Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
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 universechapters 5 to 8chapters 5 to 8
Particle Astrophysics , D. Perkins, 2nd edition, Oxford
5. The expanding universe6 Nucleosynthesis and baryogenesis6. Nucleosynthesis and baryogenesis7. Dark matter and dark energy components8. Development of structure in early universe
excercises
Slides + book http://w3 iihe ac be/~cdeclerc/astroparticlesSlides + book http://w3.iihe.ac.be/ cdeclerc/astroparticles
OverviewOb ti f d k tt it ti l ff t• Observation of dark matter as gravitational effects– Rotation curves galaxies, mass/light ratios in galaxies
V l iti f l i i l t– Velocities of galaxies in clusters– Gavitational lenses
Primordial nucleosynthesis– Primordial nucleosynthesis– Anisotropies in CMB radiation
• Nature of dark matter particles:• Nature of dark matter particles:– Baryons and MACHO’s– NeutrinosNeutrinos– Axions
• Weakly Interacting Massive Particles (WIMPs)Weakly Interacting Massive Particles (WIMPs) Experimental WIMP searches
• Dark energy• Dark energy
2011-12 Dark Matter-Dark Energy 3
Previously• Universe is flat k=0
• Dynamics given by Friedman equationDynamics given by Friedman equation
( ) ( )( ) ( )
22 8
3NR t G
R ttπ⎛ ⎞
=⎜ ⎟⎜ ⎟⎝ ⎠
H t totρ≡
• Cosmological redshift
( ) 3R t⎜ ⎟⎝ ⎠
( )( ) ( )0
01 0R t
z z t+ = =
• Closure parameter
( ) ( )0R t
( ) ( )tρΩClosure parameter
• Ener densit e ol es ith time
( ) ( )( )c
tt
ρρ
Ω =
Ω =0• Energy density evolves with time
( ) ( )( ) ( )( ) ( ) ( )2 3 4 220 01 1 1r kH t H z t z z⎡ ⎤= + +Ω + + +Ω +⎣ ⎦00m ΛΩ t Ω t
Ωk=0
2011-12 Dark Matter-Dark Energy 4
( ) ( )( ) ( )( ) ( ) ( )0 0 k⎣ ⎦00 Λ
Dark matter : Why and how much?luminous
1%
dark baryonic
4%
NeutrinoHDM<1%
• Several gravitationalobservations show that more
i i h U i h cold dark matter
18%
matter is in the Universe than wecan ‘see’
• These particles interact only
dark
• These particles interact onlythrough weak interactions and gravity dark
energy76%
gravity
• The energy density of DarkMatter today is obtained fromyfitting the ΛCDM model to CMB and other observations
( )( )
50 10
0 24rad t
t
−Ω ≈
Ω ≈( )0 0.24matter tΩ ≈
( ) ( )( ) ( )( ) ( )2 3 420 0 0 01 1m rH t H t z t z tΛ⎡ ⎤= Ω + +Ω + +Ω⎣ ⎦
2011-12 Dark Matter-Dark Energy 5
( ) ( )( ) ( )( ) ( )0 0 0 01 1m rH t H t z t z tΛΩ + +Ω + +Ω⎣ ⎦
Dark matter nature• The nature of most of the dark matter is still unknown
Is it a particle? Candidates from several models of physicsbeyond the standard model of particle physicsbeyond the standard model of particle physics
Is it something else? Modified newtonian dynamics?
