Download 1 Dark matter and dark energy comprise over 90% of the Universe

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THE SEARCH FOR DARK MATTER USING GRAVITATIONAL LENSING
RONALD E. MICKLE
Denver, Colorado 80005
©2008 Ronald E. Mickle
ABSTRACT
Dark matter and dark energy comprise over 90% of the Universe. Dark matter has
not been detected, cannot be seen and fails to emit electromagnetic radiation that we
can detect. In the Universe, the ratio of the average density of matter and energy is
the density parameter (Ω0) and is referenced in determining the fate of the Universe.
Current observations based on WMAP, combined with Baryon Acoustic Oscillations
and SNeIa indicate that ΩB = 0.0462 ± 0.0015, ΩD = 0.233 ± 0.013, and ΩΛ = 0.721 ±
0.015, using H0 = 70.1 ± km s-1 Mpc-1 . These cosmological observations means the
Universe is flat, with Ω0 = 1. The search for dark matter using gravitational lensing
provides the backdrop to explanations to what dark matter is and why it is important.
Among the myriad of particle candidates for dark matter, two stand out: the WIMP
and the axion. Gravitational lensing as a tool can help determine the mass of galaxies
and galaxy clusters, because lensing is an indicator of both the total mass of baryonic
matter AND dark matter. While a large number of dark matter studies have been
conducted using gravitational lensing, the methods continue to be improved. With the
placement of new space based observatories, such as GLAST, astronomers and other
scientist will continue to move closer to determining the composition of dark matter
and the fate of the Universe.
1. INTRODUCTION
Dark matter and dark energy are
believed to be most of what the Universe
is composed of. Thus far, it has not been
directly detected, cannot be seen and
fails to emit electromagnetic radiation
that we can detect. We believe dark
matter exists because of the motions of
stars, galaxies and galaxy clusters, but
there are alternatives such as Modified
Newtonian Dynamics, or MOND. By
measuring the velocity of these
astronomical objects, we know that the
mass has to be sufficient to keep the
stars, galaxies or galaxy clusters from
flying apart. In the case of large scale
velocity measurements, the amount of
baryonic matter or luminous matter is
only a smaller portion of the total mass
necessary to keep the objects together.
This missing mass is therefore referred
to as dark matter (Martin).
The search for dark matter using
gravitational lensing provides the
backdrop to explanations to what dark
matter is and why it is important. The
nature of dark matter has intrigued
astronomers and physicists for decades,
in much the same way black holes and
worm holes have fascinated the public
and science fiction writers. All these
mysteries are theorized and studied, but
cannot be physically observed.
Theoretical physics is rich with names of
exotic elementary particles such as
muons, bosons, leptons, up quarks, down
quarks and charm quarks. Of particular
interest in the search for dark matter is
the neutrino. Dark matter could take on
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other forms of ordinary non-luminous
matter such as planets and stars that did
not reach enough mass to start nuclear
reactions in their core, or dark remnants
of collapsed giant stars similar to black
holes (Livio 2000). Livio (2000) adds
that observations have discounted most
of these theories. According to
Kamionkowski and Koushiappas (2008)
among the myriad particle candidates for
dark matter, two classes are most
promising, the weakly interacting
massive particle (WIMP) and the axion.
WIMPs consist of subatomic particles
which have mass and interact weakly
with baryonic matter, while the axion is
a hypothetical lightweight particle with a
virtual infinite lifespan (Smoot &
Davidson 1993).
Dark matter is important because it
helps explain the disparity in the galactic
rotational curves of stars in the outer
regions of elliptical galaxies where stars
exhibit velocities higher than would be
expected, suggesting the presence of
dark matter in galaxies. On a much
larger scale dark matter plays a
considerable role in determining the fate
of the Universe. The mean density of
matter in the Universe (ρ) is the total
mass of the Universe divided by its
volume, and has been refined over the
years to approximately 10-27 kg cm-3
(Sartori 1996). By comparison, the
density of interstellar gas is 10-20 kg cm-3
while a neutron star is over 1017 kg cm-3
(Illingworth & Clark 2000). The ratio of
the average density of matter and energy
is the density parameter (Ω0) and given
as Ω0 = ρ/ρc where ρc is the critical
density and is referenced in determining
the fate of the Universe.
