Dark Matter and Dark Energy components
chapter 7
Lecture 3
See also Dark Matter awareness week December 2010
http://www.sissa.it/ap/dmg/index.html
The early universe chapters 5 to 8
Particle Astrophysics , D. Perkins, 2nd edition, Oxford
5. The expanding universe 6. Nucleosynthesis and baryogenesis 7. Dark matter and dark energy components 8. Development of structure in early universe
exercises
Slides + book http://w3.iihe.ac.be/~cdeclerc/astroparticles
Overview
• Part 1: Observation of dark matter as gravitational effects
– Rotation curves galaxies, mass/light ratios in galaxies
– Velocities of galaxies in clusters
– Gravitational lensing
– Bullet cluster
• Part 2: Nature of the dark matter :
– Baryons and MACHO’s
– Standard neutrinos
– Axions
• Part 3: Weakly Interacting Massive Particles (WIMPs)
• Part 4: Experimental WIMP searches
• Part 5: Dark energy (next lecture)
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Previously
• Universe is flat k=0
• Dynamics given by Friedman equation
• Cosmological redshift
• Closure parameter
• Energy density evolves with time
2012-13 Dark Matter 4
2
2 8
3
NR t G
R ttH t totρ
0
01 0R t
z z tR t
c
tt
t
2 3 4 22
0 01 1 1r kH t H z t z z00m ΛΩ t Ω t
Ωk=0
Dark matter : Why and how much?
2012-13 Dark Matter 5
luminous 1%
dark baryonic
4%
NeutrinoHDM <1% cold dark
matter 18%
dark energy
76%
• Several gravitational observations show that more matter is in the Universe than we can ‘see’
• It these are particles they interact only through weak interactions and gravity
• The energy density of Dark Matter today is obtained from fitting the ΛCDM model to CMB and other observations
5
0
0
10
0.24
rad
matter
t
t
2 3 42
0 0 0 01 1m rH t H t z t z t
Dark matter nature
• The nature of most of the dark matter is still unknown
Is it a particle? Candidates from several models of physics beyond the standard model of particles and their interactions
Is it something else? Modified newtonian dynamics?
• the answer will come from experiment
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PART 1 GRAVITATIONAL EFFECTS OF DARK MATTER
Velocities of galaxies in clusters and M/L ratio
Galaxy rotation curves
Gravitational lensing
Bullet Cluster
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Dark matter at different scales
• Observations at different scales : more matter in the universe than what is measured as electromagnetic radiation (visible light, radio, IR, X-rays, -rays)
• Visible matter = stars, interstellar gas, dust : light & atomic spectra (mainly H)
• Velocities of galaxies in clusters high mass/light ratios
• Rotation curves of stars in galaxies large missing mass up to large distance from centre
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1 10 500MW cluster
MW cluster
M M M
L L L
Dark matter in galaxy clusters 1
• Zwicky (1937): measured mass/light ratio in COMA cluster is much larger than expected
– Velocity from Doppler shifts (blue & red) of spectra of galaxies
– Light output from luminosities of galaxies
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Optical (Sloan Digital Sky Survey)
+ IR(Spitzer Space Telescope NASA
COMA cluster
1000 galaxies 20Mpc diameter
100 Mpc(330 Mly) from Earth
v
Dark matter in galaxy clusters 2
• Mass from velocity of galaxies around centre of mass of cluster using virial theorem
• Proposed explanation: missing ‘dark’ = invisible mass
• Missing mass has no interaction with electromagnetic radiation
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COMA SUN
M M
L L
10
7
1
2
( ) 10500
10 cluster sun
KE GPE
M velocities M M M
L LL L
Mv
Galaxy rotation curves
