Download Dark Matter and Dark Energy components chapter 7

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.
6
6.
7.
8.
The expanding universe
Nucleosynthesis and baryogenesis
Dark matter and dark energy components
Development of structure in early universe
excercises
Slides + book http://w3
http://w3.iihe.ac.be/
iihe ac be/~cdeclerc/astroparticles
cdeclerc/astroparticles
Overview
• Observation
Ob
ti off dark
d k matter
tt as gravitational
it ti
l effects
ff t
–
–
–
–
–
Rotation curves galaxies, mass/light ratios in galaxies
V l iti off galaxies
Velocities
l i iin clusters
l t
Gavitational lenses
Primordial nucleosynthesis
Anisotropies in CMB radiation
• Nature of dark matter particles:
– Baryons and MACHO’s
– Neutrinos
– Axions
• Weakly Interacting Massive Particles (WIMPs)
Experimental WIMP searches
• Dark energy
2011-12
Dark Matter-Dark Energy
3
Previously
t
o
ρt
• Universe is flat k=0
• Dynamics given by Friedman equation
2
⎛ R ( t ) ⎞ 8π GN
2
=
t)
H (t ) ≡ ⎜
(
⎜ R ( t ) ⎟⎟
3
⎝
⎠
• Cosmological redshift
• Closure parameter
1+ z =
R ( t0 )
z ( t0 ) = 0
R (t )
ρ (t )
Ω (t ) =
ρc ( t )
Dark Matter-Dark Energy
t0
+ Ω r ( t0 )(1 + z ) +
4
Ωk=0
( ) + Ωk (1 + z )
Λ
( )(1 + z )
3
Ω
t0
2011-12
=H ⎡
⎣
2
0
m
H (t )
2
Ω
• Energy
Ener density
densit evolves
e ol es with
ith time
2
⎤
⎦
4
Dark matter : Why and how much?
• Several gravitational
observations show that more
matter is
i in
i the
h Universe
U i
than
h we
can ‘see’
• These particles interact only
through weak interactions and
gravity
• The energy density of Dark
Matter todayy is obtained from
fitting the ΛCDM model to CMB
and other observations
luminous
1%
dark
baryonic
4%
Neutrino
HDM
<1%
cold dark
matter
18%
dark
energy
76%
Ω rad ( t0 ) ≈ 10−5
Ω matter ( t0 ) ≈ 0.24
0 24
3
4
⎡
H ( t ) = H Ωm ( t0 )(1+ z) +Ωr ( t0 )(1+ z) +ΩΛ ( t0 )⎤
⎣
⎦
2
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2
0
Dark Matter-Dark Energy
5
Dark matter nature
• The nature of most of the dark matter is still unknown
¾ Is it a particle? Candidates from several models of physics
beyond the standard model of particle physics
¾ 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
Galaxy
rotation
t ti curves
Gravitational lensing
Bullet Cluster
PART 1
GRAVITATIONAL EFFECTS OF DARK MATTER
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Dark Matter-Dark Energy
7
Evidence for dark matter - 1
• Observations
b
at different
d ff
scales
l : more matter in the
h
universe than what is measured as electromagnetic
radiation
d
((visible
bl llight,
h radio,
d IR, X-rays, g-rays))
• Visible matter = stars, interstellar gas, dust : light & atomic
spectra (mainly H)
g mass/light
/ g ratios
• Velocities of ggalaxies in clusters Æ high
M
=1
L
M MW
≈ 10
LMW
M cluster
≈ 500
Lcluster
• Rotation curves of stars in galaxies Æ large missing mass up
to large distance from centre
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8
Dark matter in galaxy clusters 1
• Zwicky
k (1937):
(
) measured
d mass/light
/l h ratio in COMA cluster
l
is much larger than expected
– Velocity from Doppler shifts (blue & red) of spectra of galaxies
– Light output from luminosities of galaxies
v
COMA cluster
1000 galaxies
20Mpc diameter
100 Mpc(330 Mly) from Earth
Optical (Sloan Digital Sky Survey)
+ IR(Spitzer Space Telescope
2011-12
Dark Matter-Dark Energy
NASA
9
Dark matter in galaxy clusters
• Mass from
f
velocity
l
off galaxies
l
around
d centre off mass off
cluster using virial theorem
1
KE ( v ) = GPE ( M )
2
M (velocities) > 1010 M ⎫⎪ ⎛ M ⎞
⎛M ⎞
⇒
≈
×
500
⎬ ⎜ ⎟
⎜ ⎟
7
L
L ≈ 10 L
⎝ L ⎠sun
⎪⎭ ⎝ ⎠cluster
⎛M ⎞
⎜ ⎟
⎝ L ⎠COMA
Missing mass
⎛M ⎞
⎜ ⎟