 If Ω0 > 1, the Universe’s
expansion will stop, start
contracting, leading to the big
crunch.

If Ω0 < 1, the Universe is
open and will expand forever.
 However, if Ω0 = 1, then the
Universe is considered flat
and the expansion proceeds
forever with the expansion
speed approaching zero.
Livio (2000) presents the analogy
using the kinetic energy of the Universe
as either smaller or larger than the
gravitational energy in determining the
expansion rate. In determining the
calculation Ω0, it is important to note
that (ρ) represents the total mass/energy
in the Universe, including baryonic and
dark matter, as well as dark energy and
is represented by their sums
Ω0 = ΩB + ΩD + ΩΛ
where ΩB is the density parameter for
baryonic matter, ΩD is the density
parameter of dark matter and ΩΛ is the
density parameter for dark energy.
Current observations based on WMAP
combined with Baryon Acoustic
Oscillations and SNeIa indicate that ΩB
= 0.0462 ± 0.0015, ΩD = 0.233 ± 0.013,
and ΩΛ = 0.721 ± 0.015, using H0 = 70.1
± km s-1 Mpc-1 (Hinshaw et al. 2008).
These cosmological observations mean
the Universe is flat, with Ω0 = 1.
Other evidence of dark matter is
exhibited in galaxy clusters such as
Abell 2029 (see Figures 1 and 2) which
are surrounded by x-ray emitting gas in
excess of a million degrees. The
luminous components alone do not exert
enough gravitational influence to keep
the gas from evaporating; there is a large
dark matter component distributed
roughly in a spherical halo around the
cluster. Dark halos are commonly
inferred in discussions of invisible dark
matter that permeates galaxies and
galaxy clusters. It is suggested that the
Milky Way’s dark halo extends beyond
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92 kpc, well past luminous baryonic
matter.
The search for dark matter employs
various methods, one being finding
WIMPs through the use of scintillating
crystals (Lang et al. 2008) and energetic
neutrinos from WIMP annihilation rate
in the Galactic halo (Kamionkowski &
Koushiappas 2008). These particular
Figure 1: Abell 2029 (optical image) is
a galaxy cluster composed of thousands
of galaxies. A large elliptical galaxy is
at center surrounded by smaller
galaxies. Distance: 1-Gly. Scale: 8x5
arcmin, cropped for publication.
Credit: NOAO/Kitt Peak/J.Uson, D.Dale,
S.Boughn, J.Kuhn)
2. GRAVITATIONAL LENSING
Gravitational lensing is when a
massive astronomical object referred to
as the lens, aligns with the observer’s
line of sight and another object on the far
side of the lens, referred to as the source,
as illustrated in Figure 3. When this
happens, the light rays from the source
object are bent around the lensing object
providing a distorted view of the source
which would normally not be visible
from behind the lens.
There are three general classes of
gravitational lensing: strong, weak and
micro lensing. Strong lensing exists
where there are visible distortions
created by the lensing mass, such as arcs,
studies and others are founded on the
theory that dark matter is a form of
weakly interacting massive particles and
may be detected directly in laboratory
experiments on Earth. This paper,
however, focuses on attempts to detect
dark matter through the use of
gravitational lensing.
Figure 2: Abell 2029 (x-ray image)
shows the cluster is embedded in an
enormous cloud of hot X-ray emitting
gas. This hot gas would evaporate from
the cluster if a dark halo were not
present. Scale: 8x5 arcmin, cropped
for publication. Credit:
NASA/CXC/IoA/S. Allen et al.
the Einstein rings or multiple images and
is created by a smooth mass distribution
such as a galaxy or cluster of galaxies.
This is also referred to as macrolensing
(Illingworth & Clark 2000). References
appear to use the terms macrolensing
and strong lensing interchangeably
(Falco et al. 1996; Safonova et al. 2001;
Zakharov et al. 2004). Weak lensing is
similar to previously described
macrolensing, but on a smaller scale.
Small magnifications result in small
shape changes and are independent of
source size or the lensing. Microlensing
occurs when the lens mass is sufficiently
small such that the multiple images are
separated by microarcseconds and
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cannot be resolved, but can be detected
as an increase in the source brightness.