• Stars orbiting in spiral galaxies
• gravitational force = centrifugal force
• Star inside hub
• Star far away from hub
2012-13 Dark Matter 11
2
2
Mmmv
r r
r G
v r
1v
r
NGC 1560 galaxy
2012-13 Dark Matter 12
Universal features
• Large number of rotation curves of spiral galaxies measured by Vera Rubin – up to 110kpc from centre
• Show a universal behaviour
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Dark matter halo • Galaxies are embedded in dark matter halo
• Halo extends to far outside visible region
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HALO
DISK
Dark matter halo models
• Density of dark matter is larger near centre due to gravitational attraction near black hole
• Halo extends to far outside visible region
• dark matter profile inside Milky Way is modelled from measurements of rotation curves of many galaxies
Dark Matter
15
Solar system
DM
Den
sity
(G
eV c
m-3
)
Distance from centre (kpc)
2012-13
Milky Way halo m od els
Gravitational lensing
• Gavitational lensing by galaxy clusters effect larger than expected from visible matter only
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Gravitational lensing principle
• Photons emitted by source S (e.g. quasar) are deflected by massive object L (e.g. galaxy cluster) = ‘lens’
• Observer O sees multiple images
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Lens geometries and images
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Observation of gravitational lenses
• First observation in 1979: effect on twin quasars Q0957+561
• Mass of ‘lens’ can be deduced from distortion of image
• only possible for massive lenses : galaxy clusters
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Different lensing effects
• Strong lensing:
– clearly distorted images, e.g. Abell 2218 cluster
– Sets tight constraints on the total mass
• Weak lensing:
– only detectable with large sample of sources
– Allows to reconstruct the mass distribution over whole observed field
• Microlensing:
– no distorted images, but intensity of source changes with time when lens passes in front of source
– Used to detect Machos
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Collision of 2 clusters : Bullet cluster
• Optical images of galaxies at different redshift: Hubble Space Telescope and Magellan observatory
• Mass map contours show 2 distinct mass concentrations
– weak lensing of many background galaxies
– Lens = bullet cluster
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Cluster 1E0657-56
0.72 Mpc
Bullet cluster in X-rays • X rays from hot gas and dust - Chandra observatory
• mass map contours from weak lensing of many galaxies
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Bullet cluster = proof of dark matter
• Blue = dark matter reconstructed from gravitational lensing
• Is faster than gas and dust : no electromagnetic interactions
• Red = gas and dust = baryonic matter – slowed down because of electromagnetic interactions
• Modified Newtonian Dynamics cannot explain this
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Alternative theories
• Newtonian dynamics is different over (inter)-galactic distances
• Far away from centre of cluster or galaxy the acceleration of an object becomes small
• Explains rotation curves
• Does not explain Bullet Cluster
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PART 2 THE NATURE OF DARK MATTER
Baryons
MACHOs = Massive Compact Halo Objects
Standard neutrinos
Axions
WIMPs = Weakly Interacting Massive Particles →Part 3
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What are we looking for?
