Edwin Hubble confirmed this by measuring their distances, discovering
the Hubble Law, that the recession was proportional to distance (Hubble, 1929).
It was with these early discoveries that observational cosmology was born.

Cepheid Variables
Cepheids are stars that have oscillating luminosities.
These oscillations are a result of the finite sound speed in the star.
For hydrostatic equilibrium the gravitational collapse must balance the
pressure, and thus any small contraction will ultimately be pushed back in
the time it takes for a pressure wave to traverse the star. Hence, a shorter
period would infer a smaller and therefore less luminous star. Empirically
these stars have been measured accurately to have a relation L ∝ P
very small scatter.

Type 1a Supernova
Type 1a Supernova are the result of a whitedwarf accreting mass from a
nearby star until it reaches the fundamental
Chandrasekhar limit of 1.4M, when it becomes unstable and explodes. It is
assumed to be a standardisable candle since they all share a similar form of
light curve (how the intensity of light rises and falls during the event). Using
the fact that all light curves were very similar, Phillips (1993) determined
an empirical relation between the decay of the light curve since the peak
apparent luminosity and the intrinsic peak luminosity, which could be used
as a distance estimator.
Known estimators for cosmological distances has led to discoveries that have
changed the face of cosmology (e.g. Perlmutter et al., 1998; Riess et al., 1998).
Moreover, with an increased understanding of other cosmological parameters, how
the Universe became how it is observed today is becoming increasingly clear.

Galaxy clusters
N-body simulations predict that structure in the Universe forms a web like
texture. At the nodes of this cosmic web lie huge haloes of dark matter. These
structures are among the largest known objects in the Universe and contain some
of the highest densities of dark matter. The huge collection of dark matter results
in a massive potential well that distorts the fabric of space-time and dominates the
dynamics of the local environment. As a result, it drags and pulls large quantities
of baryons into the well instigating the formation of massive galaxies and a sea
of ultra-hot ionised gas (mainly hydrogen). The consequence is a energetic mix
of galaxies, ionised gas and large quantities of dark matter.
The dynamics, constituents and behaviour of matter in galaxy clusters have
been well studied, helping to constrain cosmology and defining cluster scaling
relations. Their abundance and mass will depend heavily on how the Universe
formed and surveys such as Planck (Planck Collaboration et al., 2011), can use
these abundances to estimate the mass content of the Universe. Moreover, the
CMB is sensitive to high densities of baryons in the Universe since photons from
the surface of last scattering will scatter off electrons within intra-cluster medium
(ICM), via inverse Compton scattering. This will cause a shift in the observed
CMB spectrum, leaving an imprint (Sunyaev & Zeldovich, 1970). The SunyaevZel’dovich
effect (SZ) is independent of redshift and is a relatively new method to
study clusters, since prior to Planck they were difficult to resolve. By comparing
the observed number of Planck SZ clusters with those calculated in simulations of
different cosmological models, it is possible to constrain cosmology. Interestingly,
Planck found slightly contentious results from their SZ cluster catalogue, finding
a two-sigma tension on their constraint of Ωm = 0.29 ± 0.02 and constraints of
the power spectrum normalisation of σ8 = 0.75 ± 0.03 (Planck Collaboration
et al., 2013b). However, in order to account for potential systematics in the
X-ray masses, they need to be calibrated with a sample of lensing clusters that
overlap the sample. The study by the Planck Collaboration et al. (2013b) was
calibrated using an assumed MX/MWL = 0.8, derived from simulations. However
soon after this was published, it was postulated that they under-estimated their
cluster mass calibration and a more accurate calibration of MX/MWL ∼ 0.7 using