• the answer will come from experiment
2011-12 Dark Matter-Dark Energy 6
Velocities of galaxies in clusters and M/L ratio
G l t tiGalaxy rotation curves
Gravitational lensing
Bullet Cluster
PART 1GRAVITATIONAL EFFECTS OF DARK MATTER
Bullet Cluster
GRAVITATIONAL EFFECTS OF DARK MATTER
2011-12 Dark Matter-Dark Energy 7
Evidence for dark matter - 1 b d ff l h• Observations at different scales : more matter in the
universe than what is measured as electromagneticd ( bl l h d )radiation (visible light, radio, IR, X-rays, g-rays)
• Visible matter = stars, interstellar gas, dust : light & atomicspectra (mainly H)
• Velocities of galaxies in clusters Æ high mass/light ratiosg g / g
1 10 500MW clusterM M M= ≈ ≈1 10 500MW clusterL L L
= ≈ ≈
• Rotation curves of stars in galaxies Æ large missing mass up to large distance from centre
2011-12 Dark Matter-Dark Energy 8
Dark matter in galaxy clusters 1k ( ) d /l h l• 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
vCOMA cluster
1000 galaxies
v 1000 galaxies
20Mpc diameter100 Mpc(330 Mly) from Earth
Optical (Sloan Digital Sky Survey)
100 Mpc(330 Mly) from Earth
2011-12 Dark Matter-Dark Energy 9
Optical (Sloan Digital Sky Survey)+ IR(Spitzer Space Telescope
NASA
Dark matter in galaxy clustersf l f l d f f• Mass from velocity of galaxies around centre of mass of
cluster using virial theorem
( ) ( )10
12
KE GPE=
⎫
Mv10
7
( ) 10500
10 cluster sun
M velocities M M ML LL L
⎫> ⎪ ⎛ ⎞ ⎛ ⎞⇒ ≈ ×⎬ ⎜ ⎟ ⎜ ⎟≈ ⎝ ⎠ ⎝ ⎠⎪⎭
M ML L
⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
⎭
Missing mass
P d l ti i i ‘d k’ i i ibl
COMA SUNL L⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠Missing mass
• Proposed explanation: missing ‘dark’ = invisible mass
• Missing mass has no interaction with electromagneticradiation
2011-12 Dark Matter-Dark Energy 10
Galaxy rotation curves• Stars orbiting in spiral galaxies
• gravitational force = centrifugal forcegravitational force centrifugal force
( )2 Mmmv r G<( )2
Mmmvr r
r G<=
• Star inside hub v r∼Star inside hub
• Star far away from hub
1vr
∼
2011-12 Dark Matter-Dark Energy 11
r
NGC 1560 galaxy
Optical blue filterOptical blue filter
HI 21cm line from gas
2011-12 Dark Matter-Dark Energy 12
Universal features• Large number of rotation curves of spiral galaxies measured
by Vera Rubin – up to 110kpc from centre
• Show a universal behaviour
2011-12 Dark Matter-Dark Energy 13
Milky Way rotation curve
Solar system
2011-12 Dark Matter-Dark Energy 14
Dark matter halo G l i b dd d i d k h l• Galaxies are embedded in dark matter halo
• Halo extends to far outside visible regionHalo of dark matter
HALO
DISK
2011-12 Dark Matter-Dark Energy 15
Dark matter halo models• Density of dark matter is larger
near centre due to gravitationalMilky Way halo models
attraction near black hole
• Halo extends to far outside visible
Vcm
-3)
region
•• darkdark mattermatter profile profile inside MilkyW i d ll d f ty
(GeV
Way is modelled frommeasurements of rotation curvesof many galaxies
Solar system
M D
ensi
t
of many galaxies
DM
Dark Matter-Dark Energy
Distance from centre (kpc)
162011-12
Evidence for dark matter -2• Gavitational lensing by galaxy clusters Æ effect larger than
expected from visible matter only
2011-12 Dark Matter-Dark Energy 17
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
2011-12 Dark Matter-Dark Energy 18
Lens geometries and images
2011-12 Dark Matter-Dark Energy 19
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
Distorted behind
Gala ies in Abell cl sterGalaxies in Abell cluster
2011-12 Dark Matter-Dark Energy 20
Different lensing effects• Strong lensing:
– clearly distorted images, e.g. Abell 2218 clustery g g
– Sets tight constraints on the total mass
• Weak lensing:Weak lensing: – only detectable with large sample of sources
– Allows to reconstruct the mass distribution over whole– Allows to reconstruct the mass distribution over wholeobserved field
• Microlensing:Microlensing: – no distorted images, but intensity of source changes with time
when lens passes in front of sourcewhen lens passes in front of source
– Used to detect Machos
2011-12 Dark Matter-Dark Energy 21
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 galaxiesweak lensing of many background galaxies
– Lens = bullet cluster
0.72 Mpc0.72 Mpc
Cluster 1E0657-56
2011-12 Dark Matter-Dark Energy 22
Bullet cluster in X-raysX f h d d Ch d b• X rays from hot gas and dust - Chandra observatory
