暗物质初步

Hindawi Publishing Corporation Advances in Astronomy Volume 2011, Article ID 968283, 22 pages doi:10.1155/2011/968283 Review Article DarkMatter: A Primer Katherine Garrett and Gintaras Du¯da Department of Physics, Creighton University, 2500 California Plaza, Omaha, NE 68178, USA Correspondence should be addressed to Gintaras Du¯da, gkduda@creighton.edu Received 12 June 2010; Accepted 28 September 2010 Academic Editor: David Merritt Copyright © 2011 K. Garrett and G. Du¯da. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Dark matter is one of the greatest unsolved mysteries in cosmology at the present time. About 80% of the Universe’s gravitating matter is nonluminous, and its nature and distribution are for the most part unknown. In this paper, we will outline the history, astrophysical evidence, candidates, and detection methods of dark matter, with the goal to give the reader an accessible but rigorous introduction to the puzzle of dark matter. This paper targets advanced students and researchers new to the field of dark matter, and includes an extensive list of references for further study. 1. Introduction One of the most astounding revelations of the twentieth century in terms of our understanding of the Universe is that ordinary baryonic matter, that is, matter made up of protons and neutrons, is not the dominant form of material in the Universe. Rather, some strange new form of matter, dubbed “dark matter,” fills our Universe, and it is roughly five times more abundant than ordinary matter. Although we have yet to detect this strange material in the laboratory, there is a great deal of evidence which points to the necessity of its existence. A complete understanding of dark matter requires utilizing several branches of physics and astronomy. The creation of dark matter during the hot expansion of the Universe is understood through statistical mechanics and thermodynamics. Particle physics is necessary to propose candidates for dark matter and explore its possible interac- tions with ordinary matter. General relativity, astrophysics, and cosmology dictate how dark matter acts on large-scales and how the Universe may be viewed as a laboratory to study dark matter. Many other areas of physics come into play as well, making the study of dark matter a diverse and interdisciplinary field. Furthermore, the profusion of ground and satellite-based measurements in recent years have rapidly advanced the field making it dynamic and timely; we are truly entering the era of “precision cosmology”. This paper aims to give a general overview of the subject of dark matter suitable for nonexperts; we hope to treat this fascinating and important topic in a way such that the non- specialist will gain a strong foundation and introduction to dark matter. It is at times difficult to find understandable and appropriate literature for individuals with no background on the subject. Existing reviews are either popular-level pieces which are too general or specialized pieces for experts in the field, motivating us to create an accessible overview. We particularly hope that this paper will be helpful to graduate students beginning their study of dark matter and to other physicists and astronomers who would like to learn more about this important topic. To give such an introduction to dark matter, we will first briefly explain the first hints that dark matter exists, elaborate on the strong evidence physicists and astronomers have accumulated in the past years, discuss the neutralino and other possible candidates, and describe various detection methods used to probe the dark matter’s mysterious prop- erties. Although we will at times focus on supersymmetric theories of dark matter, other possibilities will be introduced and discussed. 2. History and Early Indications Astronomers have long relied on photometry to yield estimates on mass, specifically through well-defined mass to Administrator 高亮 Administrator 高亮 2 Advances in Astronomy luminosity ratios (M/L). This is not at all surprising, since visual astronomy relies on the light emitted from distant objects. For example, the M/L ratio for the Sun is M/L = 5.1× 103 kg/W; since this number is not terribly instructive, one usually measures mass to luminosity in terms of the Sun’s mass and luminosity such that M�/L� = 1 by definition. Thus by measuring the light output of an object (e.g., a galaxy or cluster of galaxies) one can use well-defined M/L ratios in order to estimate the mass of the object. In the early 1930s, Oort found that the motion of stars in the Milky Way hinted at the presence of far more galactic mass than anyone had previously predicted. By studying the Doppler shifts of stars moving near the galactic plane, Oort was able to calculate their velocities, and thus made the startling discovery that the stars should be moving quickly enough to escape the gravitational pull of the luminous mass in