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07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 Fundamental Cosmology: 8.Dark DARK MATTER Matter “”You Don’t understand the Power of the Dark Side.” Darth Vader - Star Wars Episode 6. 1 07/07/2015 DARK MATTER Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.1: The Fate of the Universe • It all depends on Omega Friedmann Equation 2 R2 8 G kc 2 H R2 3 R2 3 Scale Factor (Size) Rewrite Friedmann eqn. as; m 0.3 0.3 1 2 1 <1 1 >1 0.7 0 0 0 t0 time kc 2 m 1 2 2 RH m k 1 m 8G 3H 2 3H 2 kc 2 k 2 2 RH Matter Cosmological Constant Curvature 2 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.1: The Fate of the Universe • It all depends on Omega m 1 k We would like to measure o (M,) Supernova Project constrains o~1but doesn’t individually constrain M & e.g. o (0.3,0.7), o (0,0.4), o (1,1.7) all consistent with the data! Want to measure M independently accelerating empty critical We would also like to measure the contributions to M • Stars • Gas Baryons b • Cold Stellar Remnants • Neutrinos • Exotic Particles Non-Baryons d 3 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.2: Weighing the Galaxies • A Story of Mass and Light • How do we weigh the Universe ? • We can only measure what we see ! • We can measure the starlight from stars ? • If we know the Mass/Light (M/L) Ratio • for Sun M/L = 1Mo/Lo • for OB main sequence stars M/L = 0.001Mo/Lo • for M main sequence stars M/L = 1000Mo/Lo • Stellar mix of Solar Neighbourhood (3000ly) M/LB ~ 4Mo/Lo,B • Measured Luminosity Density of stars in visible Universe ~ 108Lo,B Mpc-3 • Assume stellar mix of Solar Neighbourhood ~ 4x108 MoMpc-3 • Density of the starlight in the Universe * = /c ~ 0.004 = < 0.5% Depends critically on assumed M/L: Milky Way ~ 90% stellar light from stars M*>Mo ~ 80% stellar mass from stars M*<Mo 4 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.2: Weighing the Galaxies … and Gas • Galaxy Clusters • COMA CLUSTER • Abell 1656 • in constellation of Coma Berenices, near NGP pole. • Distance 150Mpc (350 million light years ) • Size >1.5Mpc • estimated > 1000 cluster member galaxies Optical Data • Luminosity of stars in Coma Cluster LB ~ 1012Lo,B • Assume Stellar mix of Solar Neighbourhood M/LB ~ 4Mo/Lo,B Total Stellar mass in Coma Cluster M* ~ 3x1013Mo X-ray Data • ROSAT/CHANDRA Hot low density intra cluster gas T~108K • Total gas mass in Coma Cluster Mg ~ 2x1014Mo ~ 6 M* 5 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.2: Weighing the Galaxies … and Gravity • Galaxy Rotation Curves Newton’s Law of Gravitation: the force of gravity between two bodies • increases as the product of their two masses • decreases as the square of the distance between them Kepler’s Laws of Planetary Motion: • Orbital velocity is proportional to the inverse square root of the distance GMm mv 2 F 2 v r1/ 2 r r 0.6y 1y 12y 165y Motion of stars around the galactic center should slow down with increasing distance from the center of the galaxy. 6 07/07/2015 8.2: Weighing the Galaxies … and Gravity • Galaxy Rotation Curves Spiral Disks Distribution of Light 20 (r / re ) I(r) I(re )e 1/4 re = half light radius L(<re)=Ltot/2 I(r) I(0)er / rd magnitude Ellipticals Spiral Buldges DARK MATTER Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 22 Disk + Buldge 24 26 Buldge Disk rd = exponential scale length 5 10 15 distance from center (kpc) 20 Silpher 1914 Rubin & Ford 1970 Silpher 1975 1914 Roberts and Whitehurst Rubin & Ford 1970 Roberts and Whitehurst 1975 7 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.2: Weighing the Galaxies … and Gravity • Galaxy Rotation Curves 1. Rigid body rotation at centre (speed increases with distance as if a single object) 2. Curve falls off slightly from centre 3. Curve flattens (Velocity is constant with distance Mass must be increasing with distance) 4. Galaxy is spinning too fast !! Visible matter is not sufficient to hold galaxy together! 