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Unformatted text preview: 22. Dark matter 1 22. DARK MATTER Written September 2003 by M. Drees (Technical University, Munich) and G. Gerbier (Saclay, CEA). Revised September 2005. 22.1. Theory 22.1.1. Evidence for Dark Matter : The existence of Dark ( i.e. , non-luminous and non-absorbing) Matter (DM) is by now well established. The earliest , and perhaps still most convincing, evidence for DM came from the observation that various luminous objects (stars, gas clouds, globular clusters, or entire galaxies) move faster than one would expect if they only felt the gravitational attraction of other visible objects. An important example is the measurement of galactic rotation curves. The rotational velocity v of an object on a stable Keplerian orbit with radius r around a galaxy scales like v ( r ) ∝ M ( r ) /r , where M ( r ) is the mass inside the orbit. If r lies outside the visible part of the galaxy and mass tracks light, one would expect v ( r ) ∝ 1 / √ r . Instead, in most galaxies one finds that v becomes approximately constant out to the largest values of r where the rotation curve can be measured; in our own galaxy, v 220 km / s at the location of our solar system, with little change out to the largest observable radius. This implies the existence of a dark halo , with mass density ρ ( r ) ∝ 1 /r 2 , i.e. , M ( r ) ∝ r ; at some point ρ will have to fall off faster (in order to keep the total mass of the galaxy finite), but we do not know at what radius this will happen. This leads to a lower bound on the DM mass density, Ω DM > ∼ . 1, where Ω X ≡ ρ X /ρ crit , ρ crit being the critical mass density ( i.e. , Ω tot = 1 corresponds to a flat Universe). The observation of clusters of galaxies tends to give somewhat larger values, Ω DM . 2 to 0.3. These observations include measurements of the peculiar velocities of galaxies in the cluster, which are a measure of their potential energy if the cluster is virialized; measurements of the X-ray temperature of hot gas in the cluster, which again correlates with the gravitational potential felt by the gas; and—most directly—studies of (weak) gravitational lensing of background galaxies on the cluster. The currently most accurate, if somewhat indirect, determination of Ω DM comes from global fits of cosmological parameters to a variety of observations; see the Section on Cosmological Parameters for details. For example, using measurements of the anisotropy of the cosmic microwave background (CMB) and of the spatial distribution of galaxies, Ref. 2 finds a density of cold, non–baryonic matter Ω nbm h 2 = 0 . 111 ± . 006 , (22 . 1) where h is the Hubble constant in units of 100 km/(s · Mpc). Some part of the baryonic matter density , Ω b h 2 = 0 . 023 ± . 001 , (22 . 2) may well contribute to (baryonic) DM, e.g. , MACHOs  or cold molecular gas clouds ....
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This note was uploaded on 08/01/2008 for the course ASTRO 228 taught by Professor Chungpeima during the Fall '06 term at Berkeley.
- Fall '06