Visually, the source appears
elongated tangentially to the center of
the lens. In galaxy clusters, blue arclets
may be seen, although weakly lensed
(Illingworth & Clark 2000).
Microlensing occurs when there is no
distortion of the source star, only a
photometric increase in brightness. This
increase in brightness happens when the
lensing object, such as a brown dwarf or
other massive object in the dark halo of
the Milky Way, passes in front of the
source star. The amplification by the
lensing is very rare and requires precise
photometric measurements.
Figure 3. http://relativity.livingreviews.org/Articles/lrr1998-12/
QSO 0957+561 is not in perfect
alignment with our line of sight, but is
offset by approximately 6 arcsecs, with
one image almost directly behind the
lensing galaxy. Schwarzschild lens
model is considered the simplest and
most basic of setups for a point source S
and lens L. The observer O views light
emitted by the source deflected by the
While relativity predicted the
bending of star light close to the sun, the
theory has applications for objects at
great distances. Gravitational lensing
defers from optical lens in that it focuses
parallel light from infinity to a line
instead of a focal plane. Any observer
on the opposite side of the lens from the
source would see a focused image.
The first object gravitationally lensed
was the double quasar QSO 0957+561
(Figure 4) in 1979 (Walsh et al. 1979;
Weymann et al. 1979). Initial viewing
shows what appear to be two objects, but
closer scrutiny reveals three.
Figure 4: QSO 0957+561, B. Keel, Univ. of
Alabama, Dept of Physics & Astronomy.
HST/WFPC2
lens. In this basic setup (Figure 3), a
point-like lens will always result in at
least two images, S1 and S2 .
In the Schwarzschild lens model, the
mass L in the lens plane is the lensing
object. The deflection angle for the
Schwarzchild lens is
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where M (ξ) is the mass inside a radius
ξ (Wambsganss 1998), G the
gravitational constant and c the speed of
light. The closer the light ray passes to
the lensing mass, the greater the
deflection.
If the point source S is directly in
line with the observer O and the
Schwarzchild lens (L), the resultant
image is called the Einstein ring or
Einstein radius, with radius
.
The distances D are angular diameter
between O, L and S.
Astrophysicists know dark matter
exists because of the causal factors it
exhibits on other matter. Dark matter
exerts gravitational forces on the
baryonic matter and can be mapped
based on the gravitational lensing effect.
Dark matter manifests itself is through
the lumpiness in the cosmic microwave
background and the motions of galaxies
in galaxy clusters (Bally & Reipurth
2006), as well as the accelerated
expansion rate of the Universe (Riess et
al. 2004; Astier et al. 2006; Szydlowski
& Tambor 2008). The significance of
dark matter can be found in the effects it
has on cosmological objects. Studies
conducted during the early years of
searches for dark matter using
gravitational lensing in the galactic halo,
lead some scientists to speculate that the
Galaxy’s outer disk was distorted,
warped and not the flat exponential disk
we had grown accustomed believing
(Evans et al. 1998). It is interesting to
note that the Evans et al. (1998) study
referenced the stellar count toward
determining the Milky Way’s galactic
morphology and the recent press release
by the Spitzer Science Center measuring
stellar densities in determining the
Galaxy had two major arms, rather than
four (Clavin 2008).
Gravitational lensing is supported by
General Relativity’s third prediction, a
concept where a gravitational field bends
light. A mass exerting a strong
gravitational field can further focus the
light rays similar to a lens. The bending
of light postulated by Einstein can be
explained by the principle of
equivalence, using the accelerating
elevator analogy to demonstrate. The
hypothetical experiment demonstrates
the bending of light in a gravitational
field when a beam of light enters the
elevator at right angles to its direction of
travel. The elevator accelerates upward
in its reference frame, but the light beam
travels a parabolic path downward. The
upward acceleration of the elevator is
equivalent to the gravitational field
directed downward. (Sartori 1996)
Scientists were able to first test this
hypothesis during the solar eclipse on
1919 when astronomers measured the
predicted deflection of starlight passing
close to the limb of the sun.
2.1. Importance of lensing as a tool
in the Search for Dark Matter
Searches for dark matter within our
own galactic Local Group or beyond the
Milky Way, rely strongly on
gravitational lensing as a tool for several
reasons. Accurate mass measurements
of galaxies and clusters are necessary in
order to develop strong constraints on
estimates and models. Within galaxies
and clusters, the mass function and
power spectrum can be attributed to dark
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matter and dark energy, but the
dynamics are dominated by dark matter.