5. Flat rotation curve extends beyond the luminous matter (21cm, CO) The Problem of MISSING MASS Giant Dark Spherical Halos 8 07/07/2015 DARK MATTER Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.2: Weighing the Galaxies Rotation Curve for Milky Way Galaxy Rotation Curve • The Disk Component • The Buldge (+ stellar halo) Component • Dark Matter Halo Component Rotation Curve for Milky Way Rotational velocity (km/s) Missing Mass ? - Rather MISSING LIGHT !! 200 100 Total Disk Buldge Halo 10 20 Distance from centre (kpc) Mass Enclosed with increasing distance for Milky Way • M/L in Disk ~ 4 • M/L to edge of Disk ~ 10 • M/L to Dark Halo ~ 40 (75kpc)-100(300kpc) (estimated from Globular Cluster and satellite galaxy motion) (discs are unstable and would collapse to bar require halo) • >90% of galaxy mass in Dark Halo (G~0.16) • Rotation curve must fall at edge of galaxy ? Mass enclosed (Mo) 3x1011 2x1011 Total Disk Buldge Halo 1x1011 10 20 Distance from centre (kpc) 9 07/07/2015 DARK MATTER Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.2: Weighing the Galaxies Galaxy Cluster Dynamics • Zwicky 1933: Dispersion of radial velocities of Coma Cluster memebers ~ 1000kms-1 • Not enough matter in luminous form Cluster should be flying apart !! • Required “dunkle materie” Measure the dynamical mass (i.e. gravity not light) with VIRIAL THEOREM KE PE 2 Assume: • Cluster stable, self gravitating, spherical distribution of N objects, mass m, position x P.E. of system G N mi m j GM 2 2 i, j x i x j 2R M i j N K.E. of system 1 1 K mi xÝi2 M v 2 2 i 2 M = Total mass of cluster R1/2 = Radius of cluster <v>2 = Mean squared velocity of cluster members R v2 G 10 07/07/2015 8.2: Weighing the Galaxies Galaxy Cluster Dynamics - For Coma Cluster • • • • DARK MATTER Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 PE KE 2 M R v2 G z= 0.023 (from mean redshift of cluster members) Distance ~ 100Mpc (cz/Ho) Mean square velocity ~ 3vr2 (vr= Radial Velocity ~ 900kms-1) <v>2~ 2.4x106ms-1 in practice measure the half light radius (small correction~0.5), R~1.5Mpc M R v2 0.5G 2x1015 M o From optical data •Optical Luminosity of stars in Coma Cluster LB ~ 1012Lo,B • Assume Stellar mix of Solar Neighbourhood M/LB ~ 4Mo/Lo,B Total stellar mass in Coma Cluster M* ~ 3x1013Mo From X-ray Data • Total gas mass in Coma Cluster Mg ~ 2x1014Mo ~ 6 M* Assumed Solar Neighbourhood M/LB ~ 4Mo/Lo,B Correct Mass to Light ratio M/LB ~ 250Mo/Lo,B 11 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.2: Weighing the Galaxies Gravitational Lensing • General Relativity - Gravity can bend light - Gravitational Lens • Dark Matter effects both the motion of matter and light • Dark matter in intervening space distorts the background galaxies - Einstein Arcs • For a dark matter lens directly along line of sight between observer and source - Einstein Ring M 1/ 2 1/ 2 d For a lens halfway between observe and source Angular Radius ~ E 0.5 14 10 M o 1000Mpc Mass of Clusters estimated from gravitational lensing ~ consistent with estimates of mass from Virial Theorem Abell Cluster A2218 Gravitational Lensing z=0.18, d=770Mpc Distorted background galaxies at z>0.18 12 07/07/2015 DARK MATTER Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.2: Weighing the Galaxies • Weak Lensing and cosmic shear Measure of the distribution of mass in the universe, as opposed to the distribution of light (eg. Galaxy surveys) 1000 800 h-1 M/L 600 400 200 0 2 4 r(arcmin) 6 13 07/07/2015 DARK MATTER Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.3: The Need for Dark Matter • Measured, weighed and found wanting ….. M/L Mass Stars M* Solar Neighbourhood 0.004 Neutral Hydrogen (M31) 0.1M* Galaxy Disk 10 Neutral Hydrogen (DDO 240) 0.1M* Galaxy Halos 40-100 Hot Gas in clusters 6M* Galaxy Clusters 250 Solar Neighbourhood 0.004 Atomic/Molecular Gas 0.0008 Hot Gas in clusters 0.02 Galaxy Halos 0.08-0.16 Galaxy Clusters 0.2 Closed Universe 1 Superclusters M/L (solar units) 1000 Clusters 100 0.1 Groups Halos 10 0.01 Spirals 10 100 1000 Scale (kpc) 10000 LUMINOUS MATTER CANNOT ACCOUNT FOR DYNAMICS OF STRUCTURES ON ALL SCALES !!! WHERE HAS ALL THE LIGHT GONE ??? 