Cosmology and the large scale structure
The Weighing the Giants lensing sample (von der Linden et al., 2012), significantly
reduced the observed tension (von der Linden et al., 2014).
Complementary to cluster counts, it is possible to use the fraction of gas in
clusters to probe cosmology. In the absence of any expulsion mechanisms, the
amount of gas (which dominates the baryonic content in clusters) would naively
be expected to roughly equal the baryon fraction of the Universe. However, it
was realised that this was not entirely true as mechanisms such as AGN and
supernova feedback expel gas from the ICM in highly energetic events. Recent
simulations with improved models of the hydrodynamics within clusters have
derived more accurate and robust estimates of the baryon fraction in clusters
(Eke et al., 1998; Kay et al., 2004; Crain et al., 2007; Nagai et al., 2007; Young
et al., 2011; Battaglia et al., 2013; Planelles et al., 2013). As a result a recent X-ray
study of a sample of galaxy clusters analysing the fraction of gas in a cluster has
estimated ΩM = 0.27±0.04, the best current constraints from clusters of galaxies
(Mantz et al., 2014). Furthermore, by studying the fraction of gas in clusters
over a range of redshift it is possible to estimate the dark energy equation of
state (Allen et al., 2008; Mantz et al., 2014).
Dark energy equation of state
The observed expansion of the Universe and the isotropic and homogeneous CMB
has led to the widely accepted theory of the Big Bang. Naively, such a theory
would lead to an expected initial acceleration of the Universe followed by a period
of deceleration and ultimately collapse as the matter in the Universe looks to pull
itself back in. To test this theory it is possible to look for deviations from Hubble’s
Law. In the late 20th Century, whilst observing the distances from Supernova,
Perlmutter et al. (1998) found such a deviation, yet it turned out that the Universe
was actually accelerating, and not slowing as previously expected. Simultaneous
work by Riess et al. (1998) confirmed this finding and it was soon accepted that
the Universe was in fact accelerating.

Background Cosmology
This was in-line with other independent work examining the current dynamical
state of the Universe. Studies of the total matter content of the Universe
showed that ΩM < 1, and since the Universe had been shown to be flat by the
CMB, this implied some extra vacuum energy and hence cosmic acceleration.
The measurement of ΩM was carried out in two different methods. The first was
using galaxy clustering. By measuring the power spectrum of the galaxies it was
possible to estimate the dark matter power spectrum. This spectrum roughly
follows a Schechter function, where the turnover is related to the sound horizon
at the equality of matter and radiation. By measuring this turnover, it is possible
to estimate ΩM, which Percival et al. (2001a) found not to be 1. The second, is
that the relative abundance of dark matter to baryons in galaxy clusters was not
sufficient to allow ΩM = 1. Since the baryon fraction was well understood from
big bang nucleosynthesis (BBN), then the amount of dark matter that existed
was not sufficient and that in-fact Fukugita et al. (1998) found that ΩM < 0.25.
The discovery of the accelerating Universe led to the 2011 Nobel Prize in
physics and a new era of cosmology. New theories of what could be driving
this acceleration were proposed, from cosmological constants, which naturally
arise from Einstein’s equations, to more exotic scalar fields, also known as dark
energy. Even modifications to Einstein’s gravity have been proposed, however
these suffer from fine tuning as this theory has been stringently tested on solar
system scales. Since its cementation into the standard cosmological setup, it has
become normal to constrain the dark energy equation of state, w (how energy
density relates to pressure), and has been measured to be w = −1.13 ± 0.13 and
that the Universe’s energy budget is made of 68.6 ± 2% vacuum energy (Planck
Collaboration et al., 2013a).
More direct evidence from galaxy clusters has originated from studies of
colliding and merging clusters. N-body simulations predict that structures in
a CDM universe form hierarchically, resulting in merging galaxies and merging
galaxy clusters. In the latter scenario, the dynamical differences of dark matter
and baryonic are most obvious. During a merger, the haloes of dark matter and
gas of the two clusters will merge and interact. If dark matter is collisionless it
will pass directly through, seemingly undisturbed, whereas the gas will interact
with itself and in some extreme situations shock causing a bow to form in the gas
cloud. An example of this was discovered with the merging cluster, 1E0657-55,
or more commonly known as the ‘Bullet Cluster’ (Markevitch et al., 2004; Clowe
et al., 2004, 2006; Bradač et al., 2006). Figure 2.4 shows the cluster just after
collision. The blue represents the dark matter, and the red denotes the position of
the gas. A separation between the dark matter and the gas in both post-merging
haloes can clearly be seen . This particular example was one of the first pieces
of evidence for dark matter that could not be explained using a modification to
gravity (Clowe et al., 2006).

Conclusion
I have presented a new method to probe the interaction cross-section of dark
matter (σDM/m). By measuring the relative distance that a dark matter subhalo
lies from its galactic component with respect to the distance the baryonic
gas lies from the same galactic component, I have derived a new parameter
β, which is independent of any line of sight projections. In order to interpret
this parameter β as a cross-section I have developed an approximate analytic
model for substructure infall, considering all the major forces acting on the three
components. In particular, I model the DM interactions based on the type
of frequent, velocity independent interactions, outlined in K13, with particles
exchanging small amounts of momentum, resulting in a overall drag force on the
halo. This regime means that the interpretation is unique in probing types of
DM scattering similar to that of Rutherford scattering, in which the differential
cross-section is highly anisotropic.
Full publication including equations/calculations available upon request.

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