(Halkola et al. 2008) Using gravitational
lensing as a tool, we can determine the
mass of galaxies and galaxy clusters,
because lensing is an indicator of both
the total mass of baryonic matter AND
dark matter.
The angle the light ray is bent is
determined by the point lens mass,
hence, the gravitational force exerted.
Einstein’s theory of General Relativity
indicates that the energy of the
gravitational field be determined by the
matter distribution. Neither the
gravitational field nor the deflection
angle depends on the type of matter;
therefore, matter density may be
baryonic matter, dark matter, or both.
(Bartelmann and Schneider 2001)
3. LENSING-BASED SEARCHES FOR
DARK MATTER WITHIN THE MILKY
WAY GALAXY AND THE KEY
RESULTS
The idea was first proposed in 1986
to use microlensing to detect Massive
Compact Halo Objects (MACHOs) in
the galactic halo by monitoring stars in
the Large and Small Magellanic Clouds
(LMC and SMC). Objects in the halo of
the Milky Way, such as brown dwarfs or
black holes can produce microlensing of
a distant star, causing it to brighten.
These microlensing objects are referred
to as massive compact halo objects or
MACHOs for short. If a MACHO came
into alignment with the observer and the
distant star, the brightness of the star
would increase through lensing. For
detection, millions of stars in the LMC
and SMC would have to be monitored.
(Livio 2000 p93) Until the nature of
dark matter is determined, scientists of
course cannot rule out baryonic matter as
a possible dark matter candidate. Hence,
MACHOs have been suggested as
possible candidates for dark matter.
Both the Spitzer Space Telescope (SST),
launched in 2003 with its Infrared Array
Camera (IRAC) and the Hubble Space
Telescope (HST) have been used by the
MACHO collaborators to search for
MACHOs in the dark halo surrounding
the Milky Way. Spitzer IRAC is
particularly useful in searching for
brown dwarfs in the galactic halo due to
their low surface temperature emitting in
the IR and near-IR part of the spectrum.
The studies conducted by the
MACHO collaborators focused on
photometry data most likely to contain
candidates for microlensing, which was
MACHO-LMC-5 and MACHO-LMC20, hereafter referred to as Event-5 and
Event-20. Event-5 was also recorded
with HST. Great progress has been
made toward the analysis and data
reduction of gravitational microlensing
events since the first recorded detection
was published in Nature in 1993
(Nguyen et al. 2004). Since then, over
12 million stars from LMC have been
analyzed (Minniti).
Spitzer IRAC was used to record the
source star of Event-5, 10 years after the
initial imaging. In 1993, Macho
collaborators recorded a brightness
factor of 47 over 76 days. Around 2001,
HST WFPC2 was able to record both the
source and the lens. By 2004, the source
and the lensing mass had separated by
~0”.24, and again HST was used to
image the event, this time using
ACS/HRC. The conclusion was the lens
mass was probably a dwarf M5 star at
≈600 pc. Resolution of Spitzer is
reported as ~1”.8 at FWHM of the PSF.
It is unknown if removal of instrumental
effects through deconvolution was
undertaken. By removing the V-I color
index through data reduction, the
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MACHO collaborators estimated the
source contributed <10% of the
combined flux of Event-5, showing a
substantial infrared excess. Therefore,
MACHO-LMC-5 exhibited colors
corresponding to a late M dwarf or early
L dwarf star of ~0.2 Mʘ. The
collaborators felt that Spitzer’s
capabilities in detecting cool, low mass
stellar lens had been well demonstrated.
(Nguyen et al. 2004)
The data reduction and analysis of
the MACHO collaborators appears
sound but their calculations of optical
depth  appear to be in conflict with
other studies (Evans & Belokurov 2005).
In analyzing the photometry of the
source and the lensing mass, the flux is
computed using the distance. The
amount the flux is reduced after
traveling through the medium is . An
optical depth of zero means the medium
is transparent, with the opacity
decreasing as the optical depth number
increases. A larger  would be
indicative of a greater amount of dark
matter in the medium of the halo.