14 07/07/2015 DARK MATTER Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.3: The Need for Dark Matter • Limits on Baryonic Matter Density (b ) from Nucleosynthesis • Primordial Helium • depends on ratio of neutrons to protons (25% H) • weak dependence on () • Primordial Deuterium • a steeping stone to the formation of Helium • Efficiency of Helium production depends Deuterium • Denser Universe(high ) • Deuterium processed more efficiently • A high () ~ 3.7x107 h2 (T /2.7)3 • lower Deuterium Abundance • Deuterium only destroyed in Astrophysical Reactions The observed abundance of Deuterium today sets upper limit for primordial abundance 15 07/07/2015 DARK MATTER Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.3: The Need for Dark Matter • Limits on Deuterium Abundance Detection of Deuterium in absorption spectra of quasars absorption spectrum at z = 2.504 from QSO 1009+2956 (Keck+HIRES ). Deuterium Hydrogen Hydrogen Ly alpha D / H 10 6 10 4x10 < < 8x10 10 DISCREPENCY since cluster ~ 0.2……. 0.04 < b < 0.05 NOT ENOUGH BARYONS !!! 16 07/07/2015 DARK MATTER Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.3: The Need for Dark Matter • Inflation Recall: The Flatness Problem During inflation, H is constant: is driven relentlessly towards unity Inflation can make the Universe arbitrarily flat 2 kc 1 2 2 0 RH Inflation =1 17 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.3: The Need for Dark Matter • CMB • (WMAP, SDSS, SNP, 2dFGRS) DARK ENERGY BARYON MASS DARK MASS 18 07/07/2015 DARK MATTER Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.3: The Need for Dark Matter • Summing Up ! Solar Neighbourhood 0.004 Hot Gas in clusters 0.02 Galaxy Halos 0.08-0.16 Galaxy Clusters 0.2 DARK ENERGY Baryon Nucleosynthesis 0.04 Inflation 1 WMAP Dark Mass 0.23 WMAP Dark Energy 0.73 BARYON MASS DARK MASS • Baryonic matter density consistent with local solar neighbourhood and intracluster medium • Some of Halo mass possibly dark baryons - BARYONIC DARK MATTER •What is this Baryonic Dark Matter ? •Fraction of Halo and Cluster dark matter NON BARYONIC ! • What is the form of this Dark Matter ? 禁止 19 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.4: Baryonic Dark Matter • Baryonic Dark Matter ? Red Dwarf 1. 2. 3. 4. 5. Brown Dwarf Black Dwarf Black Hole Neutron Star Jupiters/Planets Primordial Helium RED DWARF STARS < 1Mo (To~2000K) •Not enough detected STELLAR REMNANTS (Black Dwarf, Neutron Stars, Black Holes) ~ 1Mo • Universe too young for so many remnants to form • Universe too young for remnants to cool to Black Dwarf BROWN DWARF < 0.08Mo (To~1000K) - failed star •Not enough detected 44AU JUPITERS / PLANETS / ROCKS ~0.001Mo • Not Seen • Huge Numbers Required L= 2x10-6 Lo T = 700 K M= 20 - 50 Mj PRIMORDIAL HELIUM • Recently detected, scattered throughout the intergalactic medium. This primordial matter may exceed all of baryonic matter previously accounted for. 20 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.4: Baryonic Dark Matter • MACHOS Baryonic dark matter in galactic halos - MAssive Compact Halo ObjectS Gravitational Microlensing Observe amplification (brightening) of background star/galaxy as it is focused by a halo object • Lensinsing Projects - detected several MACHOs, each positioned in front of stars in LMC. • Microlensing events - no information about distance to lens (Don’t know whether lens is close to the source star in LMC or observer in our galaxy, or in between.) • Use Hubble - faint red star - distance 600ly away M~0.1Mo • Located in disc/luminous main part of our galaxy not halo. 21 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.4: Baryonic Dark Matter • MACHOS Simulated image of Red dwarf MACHO population HST Observations HST detects too few Red Dwarves in the Milky Way halo Red Dwarves ruled out as significant contributors to dark matter in Milky Way ( other galaxies) 22 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.5: The Nature of Dark Matter • Welcome to the Dark Side Non - Baryonic Dark Matter • Even without constraints from Inflation/CMB • 50-100% of Galaxy Halo must be non baryonic • > 80% of Clusters must be non-baryonic • Adding constraints from inflation and CMB • 96% of Universe is non-baryonic 禁止 Candidates 1. Hot Dark Matter 2. Cold dark Matter 3. Relics 4. Dark Energy 