⎝ L ⎠ SUN
• P
Proposed
d explanation:
l ti
missing
i i ‘dark’
‘d k’ = invisible
i i ibl mass
• Missing mass has no interaction with electromagnetic
radiation
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10
Galaxy rotation curves
• Stars orbiting in spiral galaxies
• gravitational force = centrifugal force
mv 2 mM ( < r ) G
=
r
r2
• Star inside hub v ∼ r
• Star far away from hub
1
v∼
r
2011-12
Dark Matter-Dark Energy
11
NGC 1560 galaxy
Optical 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
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13
Milky Way rotation curve
Solar system
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14
Dark matter halo
Halo of dark matter
• G
Galaxies
l i are embedded
b dd d in
i dark
d k matter halo
h l
• Halo extends to far outside visible region
HALO
DISK
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Dark Matter-Dark Energy
15
Dark matter halo models
Milky Way halo models
DM
M Densitty (GeV
V cm-3)
• 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
W is
Way
i modelled
d ll d from
f
measurements of rotation curves
of many galaxies
Solar system
Dark Matter-Dark Energy
Distance from centre (kpc)
2011-12
16
Evidence for dark matter -2
• Gavitational lensing by galaxy clusters Æ effect larger than
expected from visible matter only
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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
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18
Lens geometries and images
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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
Galaxies
cluster
ster
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Dark Matter-Dark Energy
20
Different lensing effects
• Strong lensing:
– clearlyy distorted images,
g e.g.
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
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 galaxies
– Lens = bullet cluster
0.72 Mpc
Cluster 1E0657-56
2011-12
Dark Matter-Dark Energy
22
Bullet cluster in X-rays
• X rays from
f
h gas and
hot
d dust
d - Chandra
Ch d observatory
b
• 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
• Modified
d f d Newtonian Dynamics cannot explain
l this
h
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 acceleration
of an object becomes small
• Explains rotation curves
• Does
D
nott explain
l i Bullet
B ll t Cl
Cluster
t
2011-12
Dark Matter-Dark Energy
25
Baryons
MACHOs = Massive Compact
p
Halo Objects
j
Neutrinos
Axions
WIMPs = Weakly Interacting Massive Particles →Part 3
PART 2
THE 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 particles
had to be non-relativistic at time of freeze-out
fi Cold Dark Matter
2011-12
Dark Matter-Dark Energy
27
Total baryon
y content
Visible baryons
Neutral and ionised hydrogen
y g – dark baryons
y
Mini black holes
MACHOs
BARYONIC MATTER
2011-12
Dark Matter-Dark Energy
28
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
ΩB=.044
He mass fraction
D/H abundance
NB
η=
= ( 6.1 ± 0.6 ) × 10−10
Nγ
⇒ Ω B = 0.044 ± 0.005
2011-12
Dark Matter-Dark Energy
29
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
• fi 80% of baryonic mass is dark
• Ionised hydrogen H+, MACHOs, mini black holes
Ωbaryons ≈ 0.05
Ωlum ≈ 0.01
0 01
• Inter Gallactic Matter = gas of hydrogen in clusters of galaxies
• Absorption
p
of Lya
y emission from distant q
quasars yyields neutral
hydrogen fraction in inter gallactic regions
• Most hydrogen is ionised and invisible in absorption spectra fi form
dark baryonic matter
2011-12
Dark Matter-Dark Energy
30
Mini black holes
• Negligible contribution from mini black holes Ω BH < 10−7