(Illingworth & Clark 2000) A second
collaborative team, EROS, also
conducted searches for MACHOs within
the dark halo of the Milky Way and
concluded with the team of Evans and
Belokurov (2005) that the computed
optical depths are much less than that of
the MACHO team. Belokurov et al.
stated they discarded data points that
deviated by more than 3σ from its
neighbors (Evans & Belokurov 2005).
However, the study by Evans and
Belokurov (2005) which used a neural
networking method, was also challenged
as stating their analysis contained several
errors and used 0.2% of the available
MACHO dataset (Griest and Thomas
2005). There is room for humor in
scientific debates as quoted by Evans
and Belokurov (2005) in their response
to the challenge by Griest and Thomas
(2005), “Of course, there is no need to
re-enact the epic battle between the mice
and the frogs…in the pages of this
Journal.” Healthy academic
disagreement is, for science, a good
thing. Bennett et al. (2005) argues that
Evans and Belokurov (2005) over
confidence in the neural networking
method may have led them to over
interpret the results. As described by
Bennett et al. the black box nature of
neural networking is that decisions are
difficult to troubleshoot. Bennett et al.
refined previously unpublished
photometry and combined microlensing
light-curve fitting with photometry from
HST images, used difference image
photometry of images captured with the
1.3 m Skymapper at MSSSO (referenced
as the Great Melbourne telescope in their
study), and used follow up images from
the 0.9 m CTIO telescope. Bennett et al.
(2005) published the comparison results
(Table 5) of Evans’ and Belokurov’s
(2005) and MACHO in the following
table.
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TABLE 5
Event Classification
Event
MACHO Verdict
BEL Verdict
Confirmation
Mancini et al. Lens Type
1
Non-LMC
Clump giant
lens-A
lens
4
Variable
Non-LMC
CTIO+DIP phot.
lens-A
5
MW disk
Lens ID
lens-A
lens
6
--LMC
lens-A
lens-A
7
Variable
--Non-LMC
lens-A
8
Variable
--LMC
lens-A
9
--LMC
Caustic binary
lens -B
10
SN
HST: galaxy
--lens
11
SN
SN
HST: galaxy
--12
SN
SN
HST: galaxy
--13
Variable
LMC
CTIO+DIP phot
lens-A
14
LMC
CTIO+DIP phot
lens-A
lens
15
Variable
non-LMC
CTIO+DIP phot
lens-A
16
SN
--CTIO: galaxy
--17
SN
SN
CTIO: galaxy
--18
Variable
--non-LMC
lens-A
19
SN
SN
CTIO: galaxy
--20
SN
----lens-B
21
--non-LMC
lens-A
lens
22
B
MSSSO: galaxy
--lens
23
Variable
--lens-A
lens
24
SN
MACHO: galaxy
--lens
25
non-LMC
Clump giant
lens-A
lens
26
SN
Variable
----27
Variable
----lens-B
The event classification results of MACHO and BEL are compared to the results of additional data that
can confirm or reject each event. Confirmed microlensing events have boldface entries in the
confirmation column, and rejected microlensing candidates have entries in italics. (Bennett, Becker &
Tomaney 2005)
Note that certain data points in the
table for MACHO, and Evans and
Belokurov (2005), are in disagreement
with the findings of Bennett et al.,
however, Bennett et al. reduction and
analysis steps appears much improved
and refined over earlier studies.
In 2002, the EROS collaborators
published the results of five years worth
of data taken toward the SMC applying
additional reduction steps and analysis to
more accurately assess stellar blending
on the overall efficiency. The results,
four additional microlensing candidates,
were combined with previous EROS
observations placing strong limits on the
amount of galactic dark matter
comprised of MACHOs, and concluded
with a 95% confidence level that no
more than 25% of the halo mass of 4 x
1011 Mʘ out to 50 kpc could be
composed of objects between 2 x 10-7
Mʘ and 1 Mʘ. (Afonso et al. 2003)
A third group represented by the
Optical Gravitational Lensing
Experiment (OGLE) collaborators chose
to look not toward the SMC and LMC,
but toward the galactic bulge where lowmass stars were known to exist and the
microlensing rate was better than one in
a million with a much better chance of
detection. OGLE’s first report
documented nine microlensing events of
galactic bulge stars, but concluded that
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they had no evidence that the OGLE
events are related to dark matter
(Paczynski et al. 1994). They also
recorded the longest ever microlensing
event, cataloged OGLE-1999-BUL-32,
later verified by MACHO collaborators
as MACHO-99-BLG-22. The Einstein
crossing radius was reported as 640d.