23 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.5: The Nature of Dark Matter • To be born Dark, to become dark, to be made dark, to have darkness Heavy Neutrino COLD DARK MATTER WIMPs Non Relativistic at decoupling SUSY Particles Axions HOT DARK MATTER Relativistic at decoupling Light Neutrino Monopoles COSMIC RELICS Symmetry Defects Cosmic Strings Cosmic Textures COSMIC RELICS Vacuum Energy Quintessence 24 07/07/2015 DARK MATTER Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.5: The Nature of Dark Matter • Hot Dark Matter Candidates: Light Neutrinos • Neutrinos - The only non-baryonic candidate known to exist • Neutrino background nn~ 3x(3/11)ng~ 3.4x108m-3 • Extremely weakly interacting (pass through few pc’s lead) Neutrinos they are very small. They have no charge and have no mass And do not interact at all The Earth is just a silly ball To them, through which they simply pass, Like Dust maids down a drafty hall Or photons through a sheet of glass John Updike - Cosmic Gall To provide ALL non baryonic matter (DM~0.26) DM c mn ~ 4eV nn • MSW Oscillations in solar neutrinos constrain mass difference between 2 Oscillating flavours ~ 0.007eV • Observations of muon neutrinos in atmosphere constrain m-t mass difference ~ 0.05eV • Observations from Sanduleak -69 202 22 neutrinos in 12s ! (must be very light) However: If a mass for the neutrino is detected then there will be a contribution to the Dark Matter 25 07/07/2015 DARK MATTER Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.5: The Nature of Dark Matter • Cold Dark Matter Candidates : Axions Strong CP problem • CP violation predicted but not observed on order of 10-8 (c.f. flatness problem in inflation) • 1978: Peccei-Quinn Constraint- Introduce Spin 0 pseudoscalar suppress Strong CP violation • Requires symmetry breaking on GUT scales with particle mass 1/energy scale = Peccei-Quinn Scale AXION Frank Wilczek allegedly was look for an opportunity to use a washing detergent name Axions are born massless and non-relativistic, acquiring a mass after the symmetry breaks Born COLD 105 < maxion < 6x103 eV For <1 (lighter the axion the greater the energy density) Stellar core constraints Stars radiate axions which decay into photons 26 07/07/2015 DARK MATTER Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.5: The Nature of Dark Matter • Cold Dark Matter Candidates : The WIMPs • Weakly Interacting Massive Particles (opposite to MACHOS !!) • Supersymmetric Particles fermionsbosons SUPERSYMMETRY +particle spin bosonsfermions SUPER PARTICLE BOSON spin=J FERMION spin=J±1/2 Particle spin SS partner spin quark 1/2 squark 0 lepton 1/2 slepton 0 photon 1 photino 1/2 gluon 1 gluino 1/2 W/Z 1 zino / wino 1/2 graviton 2 gravitino 3/2 Higgs 0 Higgsino 1/2 axion 0 axino 1/2 27 07/07/2015 • • Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.5: The Nature of Dark Matter Cold Dark Matter Candidates : The WIMPs Supersymmetric Particles • As supersymmetry has a new symmetry, R parity, • R Parity Conservation a new stable particle • Relic particle will be the lightest Supersymmetric partner (LSP) with charge or colour CHARGED PARTICLES selectron, squark, smuon, wino, charged Higgsino RULED OUT msneutrino > msleptons gravitino - self annihilates too slowly too high abundance at present epoch Photino mass ~ 0.5GeV Possible candidate for LSP Stranger possibilities - neutralino - mixing state of photino, higgsino, wino states ?? Linear Collider at CERN - e+e- collider ~ 1TeV Successor to the LHC (LHC too much debris) Should discover Higgs, Supersymmetry, String dimensions 28 07/07/2015 • • Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.5: The Nature of Dark Matter QUINTESSENCE - The Fifth Element Dark Energy • Rolling homogeneous new scalar field behaving like a decaying cosmological constant (i.e. NOT CONSTANT ) • Eventually attain the true vacuum energy (energy zero point) • Strange that at this epoch is small but >0 m Mechanisms - many ? • k-Essence (fields from String Theory for driving inflation) • Could contribute to Dark Energy • Universe is a viscous fluid and dark matter modelled by Tachyon field and