• mass map contours from weak lensing of many galaxies
2011-12 Dark Matter-Dark Energy 23
Bullet cluster = proof of dark matter• Blue = dark matter mapped from gravitational lensing
• Is faster than gas and dust : no electromagnetic interactions
• Red = gas and dust = baryonic matter – slowed down because of electromagnetic interactions
d f d l h• Modified Newtonian Dynamics cannot explain this
2011-12 Dark Matter-Dark Energy 24
Alternative theories• Newtonian dynamics is different over (inter)-galactic
distances
• Far away from centre of cluster or galaxy the accelerationof an object becomes smallof an object becomes small
• Explains rotation curves
D t l i B ll t Cl t• Does not explain Bullet Cluster
2011-12 Dark Matter-Dark Energy 25
Baryons
MACHOs = Massive Compact Halo Objectsp jNeutrinosAxions
WIMPs = Weakly Interacting Massive Particles →Part 3
PART 2THE NATURE OF DARK MATTER
2011-12 Dark Matter-Dark Energy 26
What are we looking for?• Particles with mass – interact gravitationally
• Particles which are not observed in radio, IR, visible, X-rays, g-rays : neutral and 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 particleshad to be non-relativistic at time of freeze-out
fi Cold Dark Matter
2011-12 Dark Matter-Dark Energy 27
Total baryon contenty
Visible baryons
Neutral and ionised hydrogen – dark baryonsy g y
Mini black holes
MACHOs
BARYONIC MATTER
2011-12 Dark Matter-Dark Energy 28
Baryon content of universe ΩB=.044
• measurement of light elementabundances He mass fraction
• and of He mass fraction Y
• And of CMB anisotropies
• Interpreted in Big Bang Nucleosynthesis model D/H abundance
N ( ) 106.1 0.6 10BNNγ
η −= = ± ×
2011-12 Dark Matter-Dark Energy 29
0.044 0.005B⇒ Ω = ±
Baryon budget of universe• From BB nucleosynthesis and CMB fluctuations:
• Related to history of universe at
0.05baryonsΩ ≈
z=109 and z=1000
• Most of baryonic matter is in stars, gas, dust 0 01Ω ≈• Small contribution of luminous matter
• fi 80% of baryonic mass is dark
0.01lumΩ ≈
• Ionised hydrogen H+, MACHOs, mini black holes
• Inter Gallactic Matter = gas of hydrogen in clusters of galaxies
• Absorption of Lya emission from distant quasars yields neutralp y q yhydrogen fraction in inter gallactic regions
• Most hydrogen is ionised and invisible in absorption spectra fi formdark baryonic matter
2011-12 Dark Matter-Dark Energy 30
Mini black holes• Negligible contribution from mini black holes
• BHs must have MBH < 105 M
710BH−Ω <
BHs must have MBH 10 M
• Heavier BH would yield lensing effects which are not observedobserved
2011-12 Dark Matter-Dark Energy 31
Massive Astrophysical Compact Halo Objectsp y p j
Dark stars in the halo of the Milky Way
Observed through microlensing of large number of stars
MACHOSg g g
2011-12 Dark Matter-Dark Energy 32
MicrolensingLi h f i lifi d b i i l l• 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 p f ff pfront of source - period T
• Efficient for observation of e.g. faint starsEfficient for observation of e.g. faint stars
2011-12 Dark Matter-Dark Energy 33
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 p f p gsource 2 2
1 / 12 4x xx x
T
⎡ ⎤⎛ ⎞= + +⎢ ⎥⎜ ⎟
⎢ ⎥⎝ ⎠ ⎣ ⎦∼A t
• Typical time T : days to months – depends on distance & velocity
2 4 T⎢ ⎥⎝ ⎠ ⎣ ⎦
• Typical time T : days to months – depends on distance & velocity
• MACHO = dark astronomical object seen in microlensing• M 0 001 0 1M• M ª 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
2011-12 Dark Matter-Dark Energy 34
Optical depth – experimental challenge l d h b b l h d• Optical depth t = probability that source undergoes
gravitational lensing
• For r = NLM = Mass density of lenses along line of sight
• Optical depth depends on 2⎛ ⎞ ρDp p p
– distance of source DS
– number of lenses
23
Gc
τ π ⎛ ⎞= ⎜ ⎟⎝ ⎠
ρSD
number of lenses
• Near periphery of bulge of Milky Way
fi Need to record microlensing for millions of stars
( ) 7per source 10τ −≈
fi Need to record microlensing for millions of stars
• Experiments: MACHO, EROS, superMACHO, EROS-2
• EROS-2: 33x106 stars monitored, one candidate MACHO found fi less than 8% of halo mass are MACHOs
2011-12 Dark Matter-Dark Energy 35
Example of microlensing• source = star in Large
Magellanic Cloud (LMC, di 50k )
Blue filter
distance = 50kpc)
• Dark matter lens in form of MACHO between LMC starMACHO between LMC star and Earth
• Could it be a variable star?• Could it be a variable star?
