X. Dark Matter
ASTR378 Cosmology : X. Dark Matter 110 Mass in the Universe
• Ω0 is the ratio of the matter/energy density of the Universe to the critical density, ρcrit ... but what is the value of Ω0? Let’s do some accounting: • Visible Mass
– Stars: Ωstars ~0.005 to 0.01 – Baryons (protons and neutrons): total baryonic matter
Ωbary ~0.04 ± 0.01 (constraints from primordial nucleosynthesis) – Is that all there is?
ASTR378 Cosmology : X. Dark Matter 111 Evidence for Dark Matter
• Fritz Zwicky (1930’s): looked at the velocities of galaxies in clusters, concluded that most of the galaxy cluster’s mass must be “dark” or unseen • Vera Rubin (1970): looked at the rotation curve of gas far out in the disk of M31, found that the velocity of the gas didn’t drop with increasing radius there must be much more mass further out...
ASTR378 Cosmology : X. Dark Matter 112 Dark Matter in Galaxies
• Rotation of stars in a galaxy’s disk:
v 2 GM(r) GM(r) = ⇒ v = r r2 r
• Expect at large r, mass ~ constant, so v should fall • But v doesn’t drop off there must be extra matter that we don’t see further out
ASTR378 Cosmology : X. Dark Matter 113 Dark Matter in Galaxy Clusters
• Virial Theorem: for a self- gravitating system in a steady state (e.g., not expanding or contracting), the kinetic energy is equal to -½ × the potential energy: 1 α GM 2 M v 2 = 2 2 rh where
ASTR378 Cosmology : X. Dark Matter 114 Dark Matter in Galaxy Clusters II
• Steady-State Virial Theorem
1 α GM 2 M v 2 = 2 2 rh • With measurements of the mean square velocity and the distribution of mass within the system, can estimate the total
mass: 2 v rh M = αG
ASTR378 Cosmology : X. Dark Matter 115
Gravitational Lensing
ASTR378 Cosmology : X. Dark Matter 116 Dark Matter from Gravitational Lensing
• Mass deflects the path of light mass can act as a lens to distort the image of a background source, or even create multiple images of the same source • Can model the distribution of intervening mass from the distortion / distribution of lensed images
ASTR378 Cosmology : X. Dark Matter 117 Dark Matter from Large Scale Structure
• There is a lot of structure in the Universe, on a huge range of scales • Difficult to model the formation of the observed level of structure in the age of the Universe without significant amounts of dark matter
ASTR378 Cosmology : X. Dark Matter 118 Mass in the Universe Revisited
• From galaxy halos: Ωhalo ≈ 0.1
• From galaxy clusters: Ω0 ≈ 0.35 (?)
• From large-scale structure: Ω0 ≥ 0.2 • The geometry of the Universe
suggests: Ω0 + ΩΛ = Ωtotal ≈ 1
• Our best guess: Ω0 ≈ 0.3
ASTR378 Cosmology : X. Dark Matter 119 So What is Dark Matter?
• Fundamental Particles: – Neutrinos? WIMPS? • Compact Objects: – Black holes? MACHOS? • Modified Gravity? • What are the “observed” properties of dark matter?
ASTR378 Cosmology : X. Dark Matter 120 Gravitational Scales for Dark Matter
ASTR378 Cosmology : X. Dark Matter 121 Cold vs. Warm Dark Matter
• Warm: relativistic particles • Cold: more massive, slow moving particles • Warm: too slow to form structure observed • Cold: appears to form too much small-scale structure, but may be OK based on recent finds
ASTR378 Cosmology : X. Dark Matter 122 Cold vs. Warm Dark Matter
Structure Formation with CDM Structure Formation with WDM
ASTR378 Cosmology : X. Dark Matter 123 Formation of a Galaxy with CDM
Computer simulation of the formation of a Milky Way-like galaxy, with cold dark matter, gas, and stars
ASTR378 Cosmology : X. Dark Matter 124 CDM: The Good and the Bad
• Works for large-scale structure • However, too much small-scale structure, compared to what is observed…
ASTR378 Cosmology : X. Dark Matter 125 A Related Problem: How Do Galaxies Form and Evolve?