(Mao et al. 2002)
One result of the OGLE survey was
the discovery of an exoplanet through
gravitational lensing. Most extra solar
planet discoveries use the radial velocity
method in detecting the wobble of the
host star. The planet, designated OGLE2005-BLG-390Lb, discovered on July
11, 2005, was the third extra solar planet
discovered through microlensing. (Türler
2006)
If a summation is to be made
regarding the methods used to detect
dark matter using microlensing within
the Milky Way galaxy, it is that all
methods employed by collaborators still
have room for improvement and
refinement. The MACHO and EROS
teams have completed the microlensing
survey proposed by Paczynski in 1986
and concluded that the dark halo
surrounding the Milky Way is not
dominated by planet or stellar mass
objects, however these mass objects do
exists (Bennett et al. 2005).
4. LENSING-BASED SEARCHES FOR
DARK MATTER BEYOND THE MILKY
WAY GALAXY AND THE KEY
RESULTS
Galaxy Cluster Abell 2218 was
chosen because of its unusually high z
and CL0024+1654 because its mass is
smaller than the predicted lensing models.
Of all the galaxy clusters in the Abell
catalog, 2218 is one of the richest in
terms of number of lensing events
(Elıasdottir et al. 2007), and has itself been
used as a gravitational telescope to
discover a source at z = 5.6 (Ellis et al.
2001). A more distant source was later
discovered using Abell 2218 at z ~ 6.7
by Kneib et al. (2004).
Gravitational lensing associated with
galaxy clusters reveals the dynamics
supporting the existence of massive dark
matter halos. The halos associated with
these galactic clusters, as well as the xray emitting intracluster medium (ICM)
confined to the halo, can be used as a
locator of dark matter. If we assume
hydrostatic equilibrium within the
cluster between the gas pressure P and
the gravitational potential Φ, the relation
being ∇P = ρg ∇ Φ, with ρg
representing the gas density, the gas
pressure can constrain the shape of the
dark matter halo. However, the
reliability of the hydrostatic mass
estimates is unknown (Mahdavi et al.
2007).
Elıasdottir et al. (2007) have gone
into great detail in probing the dynamics
of Abell 2218 by explaining and
detailing the mass distribution of dark
matter clumps, based on lensing, of each
of the cluster galaxies. Mass distribution
of the cluster galaxies is identified with
central locations for the ellipticity and
position angle to the light distribution.
The total projected mass is centered on a
bright central galaxy (BCG) with mass
distribution bimodal in DM1 (dark
matter) and DM2. Referencing Figure 6,
the bright BCG is visible, with large
scale DM1 closely associated with BCG,
and DM2 to the southeast (North is up).
Unfortunately, neither DM1, nor DM2
are visible. The clumps are referred to
as large scale if their total mass in the
outer most constraint is greater than 20%
of the total mass. The team also found
evidence that the lensing constraint
could not be modeled using only the
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dark matter halos, but required the use of
the large scale halos associated with the
dark matter clumps. Within a radius of
291 kpc, the team determined that large
scale halos accounted for 85% of the
total mass, with the BCG ~9% and the
remaining galaxy clusters ~6%
(Elıasdottir et al. 2007).
Figure 6: Color image of Abell 2218 based on ACS data (filters F775W (red), F625W (green) and F475W (blue)
channel). Cluster galaxies are marked in yellow (modeled using scaling relations) or blue (individually fitted). The
multiple images are labeled in green for spectroscopically confirmed systems and red for candidate systems. The arc
for which we have obtained spectroscopic redshift, S8, is labeled in cyan. Also shown are the critical lines
corresponding to z = 0.702 (cyan), z = 2.515 (red) and z = 6.7 (green). NASA/HST/ACS (Elıasdottir et al. 2007)
In reconstructing a mass map of
Abell 2218, the team of Elıasdottir et al.
(2007) confirmed earlier models
showing that mass distribution is
bimodal, and identifying the cluster as a
strong gravitational lens through
mapping of large clumps of dark matter.