• No: because same observation of luminosity in red and blue
red filter
of luminosity in red and bluelight : expect that gravitationaldeflection is independent of wavelength
2011-12 Dark Matter-Dark Energy 36
To do• Meebrengen naar examen
2011-12 Dark Matter-Dark Energy 37
STANDARD NEUTRINOS AS DARKMATTER
2011-12 Dark Matter-Dark Energy 38
Standard neutrinos• Standard Model of Particle Physics – measured at LEP
2.984 0.009fermion familiesN = ±
→ 3 types of light left-handed neutrinos
ith M <45G V/ 2
fermion families
with Mν<45GeV/c2
• Fit of observed light element
abundances to BBN model (lecture 2)
3.5t i iN <
• Neutrinos have only weak and
3.5neutrino speciesN <
eut os a e o y ea a dgravitational interactions
2011-12 Dark Matter-Dark Energy 39
Relic neutrinos• Non-baryonic dark matter = particles
– created during hot phase of early universeg p y
– Stable and surviving till today
• Neutrino from Standard Model = weakly interacting, smallNeutrino from Standard Model weakly interacting, smallmass, stable → dark matter candidate
• Neutrino production and annihilation in early universe• Neutrino production and annihilation in early universe
sweak interaction , ,i ie e i eγ ν ν μ τ+ −↔ + ←⎯⎯⎯⎯⎯⎯→ + =
• Neutrinos freeze-out during radiation dominated era
, ,i iγ μ
g
• When interaction rate W << H expansion rate
• at kT ~ 3MeV and t > 1s• at kT 3MeV and t > 1s
2011-12 Dark Matter-Dark Energy 40
Cosmic Neutrino Background• Relic neutrino density and temperature today
• for given species (ne, nm, nt ) (lecture 2)for given species (ne, nm, nt ) (lecture 2)
-33 11311
N N cmNν γν⎛ ⎞= =⎜ ⎟⎝ ⎠
+
( ) ( )1340 0⎛ ⎞
11ν γν ⎜ ⎟⎝ ⎠
( ) ( )40 011
T Tν γ⎛ ⎞= =⎜ ⎟⎝ ⎠
1.95K
• Total density for all flavours
• Hi h densit of order of CMB b t diffi lt to dete t!
3340N cmν−≈
• High density, of order of CMB – but difficult to detect!
2011-12 Dark Matter-Dark Energy 41
Neutrino mass • If all critical density today is built up of neutrinos
ρ 2
, ,47
e
m c eVνμ τ
= ⇒∑ νm <16eV c1c
νν
ρρ
= Ω = Ω =
• Measure end of electron energy spectrum in tritium beta decay
3 31 2 eH He e ν−→ + +
2m eV c<
2011-12 Dark Matter-Dark Energy 42
m eV cν <
Neutrino mass
3 31 2 eH He e ν−→ + +
t rat
e
0.0m eVν =
Coun
t
1.0m eVν =2m eV cν <
2011-12 Dark Matter-Dark Energy 43Electron energy (keV)
Neutrinos as hot dark matter• Relic neutrinos are numerous
• have very small mass < eVhave very small mass < eV
• can only be Hot Dark Matter – HDM
W l ti i ti h d li f th tt• Were relativistic when decoupling from other matterkTª3MeV
• Relativistic particles prevent formation of large-scalestructures – through free streaming they ‘iron away’ the structures
• From simulations of structures: maximum 30% of DM is hot
2011-12 Dark Matter-Dark Energy 44
simulationsHot dark matter warm dark matter cold dark matterHot dark matter warm dark matter
2011-12 Dark Matter-Dark Energy 45
Observations2dF galaxy survey
Postulated to solve ‘strong CP’ problem
Could be cold dark matter particle
AXIONS p
2011-12 Dark Matter-Dark Energy 46
Strong CP probleml f• QCD lagrangian for strong interactions
( )QCD quark gauge standard θ= + +L L L L 2a aS Fg T F F μν=L θ
• Term Lθ is generally neglected
• violates P and T symmetry → violates CP symmetry
216F Fμνθ π
=L θ
violates P and T symmetry → violates CP symmetry
• Violation of T symmetry would yield a non-zero neutron electric dipole moment ( )15 1610predictedd θ −−electric dipole moment ( )15 16. . . 10 .predictede d m e cmθ≈ ×
