The Dark Matter Ali VGN Sections 1. Dark Matter and WIMPs (now) 2. f(R) Gravity and its relation to the interaction between DE and DM (next time) Title Dark Energy 73% (Cosmological Constant) Neutrinos Neutrinos 0.1 2% 0.1 2% Dark Matter 23% Ordinary Matter 4% (of this only about 10% luminous) 10% luminous) Mass and Gravity All mass has gravity. Gravity attracts all things with mass. Keplers Third Law tells us how mass moves due to gravity. Use Keplers Third Law to find out how much mass is where. Mass and Luminosity Most mass gives off light. Amount of light tells how much mass is present. Where theres more light, there is more mass. More light from galaxy centers vs. edges. Conclude more mass in center vs. edges. Dark Matter Look at: Our galaxy. Other galaxies. Pairs of galaxies. Clusters of galaxies. Mass due to gravity. Mass indicated by luminosity. Same? No! Dark Matter. Evidence for Dark Matter Use the fact that massive objects, even if they emit no light, exert gravitational forces on other massive objects. Study the motions (dynamics) of visible objects like stars in galaxies, and look for effects that are not explicable by the mass of the other light emmitting or absorbing objects around them. m1m1 m2m2 r 12 Suns Rotation Speed Around Milky Way In the milky way, all stars rotates around the center of the galaxy According to Newtons gravitational theory the rotation speed of the sun depends on the mass distribution and the distance to the center According to this formula, the Rotation speed of the sun Shall be around 170km/s, however The actual speed is about km/s. v(r) r Examples of Rotation Curves What do we see? From variable stars we know distances. From Doppler shift we know rotation velocity. Edges of Milky Way go too fast. Must be extra mass near edges of galaxy. Rotation Curves If HI gas is rotating or moving, the 21cm radiation will be Doppler Shifted. More Galaxy Masses Apply Keplers Laws to galaxy pairs. Get mass due to gravity. Look at total light from both galaxies. Estimate mass from luminous objects. Evidences galaxy scale From the Kepler s law, for r much larger than the luminous terms, you should have v r -1/2 However, it is flat or rises slightly. The most direct evidence of the existence of dark matter. Corbelli & Salucci (2000); Bergstrom (2000) Heres one simple way to mass a galaxy Mass of galaxy = number of stars x average mass of star It turns out that galaxies do not have enough visible mass to stay grouped in clusters. The extra mass they need must come from dark matter. Galaxy Rotation Objects in the disk, orbit in the disk. Keplers Third Law gives the total mass in orbits. Basically, it states that the square of the time of one orbital period (T 2 ) is equal to the cube of its average orbital radius (R 3 ). (1 AU = 150,000,000 km) Distributed Mass In Keplers Law, the total mass is the mass inside the orbit. What should we expect? Solar System: PlanetSeparation (AU) Velocity (km/s) Mercury0.548 Earth130 Saturn10 Pluto405 + V D M/L ~ 20 130! Even More Galaxy Masses Look for gravitational lenses near galaxy clusters. More lensing means more mass. Compare mass from lensing to luminosity. Dark Matter content in a galaxy This implies the existence of a dark halo, with mass density (r) 1/r 2, i.e., M(r) r; At some point 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, DM > 0.1, where X X / crit, crit being the critical mass density to be described later (i.e., tot = 1) Local Dark Matter Density The DM density in the neighborhood of our solar system was first estimated as early as 1922 by J.H. Jeans, who analyzed the motion of nearby stars transverse to the galactic plane. He concluded that in our galactic neighborhood, the average density of DM must be roughly equal to that of luminous matter (stars, gas, dust). Remarkably enough, the most recent estimates, based on a detailed model of our galaxy, find quite similar results local DM = 0.3 GeV/cm 3 ; This value is known to within a factor of two or so. Bullet Cluster DM content from clusters of galaxies The observation of clusters of galaxies tends to give somewhat larger values, DM 0.2 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; andmost directly studies of (weak) gravitational lensing of background galaxies on the cluster. Rotation of Stars around Galactic Centres We can measure how fast stars rotate around galactic centres by looking at the frequency shift of known spectral lines originating in the stars due to the Doppler effect. Stars motion towards you, relative to the galactic centre alters wavelength of light 21 cm Radiation as Tracer of Gas Clouds 21 cm map of our Galaxy The Correct Way to Think about Our Galaxy RECESSIONAL VELOCITIES The original evidence that the universe is expanding Now carried out to far larger distances with supernovae Constrains the acceleration of expansion: M Attractive matter vs. repulsive dark energy Hubble (1929) COSMIC MICROWAVE BACKGROUND T/T