• Particles with mass – interact gravitationally
• Particles which are not observed in radio, IR, visible, X-rays, -rays : neutral and possibly weakly interacting
• Candidates:
• Dark baryonic matter: baryons, MACHOs
• light particles : primordial neutrinos, axions
• Heavy particles : need new type of particles like neutralinos, … = WIMPs
• To explain formation of structures majority of dark matter particles had to be non-relativistic at time of freeze-out
Cold Dark Matter
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BARYONIC MATTER
Total baryon content
Visible baryons
Neutral and ionised hydrogen – dark baryons
Mini black holes
MACHOs
2012-13 Dark Matter 27
Baryon content of universe
• measurement of light element abundances
• and of He mass fraction Y
• And of CMB anisotropies
• Interpreted in Big Bang Nucleosynthesis model
2012-13 Dark Matter 28
106.1 0.6 10BN
N
BΩ = 0.044 ± 0.005
He mass fraction
D/H abundance
ΩB=.044
Baryon budget of universe
• From BB nucleosynthesis and CMB fluctuations:
• Related to history of universe at
z=109 and z=1000
• Most of baryonic matter is in stars, gas, dust
• Small contribution of luminous matter
• 80% of baryonic mass is dark
• Ionised hydrogen H+, MACHOs, mini black holes
• Inter Gallactic Matter = gas of hydrogen in clusters of galaxies
• Absorption of Ly emission from distant quasars yields neutral hydrogen fraction in inter gallactic regions
• Most hydrogen is ionised and invisible in absorption spectra form dark baryonic matter
2012-13 Dark Matter 29
0.01lum
0.05baryons
Mini black holes
• Negligible contribution from mini black holes
• BHs must have MBH < 105 M
• Heavier BH would yield lensing effects which are not observed
2012-13 Dark Matter 30
710BH
MACHOS
Massive Astrophysical Compact Halo Objects
Dark stars in the halo of the Milky Way
Observed through microlensing of large number of stars
2012-13 Dark Matter 31
Microlensing • Light of source is amplified by gravitational lens
• When lens is small (star, planet) multiple images of source cannot be distinguished : addition of images = amplification
• But : amplification effect varies with time as lens passes in front of source - period T
• Efficient for observation of e.g. faint stars
2012-13 Dark Matter 32
Period T
Microlensing - MACHOs
• Amplification of signal by addition of multiple images of source
• Amplification varies with time of passage of lens in front of source
• Typical time T : days to months – depends on distance & velocity
• MACHO = dark astronomical object seen in microlensing
• M 0.001-0.1M
• Account for very small fraction of dark baryonic matter
• MACHO project launched in 1991: monitoring during 8 years of microlensing in direction of Large Magellanic Cloud
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2 2
1 / 12 4
x xx x
TA
t
Optical depth – experimental challenge • Optical depth = probability that one source undergoes
gravitational lensing
• For = NLM = Mass density of lenses along line of sight
• Optical depth depends on – distance to source DS
– number of lenses
• Near periphery of bulge of Milky Way
Need to record microlensing for millions of stars
• Experiments: MACHO, EROS, superMACHO, EROS-2
• EROS-2: – 7x106 bright stars monitored in ~7 years
– one candidate MACHO found
– less than 8% of halo mass are MACHOs
2012-13 Dark Matter 34
2
23
Gc
SD
7per source 10
Example of microlensing
• source = star in Large Magellanic Cloud (LMC, distance = 50kpc)
• Dark matter lens in form of MACHO between LMC star and Earth
• Could it be a variable star?
• No: because same observation of luminosity in red and blue light : expect that gravitational deflection is independent of wavelength
2012-13 Dark Matter 35
Blue filter
red filter
To do
• Meebrengen naar examen
2012-13 Dark Matter 36
STANDARD NEUTRINOS AS DARK MATTER
2012-13 Dark Matter 37
Standard neutrinos
• Standard Model of Particle Physics – measured at LEP
→ 3 types of light left-handed neutrinos
with Mν<45GeV/c2
• Fit of observed light element
abundances to BBN model (lecture 2)
• Neutrinos have only weak and gravitational interactions
2012-13 Dark Matter 38
2.984 0.009fermion familiesN
3.5neutrino speciesN
Relic neutrinos
• Non-baryonic dark matter = particles
– created during radiation dominated era
– Stable and surviving till today
• Neutrino from Standard Model = weakly interacting, small mass, stable → dark matter candidate
• Neutrino production and annihilation in early universe
• Neutrinos freeze-out at kT ~ 3MeV and t ~ 1s
• When interaction rate W << H expansion rate
2012-13 Dark Matter 39
sweak interaction , ,i ie e i e
Lecture 2
Cosmic Neutrino Background
• Relic neutrino density and temperature today
• for given species (e, , ) (lecture 2)
• Total density today for all flavours
• High density, of order of CMB – but difficult to detect!