• Experimental upper limitsexperiment 2510e d m e cm−< 1010θ −≤
2011-12 Dark Matter-Dark Energy 47
p. . . 10 .e d m e cm< 1010θ ≤
Strong CP probleml b d h h l b l ( )• Solution by Peccei-Quinn : introduce higher global U(1)
symmetry, which is broken at an energy scale fa
• This extra term cancels the Lθ term2
a aS FA g T FF μνϕ⎛ ⎞⎜ ⎟L θ
• With broken symmetry comes a boson field φ = axion with
216a aS FA
A
g Ff
F μνμνπ
ϕ⎜ ⎟⎝
=⎠
L θ −
• With broken symmetry comes a boson field φa = axion withmass 1010~ 0.6A
GeVm meVf
• Axion is light and weakly interacting
AAf
• Is a pseudo-scalar with spin 0- ; Behaves like π0
• Decay rate to photons2 3A AG mγγDecay rate to photons
2011-12 Dark Matter-Dark Energy 4864A A
Aγγ
γγ πΓ =
Axion as cold dark matter• formed boson condensate in very early universe
• Therefore candidate as cold dark matter
• if mass ª eV its lifetime is larger than the lifetime of universe
Æ stable
• Production in plasma in Sun or SuperNovae
• Searches via decay to 2 photons in magnetic fieldproduction decayAγ γ γ γ+ ⎯⎯⎯⎯→ ⎯⎯⎯→ +
2 3
64A A
AG mγγ
γγ πΓ =
• CAST experiment @ CERN: axions from Sun
• If axion density = critical density today then
64π
y y y
6 3 210 10Am eV c− −≈ −1 aν
ρ= Ω = Ω =
2011-12 Dark Matter-Dark Energy 49
cν ρ
Axions were not yet observed
GeV
-1)
plin
g(G
Axion model di i
n-γ
coup predictions
Some are excluded by CAST limits
Axi
on
Axion mass (eV)Combination of mass and coupling below CAST l ll ll d b
2011-12 Dark Matter-Dark Energy 50
limit are still allowed by experimentCAST has best sensitivity
Weakly Interacting Massive Particles
PART 3y g
WIMPS AS DARK MATTER
2011-12 Dark Matter-Dark Energy 51
summary up to now
luminous1%
dark baryonic
4%
Neutrino HDM<1%
• Standard neutrinos can be Hot DM
<1%
cold dark matter
18%
• Most of baryonic matter is dark
18%• cold dark matter (CDM) is still
of unknow type
dark energy
76%• Need to search for candidates
f b i ld d k 76%for non-baryonic cold darkmatter in particle physicsbeyond the SMbeyond the SM
0.05 0.01 00.18 .24CDMmatter Baryons HDMν ΩΩ = Ω +Ω + ≈ + + =
2011-12 Dark Matter-Dark Energy 52
Non-baryonic CDM candidates• Axions
– To reach density of order ρc their mass must be very small
– No experimental evidence yet
2 6 310 10Am c eV− −≈ −p y
• Most popular candidate for CDM : WIMPsost popu a ca d date o C s
• Weakly Interacting Massive ParticlesWeakly Interacting Massive Particles• present in early hot universe – stable – relics of early universe• Cold : Non-relativistic at time of freeze-outCold : Non relativistic at time of freeze out• Weakly interacting : conventional weak couplings to standard
model particles - no electromagnetic or strong interactions
2011-12 Dark Matter-Dark Energy 53
p g g• Massive: gravitational interactions (gravitational lensing …)
WIMP candidates• Massive neutrinos:
– standard neutrinos have low masses – contribute to HDM
– Massive standard neutrinos up to MZ/2 = 45GeV/c2 are excluded by LEP
– Non-standard neutrinos in models beyond standard model
• Neutralino χ = Lightest SuperSymmetric Particle (LSP) in R-parity( ) hconserving SuperSymmetry (SUSY) theory
– Lower limit from accelerators ª 50 GeV/c2
– Stable particle – survived from primordial era of universe
• Other SUSY candidates: sneutrinos, gravitinos, axinos
• Kaluza-Klein states from models with universal extra dimensions
•
2011-12 Dark Matter-Dark Energy 54
…….
