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 ± -1 -1 0.015, using H0 = 70.1 ± km s Mpc . 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 necessary to keep the objects together. This missing mass is therefore referred Dark matter and dark energy are to as dark matter (Martin). believed to be most of what the Universe The search for dark matter using is composed of. Thus far, it has not been gravitational lensing provides the directly detected, cannot be seen and backdrop to explanations to what dark fails to emit electromagnetic radiation matter is and why it is important. The that we can detect. We believe dark nature of dark matter has intrigued matter exists because of the motions of astronomers and physicists for decades, stars, galaxies and galaxy clusters, but in much the same way black holes and there are alternatives such as Modified worm holes have fascinated the public Newtonian Dynamics, or MOND. By and science fiction writers. All these measuring the velocity of these mysteries are theorized and studied, but astronomical objects, we know that the cannot be physically observed. mass has to be sufficient to keep the Theoretical physics is rich with names of stars, galaxies or galaxy clusters from exotic elementary particles such as flying apart. In the case of large scale muons, bosons, leptons, up quarks, down velocity measurements, the amount of quarks and charm quarks. Of particular baryonic matter or luminous matter is interest in the search for dark matter is only a smaller portion of the total mass the neutrino. Dark matter could take on 2 other forms of ordinary non-luminous If Ω0 < 1, the Universe is matter such as planets and stars that did open and will expand forever. not reach enough mass to start nuclear However, if Ω0 = 1, then the reactions in their core, or dark remnants Universe is considered flat of collapsed giant stars similar to black and the expansion proceeds holes (Livio 2000). Livio (2000) adds forever with the expansion that observations have discounted most speed approaching zero. of these theories. According to Livio (2000) presents the analogy Kamionkowski and Koushiappas (2008) using the kinetic energy of the Universe among the myriad particle candidates for as either smaller or larger than the dark matter, two classes are most gravitational energy in determining the promising, the weakly interacting expansion rate. In determining the massive particle (WIMP) and the axion. calculation Ω0, it is important to note WIMPs consist of subatomic particles that (ρ) represents the total mass/energy which have mass and interact weakly in the Universe, including baryonic and with baryonic matter, while the axion is dark matter, as well as dark energy and a hypothetical lightweight particle with a is represented by their sums virtual infinite lifespan (Smoot & Ω0 = ΩB + ΩD + ΩΛ Davidson 1993). where ΩB is the density parameter for Dark matter is important because it baryonic matter, ΩD is the density helps explain the disparity in the galactic parameter of dark matter and ΩΛ is the rotational curves of stars in the outer density parameter for dark energy. regions of elliptical galaxies where stars Current observations based on WMAP exhibit velocities higher than would be combined with Baryon Acoustic expected, suggesting the presence of Oscillations and SNeIa indicate that ΩB dark matter in galaxies. On a much = 0.0462 ± 0.0015, ΩD = 0.233 ± 0.013, larger scale dark matter plays a and ΩΛ = 0.721 ± 0.015, using H0 = 70.1 considerable role in determining the fate ± km s-1 Mpc-1 (Hinshaw et al. 2008). of the Universe. The mean density of These cosmological observations mean matter in the Universe (ρ) is the total the Universe is flat, with Ω0 = 1. mass of the Universe divided by its Other evidence of dark matter is volume, and has been refined over the exhibited in galaxy clusters such as -27 -3 years to approximately 10 kg cm Abell 2029 (see Figures 1 and 2) which (Sartori 1996). By comparison, the are surrounded by x-ray emitting gas in -20 -3 density of interstellar gas is 10 kg cm excess of a million degrees. The 17 -3 while a neutron star is over 10 kg cm luminous components alone do not exert (Illingworth & Clark 2000). The ratio of enough gravitational influence to keep the average density of matter and energy the gas from evaporating; there is a large is the density parameter (Ω0) and given dark matter component distributed as Ω0 = ρ/ρc where ρc is the critical roughly in a spherical halo around the density and is referenced in determining cluster. Dark halos are commonly the fate of the Universe. inferred in discussions of invisible dark If Ω0 > 1, the Universe’s matter that permeates galaxies and expansion will stop, start galaxy clusters. It is suggested that the contracting, leading to the big Milky Way’s dark halo extends beyond crunch. 3 92 kpc, well past luminous baryonic studies and others are founded on the matter. theory that dark matter is a form of The search for dark matter employs weakly interacting massive particles and various methods, one being finding may be detected directly in laboratory WIMPs through the use of scintillating experiments on Earth. This paper, crystals (Lang et al. 2008) and energetic however, focuses on attempts to detect neutrinos from WIMP annihilation rate dark matter through the use of in the Galactic halo (Kamionkowski & gravitational lensing. Koushiappas 2008). These particular Figure 1: Abell 2029 (optical image) is Figure 2: Abell 2029 (x-ray image) a galaxy cluster composed of thousands shows the cluster is embedded in an of galaxies. A large elliptical galaxy is enormous cloud of hot X-ray emitting at center surrounded by smaller gas. This hot gas would evaporate from galaxies. Distance: 1-Gly. Scale: 8x5 the cluster if a dark halo were not arcmin, cropped for publication. present. Scale: 8x5 arcmin, cropped Credit: NOAO/Kitt Peak/J.Uson, D.Dale, for publication. Credit: S.Boughn, J.Kuhn) NASA/CXC/IoA/S. Allen et al. 2. GRAVITATIONAL LENSING the Einstein rings or multiple images and is created by a smooth mass distribution Gravitational lensing is when a such as a galaxy or cluster of galaxies. massive astronomical object referred to This is also referred to as macrolensing as the lens, aligns with the observer’s (Illingworth & Clark 2000). References line of sight and another object on the far appear to use the terms macrolensing side of the lens, referred to as the source, and strong lensing interchangeably as illustrated in Figure 3. When this (Falco et al. 1996; Safonova et al. 2001; happens, the light rays from the source Zakharov et al. 2004). Weak lensing is object are bent around the lensing object similar to previously described providing a distorted view of the source macrolensing, but on a smaller scale. which would normally not be visible Small magnifications result in small from behind the lens. shape changes and are independent of There are three general classes of source size or the lensing. Microlensing gravitational lensing: strong, weak and occurs when the lens mass is sufficiently micro lensing. Strong lensing exists small such that the multiple images are where there are visible distortions separated by microarcseconds and created by the lensing mass, such as arcs, 4 cannot be resolved, but can be detected While relativity predicted the as an increase in the source brightness. bending of star light close to the sun, the Visually, the source appears theory has applications for objects at elongated tangentially to the center of great distances. Gravitational lensing the lens. In galaxy clusters, blue arclets defers from optical lens in that it focuses may be seen, although weakly lensed parallel light from infinity to a line (Illingworth & Clark 2000). instead of a focal plane. Any observer Microlensing occurs when there is no on the opposite side of the lens from the distortion of the source star, only a source would see a focused image. photometric increase in brightness. This The first object gravitationally lensed increase in brightness happens when the was the double quasar QSO 0957+561 lensing object, such as a brown dwarf or (Figure 4) in 1979 (Walsh et al. 1979; other massive object in the dark halo of Weymann et al.