The rich galaxy cluster
CL0024+1654 lies approximately five
billion light years distance, and images
show unique blue arclets, which are
actually one galaxy twice the distance of
the foreground cluster, but
gravitationally lensed into five images.
(Colley et al. 1996) During a five year
period starting in 1998, there were
inconsistencies in the cluster velocity
dispersion which was much greater than
the measured value of σv = 1150 km s−1
which suggested a flattening of the
density profile closer to the core of the
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cluster and in conflict with simulations
of the standard CDM model. (Shapiro &
Iliev 2000) The inconsistency of the
cluster velocity dispersion with the
lensing power and X-ray luminosity was
resolved when a second velocity
dispersion was found at z ~ 0.38, and has
been suggested was the result of a
collision with another galactic group.
(Kneib et al. 2003)
However, Kneib et al. (2003)
suggests that the power law fit indicates
an asymptotic distribution and strongly
rejects an isothermal mass. Analysis of
the cluster X-ray emission in 2004 by
Ota et al. concluded the mean
temperature of 4.4 keV was a good fit
for distribution. Therefore, assuming
that the intracluster medium was in
hydrostatic equilibrium, the estimated
mass profile of CL0024 through
gravitational lensing and analysis of the
redshifts of components of the cluster
and X-ray observations indicate a mass 2
to3 times smaller than the lensing mass
prediction (Coia et al. 2006). It is
interesting to note that studies conducted
on CL0024+1654 within the past year
are referencing data from 1992
(Takahashi & Chiba 2007) which is in
conflict with data mentioned earlier
(Kneib et al. 2003).
Kneib et al.(2003) appeared to have
resolved the cluster dispersion problem
within CL0024 when a second velocity
dispersion peak was found. Referencing
their calculations, Mishchenko and Ji
(2004) suggest it is tempting, but
incorrect, to correlate equilibrium
between the dark and the visible
components in 0024+1654. To
compensate for the mass loss, they
suggest dark matter particles with a mass
between µd ≈ 200 − 1000MeV and the
Standard Model does not have a
candidate within this mass range.
Mishchenko and Ji (2004) conclude that
sufficient information is not available to
make a quantitative conclusion regarding
CL0024s thermal state using the known
mass profile.
5. CONCLUSION
In the search of dark matter,
astronomers and physicists use an array
of instruments and tools. Without
knowing what dark matter is, they gather
empirical and measureable facts, and
then conduct experiments and
formulation to test their hypothesis.
Tools used include supercolliders to
search for hypothesized subatomic
particles, or neutrino detectors deep
underground. Astronomers look for dark
matter within our Galaxy and throughout
the Universe by using gravitational
lensing as a tool to measure luminous
baryonic matter, rotational curves of
stellar objects within galaxies and to
determine mass distribution.
In addition to ground based
telescopes, over the years astronomers
have use space based observatories such
as WMAP, Hubble and COBE. Just
recently, NASA launched its newest
space based observatory, GLAST, with
one of its objectives being to look for
gamma rays of specific wavelengths
which are produced by dark matter
annihilation. Supersymmetry in particle
physics predicts a particular wavelength
of gamma ray is produced through
WIMP annihilations. These gamma rays
are distinct for those produced by
sources such as black holes or
supernovae. (Woo 2008) This is one
more step toward understanding the
composition of dark matter, and
ultimately the fate of the Universe.
12
The use of gravitational lensing to
detect the presence of dark matter is
maturing, but it is not without issues.
All that has been discussed in this
paper originates with Einstein’s general
theory of Relativity. While not relevant
to this paper, I want to note that G.B.
Shaw once said there were only eight
great men of science, all the others were
tinkers who chiseled away on the ideas
of the eight. And of those eight, there
were only three who built complete
universes – Ptolemy, Newton and
Einstein.
ACKNOWLEDGMENTS
This paper was prepared by the author as
part of the curriculum requirement of
©Swinburne Astronomy Online (SAO),
Graduate Diploma in Science
(Astronomy), Center for Astrophysics &
Supercomputing, Swinburne University
of Technology. Thanks to Dr. Chris
Fluke (SAO) for critical comments and
Joanie Mickle for editorial comments.
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