• At freeze-out : relativistic
2012-13 Dark Matter 40
0 0
134
11T t T t 1.95K meV
-33113
11N N cmN
3340N cm
p FO m
Neutrino mass
• If all critical density today is built up of neutrinos
• Measure end of electron energy spectrum in tritium beta decay
2012-13 Dark Matter 41
2
, ,
47e
m c eV 2
νm <16eV c1c
2m eV c
3 3
1 2 eH He e
Neutrino mass
2012-13 Dark Matter 42
3 3
1 2 eH He e
1.0m eV
0.0m eV
Electron energy (keV)
Co
un
t ra
te
2m eV c
Neutrinos as hot dark matter
• Relic neutrinos are numerous
• have very small mass < eV
• Were relativistic when decoupling from other matter at kT~3MeV
• → can only be Hot Dark Matter – HDM
• Relativistic particles prevent formation of large-scale structures – through free streaming they ‘iron away’ the structures
• → HDM should be limited
• From simulations of structures: maximum 30% of DM is hot
2012-13 Dark Matter 43
2012-13 Dark Matter 44
simulations Hot dark matter warm dark matter cold dark matter
Observations 2dF galaxy survey
See eg work of Carlos Frenk http://star-www.dur.ac.uk/~csf/
AXIONS
Postulated to solve ‘strong CP’ problem
Could be cold dark matter particle
2012-13 Dark Matter 45
Strong CP problem
• QCD lagrangian for strong interactions
• Term Lθ is generally neglected
• violates P and T symmetry → violates CP symmetry
• Violation of T symmetry would yield a non-zero neutron electric dipole moment
• Experimental upper limits
2012-13 Dark Matter 46
15 16. . . 10 .
predictede d m e cm
experiment 25. . . 10 .e d m e cm
QCD quark gauge standardL L L L 2
216
a aS Fg TF FL
1010
Strong CP problem
• Solution by Peccei-Quinn : introduce higher global U(1) symmetry, which is broken at an energy scale fa
• This extra term cancels the Lθ term
• With broken symmetry comes a boson field φa = axion with mass
• Axion is light and weakly interacting
• Is a pseudo-scalar with spin 0- ; Behaves like π0
• Decay rate to photons
2012-13 Dark Matter 47
1010~ 0.6A
A
GeVm meV
f
2
216
a aS FA
A
g TF
fFL
2 3
64
A AA
G m
Axion as cold dark matter
• formed boson condensate in very early universe during inflation
• Is candidate for cold dark matter
• if mass eV its lifetime is larger than the lifetime of universe
stable
• Production in plasma in Sun or SuperNovae
• Searches via decay to 2 photons in magnetic field
• CAST experiment @ CERN: axions from Sun
• If axion density = critical density today then
2012-13 Dark Matter 48
production decayA
6 3 210 10Am eV c1 A
cA
2 3
64
A AA
G m
Axions were not yet observed
2012-13 Dark Matter 49
Axion mass (eV)
Axi
on
-γ c
ou
plin
g (G
eV-1
)
Combination of mass and coupling below CAST limit are still allowed by experiment CAST has best sensitivity
Axion model predictions Some are excluded by CAST limits
PART 3 WIMPS AS DARK MATTER
Weakly Interacting Massive Particles
2012-13 Dark Matter 50
luminous 1%
dark baryonic
4%
Neutrino HDM <1%
cold dark matter
18%
dark energy
76%
summary up to now
• Standard neutrinos can be Hot DM
• Most of baryonic matter is dark
• cold dark matter (CDM) is still of unknow type
• Need to search for candidates for non-baryonic cold dark matter in particle physics beyond the SM
2012-13 Dark Matter 51
0.05 0.01 00.18 .24CDMmatter Baryons HDM
2012-13 Dark Matter 52
Non-baryonic CDM candidates • Axions
– To reach density of order ρc their mass must be very small
– No experimental evidence yet
• Most popular candidate for CDM : WIMPs
• Weakly Interacting Massive Particles
• present in early hot universe – stable – relics of early universe
• Cold : Non-relativistic at time of freeze-out
• Weakly interacting : conventional weak couplings to standard model particles - no electromagnetic or strong interactions
• Massive: gravitational interactions (gravitational lensing …)
2 6 310 10Am c eV
2012-13 Dark Matter 53
Weakly interacting and massive • Massive neutrinos:
– The 3 standard neutrinos have very low masses – contribute to Hot DM
– Massive standard neutrinos up to MZ/2 = 45GeV/c2 are excluded by LEP
– Massive non-standard neutrinos : 4th generation of letons and quarks?