Chaplygin gas • Quintessence fields from c, h, G • only fundamental constants • Quintessence filed “turns on” at some epoch and dominates the expansion of the Universe 29 07/07/2015 DARK MATTER Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.5: The Nature of Dark Matter • Dark Matter Candidates Identity Parade Candidate Mass Neutrino 4 eV Hot Dark Matter Axion 10-5 eV Cold Dark Matter Photino 0.5 GeV LSP Neutralino 10GeV LSP Axino ~ keV LSP Cosmion 5-10 GeV Created by P± annihilation, useful for Solar Neutrino Problem Quark Nuggets ~ 1015 kg Created in initial stages of Big Bang but predicted flux of 106kg yr-1 not detected Shadow Matter ~ GeV Predicted by E8xE8 Superstring Theories, Decouples 10-43 s after Big Bang Primordial Black Holes >1012kg Collapse of Space time on scales of Horizon due to fluctuations Relics ?? Monopoles, Strings, Textures 30 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.6: Structure Formation in a Dark Matter Universe • Dark Matter is needed for Structure Formation •CMB ~ smooth to 1 part in 107 • Baryons coupled to radiation until de-coupling • NOT ENOUGH TIME TO FORM STRUCTURE • Need Dark Matter • Dark Matter Condenses at earlier time • Matter then falls into the DM gravitational wells 31 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.6: Structure Formation in a Dark Matter Universe • Dark Matter Structure Formation Scenarios HDM - Top-Down Pancake Scenario CDM - Bottom-Up Hierarchical Scenario 32 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.7: The Search for Dark Matter • Detection of WIMPs WIMP : interact weakly with matter WIMP DETECTION REQUIRES • • • • sensitive to few keV - GeV energies Large Deposition of Mass of detector material Superb background rejection (expected event rate < 1 kg-1 day-1) Stable over long periods Search for 2 asymmetries • 10% annual modulation of the event rate due to the Earth's motion around the Sun • Asymmetry in the direction of the WIMP flux due to the Sun's motion through the galactic halo 33 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK MATTER 8.7: The Search for Dark Matter • Detection of WIMPs • First generation of WIMP experiments were rare-event experiments (proton decay, solar neutrinos) that were adapted to search for dark matter. e.g. ultra-low background germanium semiconductor experiments developed for double beta-decay modified into dark matter detectors. (recoiling Ge nucleus produces -hole pairs that are detectable down to recoil energies keV). • Gas Detectors - Time-Projection Chamber (TPC) detectors used in particle physics. experiments. To Detect a WIMP require enormous volume, possibility could detect asymmetric direction of WIMP recoil due to the Earth's motion around the Sun. • Superconducting Grain Detectors - ~1mm size superconducting grains. WIMP recoil heating phase transition. Resultant change in magnetic field detected by a SQUID. • Ancient Mica - WIMP detection requires detectors/exposure times of kg/yr. Instead of 100 kg detector use with small amounts of material that has been exposed for 109yr. • Atomic Detectors - Detect inelastic collisions of SUSY relics with atoms. X-section for atomic interactions smaller than nuclear interactions but there is a wider range of usable material. (not yet any such experiments to look for WIMP-atom scattering) 34 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.8: Summary DARK MATTER • SUMMARY • In the last 100 years the Copernican Principal has grown in strength • Hubble: Universe is expanding - all galaxies are receding from each other • Zwicky: Presence of Dark Matter - Dark Baryons •Massive Halos/Clusters + Nucleosynthesis = Existence of Non-baryonic Dark Matter • COBE: Baryonic Matter is not dominant in the structure formation process • WMAP 75% of Universe is in the form of Dark energy •BIG BANG has been very succesful……. BUT in truth •We can still only understand 4% of the Universe It’s a very exciting time to be an Astrophysicist 35 07/07/2015 Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.8: Summary DARK MATTER • Summary Fundamental Cosmology 8. Dark Matter Fundamental Cosmology 終 終 36