the galaxy. Oort postulated that there must be more mass present within the Milky Way to hold these stars in their observed orbits. However, Oort noted that another possible explanation was that 85% of the light from the galactic center was obscured by dust and intervening matter or that the velocity measurements for the stars in question were simply in error [1]. Around the same time Oort made his discovery, Swiss astronomer Zwicky found similar indications of missing mass, but on a much larger scale. Zwicky studied the Coma cluster, about 99 Mpc (322 million lightyears) from Earth, and, using observed Doppler shifts in galactic spectra, was able to calculate the velocity dispersion of the galaxies in the Coma cluster. Knowing the velocity dispersions of the individual galaxies (i.e., kinetic energy), Zwicky employed the virial theorem to calculate the cluster’s mass. Assuming only gravitational interactions and Newtonian gravity (F ∝ 1/r2), the virial theorem gives the following relation between kinetic and potential energy: 〈T〉 = −1 2 〈U〉, (1) where 〈T〉 is the average kinetic energy and 〈U〉 is the average potential energy. Zwicky found that the total mass of the cluster was Mcluster ≈ 4.5 × 1013M�). Since he observed roughly 1000 nebulae in the cluster, Zwicky calculated that the average mass of each nebula was Mnebula = 4.5× 1010M�. This result was startling because a measurement of the mass of the cluster using standard M/L ratios for nebulae gave a total mass for the cluster approximately 2% of this value. In essence, galaxies only accounted for only a small fraction of the total mass; the vast majority of the mass of the Coma cluster was for some reason “missing” or nonluminous (although not known to Zwicky at the time, roughly 10% of the cluster mass is contained in the intracluster gas which slightly alleviates but does not solve the issue of missing mass) [2, 3]. Roughly 40 years following the discoveries of Oort, Zwicky, and others, Vera Rubin and collaborators conducted an extensive study of the rotation curves of 60 isolated galaxies [4]. The galaxies chosen were oriented in such a way so that material on one side of the galactic nucleus was approaching our galaxy while material on the other side was receding; thus the analysis of spectral lines (Doppler shift) gave the rotational velocity of regions of the target galaxy. Additionally, the position along the spectral line gave angular information about the distance of the point from the center of the galaxy. Ideally one would target individual stars to determine their rotational velocities; however, individual stars in distant galaxies are simply too faint, so Rubin used clouds of gas rich in hydrogen and helium that surround hot stars as tracers of the rotational profile. It was assumed that the orbits of stars within a galaxy would closely mimic the rotations of the planets within our solar system. Within the solar system, v(r) = √ G m(r) r , (2) where v(r) is the rotation speed of the object at a radius r, G is the gravitational constant, and m(r) is the total mass contained within r (for the solar system essentially the Sun’s mass), which is derived from simply setting the gravitational force equal to the centripetal force (planetary orbits being roughly circular). Therefore, v(r) ∝ 1/√r, meaning that the velocity of a rotating body should decrease as its distance from the center increases, which is generally referred to as “Keplerian” behavior. Rubin’s results showed an extreme deviation from pre- dictions due to Newtonian gravity and the luminous matter distribution. The collected data showed that the rotation curves for stars are “flat,” that is, the velocities of stars continue to increase with distance from the galactic center until they reach a limit (shown in Figure 1). An intuitive way to understand this result is through a simplified model: consider the galaxy as a uniform sphere of mass and apply Gauss’s law for gravity (in direct analogy with Gauss’s Law for the electric field)∫ S �g · d �A = 4πGMencl, (3) where the left hand side is the flux of the gravitational field through a closed surface and the right hand side is proportional to the total mass enclosed by that surface. If, as the radius of the Gaussian surface increases, more and more mass in enclosed, then the gravitational field will grow; here velocities can grow or remain constant as a function of radius r (with the exact behavior depending on the mass profile M(r)). If, however, the mass enclosed decreases or remains constant as the Gaussian surface grows, then the gravitational field will fall, leading to smaller and smaller rotational velocities as r increases. Near the center of the galaxy where the luminous mass is concentrated falls under the former condition, whereas in the outskirts of the galaxy where little to no additional mass is being added (the majority of the galaxy’s mass being in the central