No evidence yet
• Neutralino χ = Lightest SuperSymmetric Particle (LSP) in R-parity conserving Minimal SuperSymmetry (SUSY) theory
– Lower limit from accelerators 50 GeV/c2
– Stable particle – survived from primordial era of universe
• Other SUSY candidates: sneutrinos, gravitinos, axinos
• New particles from models with extra space dimensions
• …….
MSSM
Expected mass range
• Assume WIMP interacts weakly and is non-relativistic at freeze-out
• Which mass ranges are allowed?
• Cross section for WIMP annihilation vs mass leads to abundance vs mass
2012-13 Dark Matter 54
2 2
22
1) 4 ~ ~
1 12) 4 ~ ~
M s M
Ms M
2W
2W
s > M
s < M
0
1~
vt
Expected mass range: GeV-TeV
• Assume WIMP interacts weakly and is non-relativistic at freeze-out
• Which mass ranges are allowed?
• Cross section for WIMP annihilation vs mass leads to abundance vs mass
2012-13 Dark Matter 55
MWIMP (eV)
2 2
22
1) 4 ~ ~
1 12) 4 ~ ~
M s M
Ms M
2W
2W
s > M
s < M
HDM neutrinos
CDM WIMPs
0
1~
vt
2012-13 Dark Matter 56
WIMP annihilation rate at freeze-out
• WIMP with mass M must be non-relativistic at freeze-out
• gas in thermal equilibrium
• Annihilation rate
• Cross section depends on model parameters : weak interactions
AnnihilationW T N T χv
2
32
2
Boltzman gas
number density2
MckT
kT Mc
MTeTN
, ...f f
Could be neutralino or other weakly interacting
massive particle
WIMP velocity at FO
TFO
2012-13 Dark Matter 57
Freeze-out temperature
• assume that couplings are of order of weak interactions
• Rewrite expansion rate
• Freeze-out condition
• f = constants ≈ 100
• Set solve for P
2
Fv G M
1* 221.66
PL
g TH T
M
22
322
2
~F
PL
MTc
ke G
M
TMT M f
2
~ 25FO
cP FO
k
M
T
FO FOW T H T
GF = Fermi constant
2
PM
T
c
k
2
~25
FO
M ckT
2012-13 Dark Matter 58
P=M/T (time ->)
Nu
mb
er d
ensi
ty N
(T)
today
Increasing <σAv>
Depends on model
P~25
2012-13 Dark Matter 59
Relic abundance today Ω(T0) - 1
• At freeze-out annihilation rate ≈ expansion rate
• WIMP number density today for T0 = 2.73K
• Energy density today
3
0 FO
A
T
vT
T0N
2
FO PLT M
A FOv H TFON T
3
000
A
N TT
T Mv
O
PL
FP
M
253
0
110
c FO
m sv
t c
0 T
L
FO
P
P
M
3
3
0
FOR T
RT
TFON T0N
311
0
6 10
A
T GeV sv
2012-13 Dark Matter 60
Relic abundance today Ω(t0) - 2
• Relic abundance of WIMPs today
• For
• O(weak interactions) weakly interacting particles can make up cold dark matter with correct abundance
• Velocity of relic WIMPs at freeze-out from kinetic energy
FOv ≈ 0.3 c
35 210X cm O pb1
253 1
0
10~
FO
t cm sv
2 31
2 2
FOkTM v
12
3~ 0.3v
c FOP
WIMP miracle
SUPERSYMMETRY : POPULAR CANDIDATES
Neutralino is good candidate for cold dark matter
SUSY = extension of standard model at high energy
2012-13 Dark Matter 61
What are we looking for?
