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1 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 2 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 3 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 4 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 5 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 6 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 7 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. 8 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 9 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 10 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 11 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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