bulge) one expects the situation to be that of the latter. Therefore, if the rotational velocities remain constant with increasing radius, the mass interior to this radius must be increasing. Since the density of luminous mass falls past the central bulge of the galaxy, the “missing” mass must be nonluminous. Rubin summarized, “The conclusion is inescapable: mass, unlike luminosity, Advances in Astronomy 3 0 50 100 V el oc it y (k m /s ) 150 0 NGC 3198 data Keplerian prediction 10 Radius (Arcmin) 20 30 Figure 1: Measured rotational velocities of HI regions in NGC 3198 [5] compared to an idealized Keplerian behavior. is not concentrated near the center of spiral galaxies. Thus the light distribution in a galaxy is not at all a guide to mass distribution” [4]. In the 1970s, another way to probe the amount and distribution of dark matter was discovered: gravitational lensing. Gravitational lensing is a result of Einstein’s Theory of Relativity which postulates that the Universe exists within a flexible fabric of spacetime. Objects with mass bend this fabric, affecting the motions of bodies around them (objects follow geodesics on this curved surface). The motions of planets around the Sun can be explained in this way, much like how water molecules circle an empty drain. The path of light is similarly affected; light bends when encountering massive objects. To see the effects of gravitational lensing, cosmologists look for a relatively close, massive object (often a cluster of galaxies) behind which a distant, bright object (often a galaxy) is located (there is actual an optimal lens- observer separation, so this must be taken into account as well). If the distant galaxy were to be located directly behind the cluster, a complete “Einstein ring” would appear; this looks much like a bullseye, where the center is the closer object and the ring is the lensed image of the more distant object. However, the likelihood of two appropriately bright and distant objects lining up perfectly with the Earth is low; thus, distorted galaxies generally appear as “arclets,” or partial Einstein rings. In 1979, Walsh et al. were the first to observe this form of gravitational lensing. Working at the Kitt Peak National Observatory, they found two distant objects separated by only 5.6 arc seconds with very similar redshifts, magnitudes, and spectra [6]. They concluded that perhaps they were seeing the same object twice, due to the lensing of a closer, massive object. Similar observations were made by Lynds and V. Petrosian in 1988, in which they saw multiple arclets within clusters [7]. We can study a distant galaxy’s distorted image and make conclusions about the amount of mass within a lensing cluster using this expression for θE, the “Einstein radius” (the radius of an arclet in radians) θE = √ 4GM c2 dLS dLdS , (4) where G is the gravitational constant, M is the mass of the lens, c is the speed of light,and dLS, dL, and dS are the distance between the lens and source, the distance to the lens, and the distance to the source, respectively (note: these distances are angular-diameter distances which differ from our “ordinarily” notion of distance, called the proper distance, due to the expansion and curvature of the Universe). Physicists have found that this calculated mass is much larger than the mass that can be inferred from a cluster’s luminosity. For example, for the lensing cluster Abell 370, Bergmann, Petrosian, and Lynds determined that the M/L ratio of the cluster must be about 102–103 solar units, necessitating the existence of large amounts of dark matter in the cluster as well as placing constraints on its distribution within the cluster [8]. 3. Modern Understanding and Evidence 3.1. Microlensing. To explain dark matter physicists first turned to astrophysical objects made of ordinary, baryonic matter (the type of matter that we see every day and is made up of fundamental particles called quarks, which we will discuss in further detail in Section 4). Since we know that dark matter must be “dark,” possible candidates included brown dwarfs, neutron stars, black holes, and unassociated planets; all of these candidates can be classified as MACHOs (MAssive Compact Halo Objects). To hunt for these objects two collaborations, the MACHO Collaboration and the EROS-2 Survey, searched for gravitational microlensing (the changing brightness of a distant object due to the interference of a nearby object) caused by possible MACHOs in the Milky Way halo. (Other collaborations have studied this as well, such as MOA, OGLE, and SuperMACHO [9–11]). The MACHO Collaboration painstakingly observed and statistically analyzed the skies for such lensing; 11.9 million stars were studied, with only 13–17 possible lensing events detected [12]. In April of 2007, the EROS-2 Survey reported even fewer events, observing a sample of 7 million bright stars with only one lensing candidate found [13]. This low number of possible MACHOs can only account for a very small percentage of the nonluminous mass in our galaxy, revealing that most dark matter cannot be strongly concentrated or exist in the form of baryonic astrophysical objects. Although microlensing surveys rule out baryonic objects like brown dwarfs, black holes, and neutron stars in our galactic halo, can other forms of baryonic matter make up the bulk of dark matter? The answer, surprisingly, is no, and the evidence behind this 4 Advances in Astronomy claim comes from Big Bang Nucleosynthesis (BBN) and the Cosmic Microwave Background (CMB). 