• Particle with charge = 0
• With mass in [GeV-TeV] domain
• Only interacting through gravitational and weak interactions
• Stable
• Decoupled from radiation before BBN era
• Has not yet been observed in laboratory = accelerators
2012-13 Dark Matter 62
2012-13 Dark Matter 63
Why SuperSymmetry
• Gives a unified picture of matter (quarks and leptons) and interactions (gauge bosons and Higgs bosons)
• Introduces symmetry between fermions and bosons
• Fills the gap between electroweak and Planck scale
• Solves problems of Standard Model, like the hierarchy problem: = divergence of radiative corrections to Higgs mass
• Provides a dark matter canndidate
217
19
1010
10
W
PL
M GeV
M GeV
Q fermion boson Q boson fermion
2012-13 Dark Matter 64
SuperSymmetric particles
• Need to introduce new particles: supersymmetric particles
• Associate to all SM particles a superpartner with spin 1/2 (fermion ↔ boson) sparticles
• minimal SUSY: minimal supersymmetric extension of the SM – reasonable assumptions to reduce nb of parameters
• Parameters = masses, couplings - must be determined from experiment
• Searches at colliders: so particles seen yet
M accessible range production sensitivity
2012-13 Dark Matter 65
The new particle table
Particle table (arXiv:hep-ph/0404175v2)
2012-13 Dark Matter 66
Neutralinos as dark matter
• Supersymmetric partners of gauge bosons mix to neutralino mass eigenstates
• Lightest neutralino
• R-parity quantum number
• baryon number B, lepton number L, spin s
• SM particles: R = 1 and sparticles: R = -1
• In R-parity conserving models Lightest Supersymmetric Particle (LSP) is stable
• LSP = lightest neutralino dark matter candidate
1 0 0
0 11 12 3 13 1 14 2N B N W N H N H
3 21
B L sR
Expected abundance vs mass
2012-13 Dark Matter 67
Neutralino mass (GeV)
h
2
=[.05-0.5]
• variation of neutralino density as function of mass
• Allowed by collider and direct search upper limits on cross sections
• Expected mass range 50GeV – few TeV
Ω= [0.04 – 1.0]
M GeV
2h
PART 5: WIMP DETECTION
The difficult path to discovery
2012-13 Dark Matter 68
2012-13 Dark Matter 69
three complementary strategies
production at accelerators
• Controlled production in laboratory: particle accelerators
• LHC @ CERN
2012-13 Dark Matter 70
Example from LHC
2012-13 Dark Matter 71
H. Bachacou EPS2011
0 01 1p p q g jets
Probed masses up to ~ TeV So signal was observed
2012-13 Dark Matter 72
N N
44 2 810 10p cm pbexperiment
Very small effects
Indirect detection of WIMPs • Search for signals of annihilation of WIMPs in the Milky Way halo
• Detect the produced antiparticles, gamma rays, neutrinos
• accumulation near galactic centre or in heavy objects like the Sun due to gravitational attraction
2012-13 Dark Matter 73
Overview
• Part 1: Observation of dark matter as gravitational effects
– Rotation curves galaxies, mass/light ratios in galaxies
– Velocities of galaxies in clusters
– Gravitational lensing
– Bullet cluster
• Part 2: Nature of the dark matter :
– Baryons and MACHO’s
– Standard neutrinos
– Axions
• Part 3: Weakly Interacting Massive Particles (WIMPs)
• Part 4: Experimental WIMP searches (lecture 4)
• Part 5: Dark energy (lecture 4)
2012-13 Dark Matter 74