• BHs must have MBH < 105 M
• Heavier BH would yield lensing effects which are not
observed
2011-12
Dark Matter-Dark Energy
31
Massive Astrophysical
p y
Compact
p Halo Objects
j
Dark stars in the halo of the Milky Way
Observed through
g microlensingg of large
g number of stars
MACHOS
2011-12
Dark Matter-Dark Energy
32
Microlensing
• Li
Light
h off source is
i amplified
lifi d by
b gravitational
i i
l lens
l
• When lens is small (star, planet) multiple images of source
cannot be distinguished : addition of images = amplification
p f
effect
ff varies with time as lens p
passes in
• But : amplification
front of source - period T
• Efficient for observation of e.g. faint stars
Period T
2011-12
Dark Matter-Dark Energy
33
Microlensing - MACHOs
• Amplification of signal by addition of multiple images of source
• Amplification
p
varies with time off p
passage
g of lens in front of
source
⎛ x2 ⎞ ⎡
x2 ⎤
t
A = ⎜1 + ⎟ / ⎢ x 1 + ⎥
2 ⎠ ⎢⎣
4 ⎥⎦
⎝
x∼
T
• Typical time T : days to months – depends on distance & velocity
• MACHO = dark astronomical object seen in microlensing
• M ª 0.001-0.1M
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
• Opticall depth
d h t = probability
b b l that
h source undergoes
d
gravitational lensing
• For r = NLM = Mass density of lenses along line of sight
2
p
depth
p depends
p
on
• Optical
⎛ DS ⎞ ρ
τ = 2π G ⎜
– distance of source DS
⎟ 3
c
⎝
⎠
– number of lenses
−7
τ
per
source
≈
10
(
)
• Near periphery of bulge of Milky Way
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
distance
= 50k
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
2011-12
Blue filter
red filter
Dark Matter-Dark Energy
36
To do
• Meebrengen naar examen
2011-12
Dark Matter-Dark Energy
37
STANDARD NEUTRINOS AS DARK
MATTER
2011-12
Dark Matter-Dark Energy
38
Standard neutrinos
• Standard Model of Particle Physics – measured at LEP
N fermion families = 2.984 ± 0.009
→ 3 types of light left-handed neutrinos
with
ith Mν<45GeV/c2
<45G V/ 2
• Fit of observed light element
abundances to BBN model (lecture 2)
N neutrino
t i species
i < 3.5
• Neutrinos
eut os have
a eo
onlyy weak
ea aand
d
gravitational interactions
2011-12
Dark Matter-Dark Energy
39
Relic neutrinos
• Non-baryonic dark matter = particles
– created duringg hot p
phase of earlyy universe
– Stable and surviving till today
• Neutrino from Standard Model = weakly interacting, small
mass, stable → dark matter candidate
• Neutrino production and annihilation in early universe
weak interactions
γ ↔ e+ + e − ←⎯⎯⎯⎯⎯⎯
→ν i + ν i
i = e, μ ,τ
• Neutrinos freeze-out duringg radiation dominated era
• When interaction rate W << H expansion rate
• 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)
⎛3⎞
Nν + Nν = ⎜ ⎟ Nγ = 113 cm-3
⎝ 11 ⎠
⎛4
Tν ( 0 ) = ⎜ ⎟ Tγ ( 0 ) =
⎝ 11 ⎠
K
5
9
.
1
1
⎞ 3
−3
N
≈
340
cm
• Total density for all flavours
ν
• High
Hi h density,
densit of order of CMB – but
b t difficult
diffi lt to detect!
dete t!
2011-12
Dark Matter-Dark Energy
41
Neutrino mass
• If all critical density today is built up of neutrinos
2
m
c
∑ ν = 47 eV ⇒
c
V
e
6
1
<
ν
m
ρν
1 = Ω = Ων =
ρc
e , μ ,τ
• Measure end of electron energy spectrum in tritium beta
decay
3
1
H → 23 He + e − + ν e
mν < eV c
2011-12
Dark Matter-Dark Energy
2
42
Neutrino mass
Countt rate
3
1
mν = 0.0eV
mν < eV c
mν = 1.0eV
2011-12
H → 23 He + e − + ν e
2
Electron energy (keV)
Dark Matter-Dark Energy
43
Neutrinos as hot dark matter
•
•
•
•
Relic neutrinos are numerous
have very small mass < eV
can only be Hot Dark Matter – HDM
W
Were
relativistic
l ti i ti when
h decoupling
d
li from
f
other
th matter
tt
kTª3MeV
• Relativistic particles prevent formation of large-scale