Expected mass range • Assume WIMP interacts weakly and is non-relativistic at freeze-
out
Whi h ll d?• Which mass ranges are allowed?
• Cross section for WIMP annihilation vs mass leads to abundancevs massvs mass
2 21) 4 ~ ~M s Mσ= →2s2
2
1) 41 12) 4 ~ ~
M s M
M s M
χ χ
χχ
σ
σ
→
= →2Ws > M
s < M
χ
( ) 1~tΩ ( )0 vtχΩ
σ
2011-12 Dark Matter-Dark Energy 55
Expected mass range: GeV-TeV• Assume WIMP interacts
weakly and is non-relativisticat freeze out
HDM neutrinos
CDM WIMPsat freeze-out
• Which mass ranges are allowed?
neutrinos
allowed?
• Cross section for WIMP annihilation vs mass leads to
Wannihilation vs mass leads to abundance vs mass
2 21) 4M s Mσ→2s2
2
1) 4 ~ ~1 12) 4 ~ ~
M s M
M s M
χ χ
χ
σ
σ
= →
= →2W
W
s > M
s < M
MWIMP (eV)
s M χ
( )01~v
tχΩσ
2011-12 Dark Matter-Dark Energy 56
vσ
Cross sections and densities -1• WIMP with mass M must be non-relativistic at freeze-out • gas in thermal equilibrium Could be neutralino or
h kl2
2
Boltzman gaskT Mc⎛ ⎞
→other weakly interacting
massive particle
( )3
22
number density2
MckTMT eT
π
⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠
−⎛ ⎞= ⎜ ⎟⎝ ⎠
N, ...f fχ χ+ ↔ +
• Freeze-out when annihilation rate < expansion rate H
2π⎝ ⎠
( )freeze oAnnihilation utW H tσ −= ≤χvN
, , ,...f f W W e eχ χ + − + −→ ++ + +
2011-12 Dark Matter-Dark Energy 57
• Cross section s depends on model parameters
Cross sections and densities -2
• assume that couplings are of order of weak interactions2v G M∼σ GF = Fermi
R it i t
Fv G M∼σ
( )1* 221 66 g T
GF Fermi constant
• Rewrite expansion rate ( ) ( )1.66
PL
g TH T
M=
• Freeze-out condition
( ) 223
2 2
2
F
MTc
ke G TMT M f
⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠
−⎡ ⎤⎢ ⎥ ⎡ ⎤ ≈⎣ ⎦⎢ ⎥( )W N H Tσ
f t t 100
( ) FPL
e GM
MT M f⎡ ⎤⎣ ⎦⎢ ⎥⎢ ⎥⎣ ⎦
( )FOW N v H Tσ= ≈
• f = constants ≈ 100
• Solve for P = Mcc2/kT at freeze-out ( )2
25c
P FOkM
Tχ= ≈
2011-12 Dark Matter-Dark Energy 58
FOkT
Cross sections and densities - 3
• At freeze-out annihilation rate ≈ expansion rate( ) ( )FOv H Tσ ≈FON T
• WIMP number density today for T0 = 2.73K
( ) ( )FOv H TσFON T
( ) ( ) ( )( )
( ) ( )3 230
3FO FOFO PLT T TR T
R TM×
≈=0N t FON T
• Energy density today
( ) ( ) ( )30R T vσ0 FO
Energy density today
( )0
3 3110 6 10TM GeV s
vt
vNχ χρ
σ σ
−−×= ∼ ∼P
M
2
25FO
ckM
Tχ= ≈P
v vσ σPLM
( )2
3 1510 mt c sχρ −
−=Ω
1910FOk
GeV
T
≈PLM
2011-12 Dark Matter-Dark Energy 59
( )0c
mv
t c sχ ρ=Ω ∼
σ
Dependspon model
y Increasing <σAv>
dens
ity
today
Num
ber
P~25
N
P=M/T (time ->)
( )25
3 110~t cm s−
−Ω
2011-12 Dark Matter-Dark Energy 60
( )0 ~t cm svχΩ
σ
Cross sections and densities - 4• Relic abundance of WIMPs today
2510−
( ) 3 10 ~ 10t cm s
vχ−Ω
σ
• For ( ) ( )35 210X cm O pbσ χ χ −+ → ≈ ≈1χΩ =
• O(weak interactions) fi weakly interacting particles canmake up cold dark matter with correct abundancemake up cold dark matter with correct abundance
• Velocity of relic WIMPs at freeze-out from kinetic energy
0.3v cχ ≈2 312 2
FOkTM vχ = ( )123~ 0.3v
c≈P
2011-12 Dark Matter-Dark Energy 61
2 2 c
Neutralino is good candidate for cold dark matter
SUSY = extension of standard model at high energy
SUPERSYMMETRYg gy
2011-12 Dark Matter-Dark Energy 62
What are we looking for?• Particle with charge = 0
• With mass in [GeV-TeV] domainWith mass in [GeV TeV] domain
• Only interacting through gravitational and weakinteractionsinteractions
• Stable
• Decoupled from radiation before BBN era
• Has not yet been observed in laboratory = accelerators
