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“ ” You Don’t understand the Power of the Dark Side.” Darth Vader - Star Wars Episode 6.

Fundamental Cosmology: 8. Dark Matter. “ ” You Don’t understand the Power of the Dark Side.” Darth Vader - Star Wars Episode 6. Friedmann Equation. W L. W m. W=1. 0.3. 0.7. Rewrite Friedmann eqn. as;. W<1. 0.3. 0. W=1. 1. 0. Scale Factor (Size). W>1. 2. 0. Matter.

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“ ” You Don’t understand the Power of the Dark Side.” Darth Vader - Star Wars Episode 6.

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  1. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 Fundamental Cosmology: 8.Dark Matter “”You Don’t understand the Power of the Dark Side.” Darth Vader - Star Wars Episode 6.

  2. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 Friedmann Equation WL Wm W=1 0.3 0.7 Rewrite Friedmann eqn. as; W<1 0.3 0 W=1 1 0 Scale Factor (Size) W>1 2 0 Matter Cosmological Constant t0 time Curvature 8.1: The Fate of the Universe • It all depends on Omega

  3. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 accelerating empty critical Baryons Wb Non-Baryons Wd 8.1: The Fate of the Universe • It all depends on Omega We would like to measure Wo (WM,WL) Supernova Project constrains Wo~1 but doesn’t individually constrain WM & WL e.g. Wo(0.3,0.7), Wo(0,0.4), Wo(1,1.7) all consistent with the data! Want to measure WM independently • We would also like to measure the contributions to WM • Stars • Gas • Cold Stellar Remnants • Neutrinos • Exotic Particles

  4. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 • 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 8.2: Weighing the Galaxies • A Story of Mass and Light • Measured Luminosity Density of stars in visible Universe ~ 108Lo,B Mpc-3 • Assume stellar mix of Solar Neighbourhood  r~ 4x108 MoMpc-3 • Density of the starlight in the Universe W*= r / rc ~ 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

  5. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 • 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* 8.2: Weighing the Galaxies • 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 … and Gas • Galaxy Clusters

  6. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 0.6y 1y 12y 165y 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  Motion of stars around the galactic center should slow down with increasing distance from the center of the galaxy.

  7. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 Distribution of Light Ellipticals Spiral Buldges Disk + Buldge rd = exponential scale length magnitude Disk Spiral Disks Buldge re = half light radius L(<re)=Ltot/2 distance from center (kpc) 20 22 Silpher 1914 Rubin & Ford 1970 Roberts and Whitehurst 1975 Silpher 1914 Rubin & Ford 1970 Roberts and Whitehurst 1975 24 26 5 10 15 20 8.2: Weighing the Galaxies … and Gravity • Galaxy Rotation Curves

  8. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.2: Weighing the Galaxies … and Gravity • Galaxy Rotation Curves Rigid body rotation at centre (speed increases with distance as if a single object) Curve falls off slightly from centre Curve flattens (Velocity is constant with distance Mass must be increasing with distance) Galaxy is spinning too fast !! Visible matter is not sufficient to hold galaxy together! Flat rotation curve extends beyond the luminous matter (21cm, CO) The Problem of MISSING MASS  Giant Dark Spherical Halos

  9. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 Rotation Curve for Milky Way Mass Enclosed with increasing distance for Milky Way Rotation Curve for Milky Way 3x1011 200 2x1011 Rotational velocity (km/s) Mass enclosed (Mo) 100 Total Disk Buldge Halo Total Disk Buldge Halo 1x1011 20 10 10 20 Distance from centre (kpc) Distance from centre (kpc) 8.2: Weighing the Galaxies Missing Mass ? - Rather MISSING LIGHT !! • Galaxy Rotation Curve • The Disk Component • The Buldge (+ stellar halo) Component • Dark Matter Halo Component • 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 (WG~0.16) • Rotation curve must fall at edge of galaxy ?

  10. 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 • Assume: • Cluster stable, self gravitating, spherical distribution of N objects, mass m, position x P.E. of system K.E. of system M = Total mass of cluster R1/2 = Radius of cluster <v>2 = Mean squared velocity of cluster members

  11. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.2: Weighing the Galaxies Galaxy Cluster Dynamics - For Coma Cluster • 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 • 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 WRONG Correct Mass to Light ratio M/LB ~ 250Mo/Lo,B

  12. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 For a lens halfway between observe and source Angular Radius ~ 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 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

  13. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 1000 800 600 h-1 M/L 400 200 0 2 4 6 r(arcmin) 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)

  14. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 Closed Universe 1 1000 Superclusters W Clusters M/L (solar units) 0.1 100 Groups Halos 0.01 10 Spirals 10 100 1000 10000 Scale (kpc) 8.3: The Need for Dark Matter • Measured, weighed and found wanting ….. LUMINOUS MATTER CANNOT ACCOUNT FOR DYNAMICS OF STRUCTURES ON ALL SCALES !!! WHERE HAS ALL THE LIGHT GONE ???