Two general approaches: • “Lookback”: studying objects in the redshifted Universe to learn about their properties in the past (Nobjects = many) • “Archaeology”: studying objects in the nearby (present-day) Universe for clues to their past histories (Nobjects = few)
ASTR378 Cosmology : X. Dark Matter 126 Galactic Archaeology / Near Field Cosmology
• We can study the The Local Group (as of 2005) kinematic (velocity) and chemical (composition) properties of Local Group galaxies in detail • Dwarf galaxies are the smallest dark matter dominated systems • CDM predictions ≠ observations on ~the scale of the Local Group
ASTR378 Cosmology : X. Dark Matter 127 Hierarchical Galaxy Formation
• Large galaxies form via merger and accretion of smaller systems; stellar streams and satellites are relics of galaxy formation • We expect to see many stellar streams and surviving satellites at the present day (CDM: hundreds of subhalos in the Local Group) Bullock & Johnston 2004
ASTR378 Cosmology : X. Dark Matter 128 The “Missing Satellite” Problem
Dark Matter • CDM models predict far more low- mass dark substructure than the dwarf galaxies and stellar streams † observed -- “missing satellites” • Some theoretical solutions: Diemand+ 2006 inhibited star formation*; observed Luminous Matter satellites much more massive; observed satellites originally more massive but tidally stripped‡
† Klypin+ 1999, Moore+ 1999, Benson+ 2002 Bullock & Johnston 2005 ‡ Somerville 2002, Benson+ 2002; Stoehr+ 2002; Kravtsov+ 2004
ASTR378 Cosmology : X. Dark Matter 129 The Observational Perspective: Local Group Satellites, circa 2005
• 2003: only 9 Milky Way Cetus AnddSph IX (MW) dwarf spheroidal galaxies (dSphs), still fewer around M31 • 2004: Andromeda IX • 2005: Ursa Major, Andromeda X; runts or tip of an iceberg?
Whiting+Subaru 1999 g,r,i
ASTR378 Cosmology : X. Dark Matter 130 The Observational Perspective: Local Group Stellar Streams, circa 2005
• Milky Way stellar streams/ structures included Sagittarius and Monoceros • M31 structures included Giant Stellar Stream, Andromeda NE Sgr Stream traced with M giants: Majewski+ 2003 Halo of M31 traced with RGB stars: Ferguson+ 2002 Bullock & Johnston 2005
ASTR378 Cosmology : X. Dark Matter 131 The Sloan Digital Sky Survey
• SDSS-I: Large-area imaging and spectroscopic survey, covered ~25% of the sky • SDSS-II: finished, SDSS-III now underway
ASTR378 Cosmology : X. Dark Matter 132 Stellar Density in SDSS DR5
• SDSS DR5 data for the North Galactic Cap cover ~8000 sq. deg. • ~56 million stellar objects identified by SDSS pipeline
ASTR378 Cosmology : X. Dark Matter 133 Using Colour-Magnitude Diagrams
Tip of the Red Giant Branch (TRGB)
Horizontal Branch (HB) CMD of 56 millionRed stars Giant Branch (RGB) from SDSS DR5
Main Sequence Turn-Off (MSTO) Main Sequence (MS)
Mochejska et al. 2001
ASTR378 Cosmology : X. Dark Matter 134 The SDSS “Field of Streams”
Density composite from magnitude slices: probing distances in upper main sequence and turn-off stars
ASTR378 Cosmology : X. Dark Matter 135 The SDSS “Field of Streams”
Density composite from colour slices: probing stellar populations (and distances)
ASTR378 Cosmology : X. Dark Matter 136 A Field of Streams...and Dots
Canes Venatici I
NGC 5466
NGC 5272
ASTR378 Cosmology : X. Dark Matter 137 More Dots in the Field of Streams
MSTO: Closest Intermediate Farthest
ASTR378 Cosmology : X. Dark Matter 138 The Ultra-Low-Luminosity “Explosion”
• Wide-area surveys (SDSS,CFHT) 20+ new low-luminosity LG dwarfs since 2004, almost all dSphs • Many of the new dwarfs have very low measured 8 masses (< 10 M) most sensitive to reionisation and feedback processes
Walsh+ 2008
ASTR378 Cosmology : X. Dark Matter 139 MV vs. rh for the New Dwarfs
• Few objects with rh between ~40 pc and ~100 pc characteristic size Gap? Luminosity scale for objects with dark matter? Implications+? • What is the nature of No DM DM the objects in the “gap” --star clusters Size or dwarfs? + e.g. Gilmore+ 2008, Strigari+2008
ASTR378 Cosmology : X. Dark Matter 140 A Common (Minimum) Mass for Galaxies?
ASTR378 Cosmology : X. Dark Matter 141 Models and Observations
Bullock & Johnston 2005 Recent SDSS detections
The data from current and future large-area surveys and projects will allow us to test theories of galaxy formation – and the properties and nature of dark matter
ASTR378 Cosmology : X. Dark Matter 142