3.2. Cosmological Evidence. BBN is a period from a few seconds to a few minutes after the Big Bang in the early, hot universe when neutrons and protons fused together to form deuterium, helium, and trace amounts of lithium and other light elements. In fact, BBN is the largest source of deuterium in the Universe as any deuterium found or produced in stars is almost immediately destroyed (by fusing it into 4He); thus the present abundance of deuterium in the Universe can be considered a “lower limit” on the amount of deuterium created by the Big Bang. Therefore, by considering the deuterium to hydrogen ratio of distant, primordial-like areas with low levels of elements heavier than lithium (an indication that these areas have not changed significantly since the Big Bang), physicists are able to estimate the D/H abundance directly after BBN (it is useful to look at the ratio of a particular element’s abundance relative to hydrogen). Using nuclear physics and known reaction rates, BBN elemental abundances can be theoretically calculated; one of the triumphs of the Big Bang model is the precise agreement between theory and observational determinations of these light elemental abundances. Figure 2 shows theo- retical elemental abundances as calculated with the BBN code nuc123 compared with experimental ranges [14]. It turns out that the D/H ratio is heavily dependent on the overall density of baryons in the Universe, so measuring the D/H abundance gives the overall baryon abundance. This is usually represented by Ωbh2, where Ωb is the baryon density relative to a reference critical density (ρc) and h = H/100 km sec−1 Mpc−1 (the reduced Hubble constant, which is used because of the large historical uncertainty in the expansion rate of the Universe). Cyburt calculated two possible values for Ωbh2 depending on what deuterium observation is taken: Ωbh2 = 0.0229 ± 0.0013 and Ωbh2 = 0.0216+0.0020−0.0021, both which we will see accounts for only about 20% of the total matter density [15]. The CMB, discovered by Penzias and Wilson in 1964 (but theorized by others much earlier) as an excess back- ground temperature of about 2.73 K, is another way in which we can learn about the composition of the Universe [16]. Immediately after the Big Bang, the Universe was an extremely dense plasma of charged particles and photons. This plasma went through an initial rapid expansion, then expanded at a slower, decreasing rate, and cooled for about 380,000 years until it reached what is known as the epoch of recombination. At this time, neutral atoms were formed, and the Universe became transparent to electromagnetic radiation; in other words, photons, once locked to charged particles because of interactions, were now able to travel unimpeded through the Universe. The photons released from this “last scattering” exist today as the CMB. COBE (COsmic Background Explorer) launched in 1989, verified two fundamental properties of the CMB: (1) the CMB is remarkably uniform (2.73 K across the sky) and (2) the CMB, and thus the early universe, is a nearly perfect blackbody (vindicating the use of statistical 10−11 10−10 10−9 10−8 7Li 3He 4He D 10−7 10−6 10−5 10−4 Y 10−3 10−2 10−1 100 10−10 10−9 η Figure 2: Light elemental abundances versus the photon to baryon ratio, η. The horizontal lines show measured abundances of the respective elements and the vertical lines show the photon to baryon ratio as measured by WMAP. thermodynamics to describe the early universe). Although the CMB is extraordinarily uniform, COBE’s Differential Microwave Radiometer (DMR) discovered in its first year fundamental anisotropies (fluctuations) within the CMB, beyond the signal due to our motion relative to the CMB frame and foregrounds, such as emission from dust in the Milky Way. These fundamental fluctuations are due to two different effects. Large scale fluctuations can be attributed to the Sachs-Wolfe effect: lower energy photons are observed today from areas that were more dense at the time of last scattering (these photons, once emitted, lost energy escaping from deeper gravitational potential wells). On small scales, the origin of the CMB anisotropies are due to what are called acoustic oscillations. Before photon decoupling, protons and photons can be modeled as a photon-baryon fluid (since elect