2011-12 Dark Matter-Dark Energy 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
Q fermion boson Q boson fermion= =
• Fills the gap between electroweak and Grand Unified Theoryl
Q f Q f
scale2
1710 10WM GeV −≈ =19 1010PLM GeV
≈ =
• Solves problems of Standard Model, like the hierarchy problem: = divergence of radiative corrections to Higgs massP id d k tt did t
2011-12 Dark Matter-Dark Energy 64
• Provides a dark matter canndidate
SuperSymmetric particles• Need to introduce new particles: supersymmetric particles
• Associate to all SM particles a superpartner with spin ±1/2Associate to all SM particles a superpartner with spin ±1/2 (fermion ↔ boson) fi sparticles
• minimal SUSY: minimal supersymmetric extension of the• minimal SUSY: minimal supersymmetric extension of the SM – reasonable assumptions to reduce nb of parameters
P t li t b d t i d f• Parameters = masses, couplings - must be determined fromexperiment
• Searches at colliders: so particles seen yet
M accessible range> d i sensitivityσ <M accessible range> production sensitivityσ <
2011-12 Dark Matter-Dark Energy 65
The new particle table
Particle table (arXiv:hep-ph/0404175v2)
2011-12 Dark Matter-Dark Energy 66
( p p / )
Neutralinos as dark matter• Supersymmetric partners of gauge bosons mix to
neutralino mass eigenstates
• Lightest neutralino
• R-parity quantum number
1 0 00 11 12 3 13 1 14 2N B N W N H N Hχ χ= = + + +
R parity quantum number
• baryon number B, lepton number L, spin s
SM ti l R 1 d ti l R 1
( )3 21 B L sR + +≡ −
• SM particles: R = 1 and sparticles: R = -1p p q g X+ → + +
• In R-parity conserving models Lightest Supersymmetric
0 01 1q q g qqχ χ→ + → +
In R parity conserving models Lightest SupersymmetricParticle (LSP) is stable
• LSP = lightest neutralino fi dark matter candidate
2011-12 Dark Matter-Dark Energy 67
• LSP = lightest neutralino fi dark matter candidate
Expected abundance vs mass
Wch
2• variation of neutralinodensity as function of
2hχΩ
Wmass
• Allowed by collider and direct search upper limitsdirect search upper limitson cross sections
W=[.05-0.5]
Ω [ ]
Predictions of Constrained Minimal
Supersymmetric extension of the Ω= [0.04 – 1.0]Supersymmetric extension of the Standard Model with 7 free
parameters
N li (G V)
• Expected mass range 50GeV – few TeV
2011-12 Dark Matter-Dark Energy 68
Neutralino mass (GeV)50GeV few TeV ( )M GeVχ
The difficult path to discovery
WIMP DETECTIONp y
2011-12 Dark Matter-Dark Energy 69
three complementary strategies
2011-12 Dark Matter-Dark Energy 70
Production at accelerators• Controlled production in laboratory: particle accelerators
• LHC @ CERNLHC @ CERN
2011-12 Dark Matter-Dark Energy 71
Example from LHC
Probed masses up to ~ TeVProbed masses up to TeVSo signal was observed
H. Bachacou EPS2011
0 0j t 0 01 1p p q g jets χ χ+ → + → + +
2011-12 Dark Matter-Dark Energy 72
N Nχ χ ′+ → +
2011-12 Dark Matter-Dark Energy 73
( ) 44 2 810 10p cm pbσ χ − −< =experiment
WIMPs in the Milky Way halo• Assume galaxy with dark halo• Energy density in galactic halo gy y g
from rotation curves and simulationssimulations
3~ 0.3GeV cmχρ
• WIMP velocity in halo
χρ
O(galactic objects)
1~ 270v km sχ−
2011-12 Dark Matter-Dark Energy 74
Direct detection challenges
pRM
N χχ
ρσ∝ pM χ
χ
• low rate Ælarge detectorg
• very small signal Æ low thresholdÆ low threshold
• large background : protect againstprotect againstcosmic rays, radioactivityradioactivity, …
2011-12 Dark Matter-Dark Energy 75
Annual and diurnal modulation• Annual modulations due to movement of solar system in