structures – 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
simulations
Hot dark matter
2011-12
warm dark matter
Observations
2dF galaxy Dark
survey
Matter-Dark Energy
cold dark matter
45
Postulated to solve ‘strong CP’ problem
Could be cold dark matter p
particle
AXIONS
2011-12
Dark Matter-Dark Energy
46
Strong CP problem
• QCD lagrangian
l
f strong interactions
for
LQCD = Lquark + Lgauge ( standard ) + Lθ
g S2TF a aμν
Lθ = θ
Fμν F
2
16π
• 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 e.d .m. predicted ≈ θ × 10−(15−16) e.cm
• Experimental upper limits
p
e.d .m.experiment
< 10−25 e.cm
2011-12
Dark Matter-Dark Energy
θ ≤ 10
−10
47
Strong CP problem
• Solution
l
b
by Peccei-Quinn : introduce
d
h h global
higher
l b l U(1)
( )
symmetry, which is broken at an energy scale fa
• This extra term cancels the Lθ term
⎛
ϕ A ⎞ g S2TF a aμν
L = ⎜θ −
Fμν F
⎟
2
f A ⎠ 16π
⎝
• With broken symmetry comes a boson field φa = axion with
mass
1010 GeV
m A ~ 0.6meV
fA
• Axion is light and weakly interacting
• Is a pseudo-scalar with spin 0- ; Behaves like π0
2
3
G
m
• Decay rate to photons
Aγγ A
Γ Aγγ =
64π
2011-12
Dark Matter-Dark Energy
48
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 field
γ + γ ⎯⎯⎯⎯→ A ⎯⎯⎯
→γ + γ
production
decay
Γ Aγγ =
• CAST experiment @ CERN: axions from Sun
• If axion densityy = critical densityy todayy then
ρa
1 = Ω = Ων =
ρc
2011-12
G A2 γγ m3A
64π
mA ≈ 10−6 − 10−3 eV c 2
Dark Matter-Dark Energy
49
Axion
n-γ coup
pling (G
GeV-1)
Axions were not yet observed
Axion model
predictions
di i
Some are excluded by
CAST limits
Combination of mass and coupling below CAST
Axion mass (eV)
llimit are stillll allowed
ll
d by
b experiment
CAST has best sensitivity
2011-12
Dark Matter-Dark Energy
50
Weaklyy Interactingg Massive Particles
PART 3
WIMPS AS DARK MATTER
2011-12
Dark Matter-Dark Energy
51
summary up to now
• Standard neutrinos can be Hot
DM
• Most of baryonic matter is dark
dark
baryonic
4%
luminous
1%
cold dark
matter
18%
• cold dark matter (CDM) is still
of unknow type
• Need to search for candidates
f non-baryonic
for
b
i cold
ld dark
d k
matter in particle physics
beyond the SM
Neutrino
HDM
<1%
dark
energy
76%
Ω matter = Ω Baryons + Ων HDM + ΩCDM ≈ 0.05 + 0.01 + 0.18 = 0.24
2011-12
Dark Matter-Dark Energy
52
Non-baryonic CDM candidates
• Axions
– To reach density of order ρc their mass must be very small
−6
−3
mAc ≈ 10 − 10 eV
2
– No experimental
p
evidence yyet
• Most
ost popu
popular
a ca
candidate
d date for
o CDM
C
: WIMPss
•
•
•
•
Weakly Interacting Massive Particles
present in early hot universe – stable – relics of early universe
Cold : Non
Non-relativistic
relativistic at time of freeze
freeze-out
out
Weakly interacting : conventional weak couplings to standard
model p
particles - no electromagnetic
g
or strongg interactions
• Massive: gravitational interactions (gravitational lensing …)
2011-12
Dark Matter-Dark Energy
53
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
conserving SuperSymmetry (SUSY)
(
) theory
h
– 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 freezeout
• Which
Whi h mass ranges are allowed?
ll
d?
• Cross section for WIMP annihilation vs mass leads to abundance
vs mass
→ σ ~ s ~ M χ2
2W
2) 4 M χ2 =
2
M M
< >
s s
1) 4 M χ2 =
→σ ~ 1 ~ 1 2
s
Mχ
1
Ω χ ( t0 ) ~
σv
2011-12
Dark Matter-Dark Energy
55
Expected mass range: GeV-TeV
2) 4 M χ2 =
HDM
neutrinos
→ σ ~ s ~ M χ2
→σ ~ 1 ~ 1 2
s
Mχ
1
Ω χ ( t0 ) ~
σv
2011-12
CDM WIMPs
2W
1) 4
4M
M χ2 =
2W
M M
< >
s s
• Assume WIMP interacts
weakly and is non-relativistic
at freeze-out
freeze out
• Which mass ranges are
allowed?