  15. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.3: The Need for Dark Matter • Limits on Baryonic Matter Density (Wb ) from Nucleosynthesis • Primordial Helium • depends on ratio of neutrons to protons (25% H) •  weak dependence on W () • 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 W() •  lower Deuterium Abundance • Deuterium only destroyed in Astrophysical Reactions The observed abundance of Deuterium today sets upper limit for primordial abundance

  16. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 Deuterium absorption spectrum at z = 2.504 from QSO 1009+2956 (Keck+HIRES ). Hydrogen Hydrogen Ly alpha 8.3: The Need for Dark Matter • Limits on Deuterium Abundance Detection of Deuterium in absorption spectra of quasars DISCREPENCY since Wcluster ~ 0.2……. NOT ENOUGH BARYONS !!!

  17. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 Recall: The Flatness Problem 8.3: The Need for Dark Matter • Inflation During inflation, H is constant: W is driven relentlessly towards unity Inflation can make the Universe arbitrarily flat Inflation  W=1

  18. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK ENERGY BARYON MASS DARK MASS 8.3: The Need for Dark Matter • CMB • (WMAP, SDSS, SNP, 2dFGRS)

  19. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 DARK ENERGY BARYON MASS DARK MASS 禁止 8.3: The Need for Dark Matter • Summing Up ! • 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 ?

  20. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 44AU L= 2x10-6 Lo T = 700 K M= 20 - 50 Mj Red Dwarf Brown Dwarf Black Dwarf Black Hole Neutron Star Jupiters/Planets Primordial Helium 8.4: Baryonic Dark Matter • Baryonic Dark Matter ? • 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 • JUPITERS / PLANETS / ROCKS ~0.001Mo • Not Seen • Huge Numbers Required • PRIMORDIAL HELIUM • Recently detected, scattered throughout the intergalactic medium. This primordial matter may exceed all of baryonic matter previously accounted for.

  21. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 Gravitational Microlensing Observe amplification (brightening) of background star/galaxy as it is focused by a halo object 8.4: Baryonic Dark Matter Baryonic dark matter in galactic halos - MAssive Compact Halo ObjectS • MACHOS • 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.

  22. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 Simulated image of Red dwarf MACHO population HST Observations 8.4: Baryonic Dark Matter • MACHOS 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)

  23. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 禁止 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 • Candidates • Hot Dark Matter • Cold dark Matter • Relics • Dark Energy

  24. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 Heavy Neutrino WIMPs SUSY Particles COLD DARK MATTER Non Relativistic at decoupling Axions HOT DARK MATTER Relativistic at decoupling Light Neutrino Monopoles Cosmic Strings COSMIC RELICS Symmetry Defects Cosmic Textures L COSMIC RELICS Vacuum Energy Quintessence 8.5: The Nature of Dark Matter • To be born Dark, to become dark, to be made dark, to have darkness

  25. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 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 (WDM~0.26) 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) • 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

  26. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 AXION Axions are born massless and non-relativistic, acquiring a mass after the symmetry breaks  Born COLD For W<1 (lighter the axion the greater the energy density) Stellar core constraints Stars radiate axions which decay into photons 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 Frank Wilczek allegedly was look for an opportunity to use a washing detergent name

  27. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 fermionsbosons bosonsfermions SUPER PARTICLE BOSON spin=J FERMION spin=J±1/2 8.5: The Nature of Dark Matter • Cold Dark Matter Candidates : The WIMPs • Weakly Interacting Massive Particles (opposite to MACHOS !!) • Supersymmetric Particles SUPERSYMMETRY +particle spin

  28. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 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

  29. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 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 WL  Wm • 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

  30. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.5: The Nature of Dark Matter • Dark Matter Candidates Identity Parade

  31. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 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

  32. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 HDM - Top-Down Pancake Scenario CDM - Bottom-Up Hierarchical Scenario 8.6: Structure Formation in a Dark Matter Universe • Dark Matter Structure Formation Scenarios

  33. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 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

  34. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 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)

  35. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 Our significance is getting less and less 8.8: Summary • 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

  36. Chris Pearson : Fundamental Cosmology 8: Dark Matter ISAS -2003 8.8: Summary • Summary 終 Fundamental Cosmology 8. Dark Matter 終 Fundamental Cosmology

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