galactic WIMP halo – 30% effect
• Diurnal modulations due to Earth rotation – 2% effect
• Observed by DAMA – not confirmed by other experimentsObserved by DAMA not confirmed by other experiments
2011-12 Dark Matter-Dark Energy 76
DAMA/LIBRA experiment• In Gran Sasso underground laboratory
• Measure scintillation light from nuclear recoil in NaI crystalsMeasure scintillation light from nuclear recoil in NaI crystals
• Observe modulation of 1 year (full curve) with phase of 152 5 days152.5 days
• If interpreted as SUSY dark matter: M ~ 10-50 GeV/c2
2011-12 Dark Matter-Dark Energy 77
Combining different experiments
2011-12 Dark Matter-Dark Energy 78
d l ( l ) l
Noble liquids: XENON100• 1400m under mountain in Gran Sasso tunnel (Italy) : lower
rate of cosmic background
• Sensitive core = 100kg liquid Xenon at -106°C• Pure materials – low radioactivityy
• Recoil nucleus ionises liquid Xenon
• Measure signal from ionisation and scintillation light• Measure signal from ionisation and scintillation light produced during recoil of nucleon
D bl i l h l i f k• Double signal helps against fake events
• Started data taking in 2009
2011-12 Dark Matter-Dark Energy 79
2011-12 Dark Matter-Dark Energy 80
XENON100
2011-12 Dark Matter-Dark Energy 81
Combining different experiments
2011-12 Dark Matter-Dark Energy 82
Indirect detection of WIMPsS h f i l f ihil i f WIMP i h Milk W h l• 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
2011-12 Dark Matter-Dark Energy 83
Neutrino signals• Expect WIMPs to accumulate in heavy objects like Sun
χχ Earthρχ velocity
distribution
Sun
νμσcΝ ν int.
Detectorμμ
Gcapture
qq Detector
Gannihilation
qqll μχχ ν→ → →
2011-12 Dark Matter-Dark Energy 84
annihilation
, ,W Z Hμ
±
Neutrino detection
South Pole station Cherenkov light pattern emitted by the muon isemitted by the muon isregistered by an array of photomultiplier tubes (PMT)
ayer Photomultiplier tubes
photomultiplier tubes (PMT)
m ic
e la
p
3km
νµ*
85
νμ2011-12 Dark Matter-Dark Energy
Signal and background
A few 10’000 atmosphericneutrinos per year fromBG neutrinos per year fromnorthern hemisphere
BG
Max. a few neutrinos per year from WIMPs
signalper year from WIMPs
~1010 atmospheric~10 atmosphericmuons per year fromsouthern hemisphere
BG
86
p
2011-12 Dark Matter-Dark Energy
IceCube search resultsNeutralino 250 GeV to WWDataBackgroundBackground
s
• Search for neutrinos fromf eve
nts
• Search for neutrinos fromWIMP annihilation in the Sun
• No significant signal foundmbe
rof
No significant signal found
• Rate is compatible withatmospheric background
Num
atmospheric background
• Set upper limit on possible flux
ψ(deg)
nal?
2011-12 Dark Matter-Dark Energy 87
Sign
Combining the experimental searches( ) 2
SD p cmσ χ ⎡ ⎤⎣ ⎦
Direct detectionIceCube
SUSY modelsallowed by
2011-12 Dark Matter-Dark Energy 88
experiments IceCube allowed by accelerator results
SummaryOb ti f d k tt it ti l ff t• Observation of dark matter as gravitational effects– Rotation curves galaxies, mass/light ratios in galaxies– Velocities of galaxies in clusters– Gavitational lenses– Primordial nucleosynthesis– Anisotropies in CMB radiation
• Nature of dark matter particles:– Baryons and MACHO’s– Neutrinos– Neutrinos– Axions
• Weakly Interacting Massive Particles (WIMPs) • Experimental WIMP searches
– Accelerators– Direct detection experimentsDirect detection experiments– Indirect detection
• Dark energy2011-12 Dark Matter-Dark Energy 89