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 ...
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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
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
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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
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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