W
• Cross section for WIMP
annihilation vs mass leads to
abundance vs mass
MWIMP (eV)
Dark Matter-Dark Energy
56
Cross sections and densities -1
• WIMP with mass M must be non-relativistic at freeze-out
Could be neutralino or
• gas in thermal equilibrium
kT
other
h weakly
kl interacting
massive particle
Mc 2 → Boltzman gas
3
⎛ MT ⎞ 2
N (T ) = ⎜
⎟ e
⎝ 2π ⎠
⎛ − Mc 2 ⎞
⎜
⎟
⎜ kT ⎟
⎝
⎠
number density
χ + χ ↔ f + f , ...
χ
W = N σ Annihilation
v
• Freeze-out when annihilation rate < expansion rate H
(
≤ H t freeze−out
)
χ + χ → f + f , W + + W − , e + + e− ,...
• Cross section s depends on model parameters
2011-12
Dark Matter-Dark Energy
57
Cross sections and densities -2
• assume that couplings are of order of weak interactions
σ v ∼ GF M 2
• Rewrite
R
it expansion
i rate
t H (T ) =
• Freeze-out condition
W = N σ v ≈ H (TFO )
1 66 ( g
1.66
)
1
2
T2
M PL
⎛ − Mc 2 ⎞
⎡
⎜
⎟⎤
2
⎜
⎟
3
k
T
T
⎢
2
2
⎠⎥
2 ⎝
⎡
⎤⎦ ≈
MT
e
G
M
f
)
⎢(
⎥⎣ F
M PL
⎢⎣
⎥⎦
• f = constants
t t ≈ 100
• Solve for P = Mcc2/kT at freeze-out
2011-12
*
GF = Fermi
constant
Dark Matter-Dark Energy
P ( FO ) =
M χ c2
kTFO
kT
≈ 25
58
Cross sections and densities - 3
• At freeze-out annihilation rate ≈ expansion rate
N (TFO ) σ v ≈ H (TFO )
• WIMP number density today for T0 = 2.73K
t0
N
R (TFO )
≈
) = N (TFO ) 3
R (T0 )
(
3
(T0 TFO ) × (TFO2 M PL )
3
σv
• Energy density today
ρ χ = M χ N ( t0 ) ∼
6 ×10
∼
σv
σv
3
0
PT
M PL
−31
GeV s −1
ρ χ 10−25 3 −1
Ω χ ( t0 ) =
∼
cm s
ρc
σv
2011-12
Dark Matter-Dark Energy
P=
M χ c2
kTFO
≈ 25
M PL ≈ 1019 GeV
59
N
Number
densityy
Depends
p
on model
Increasing <σAv>
today
P~25
P=M/T (time ->)
10−25 3 −1
Ω χ ( t0 ) ~
cm s
σv
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60
Cross sections and densities - 4
• Relic abundance of WIMPs today
10−25 3 −1
Ω χ ( t0 ) ~
cm s
σv
• For
Ωχ = 1
σ ( χ + χ → X ) ≈ 10 cm ≈ O ( pb )
−35
2
• O(weak interactions) fi weakly interacting particles can
make up cold dark matter with correct abundance
• Velocity of relic WIMPs at freeze-out from kinetic energy
3kTFO
1
2
Mχv =
2
2
2011-12
( )
v
~ 3
P
c
1
2
≈ 0.3
Dark Matter-Dark Energy
vχ ≈ 0.3 c
61
Neutralino is good candidate for cold dark matter
SUSY = extension of standard model at high
g energy
gy
SUPERSYMMETRY
2011-12
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62
What are we looking for?
• Particle with charge = 0
[GeV TeV] domain
• With mass in [GeV-TeV]
• Only interacting through gravitational and weak
interactions
• Stable
• Decoupled from radiation before BBN era
• Has not yet been observed in laboratory = accelerators
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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 ffermion = boson
Q boson = ffermion
• Fills the gap between electroweak and Grand Unified Theory
scale
l
M W 102 GeV
≈ 19
= 10−17
M PL 10 GeV
• Solves problems of Standard Model, like the hierarchy problem:
= divergence of radiative corrections to Higgs mass
• Provides
P id a dark
d k matter
tt canndidate
did t
2011-12
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64
SuperSymmetric particles
• Need to introduce new particles: supersymmetric particles
• Associate to all SM particles a superpartner with spin ±1/2
(fermion ↔ boson) fi sparticles
• minimal SUSY: minimal supersymmetric extension of the
SM – reasonable assumptions to reduce nb of parameters
• Parameters
P
t = masses, couplings
li
- mustt be
b determined
d t
i d from
f
experiment
• Searches at colliders: so particles seen yet
M > accessible range σ production
d i < sensitivity
2011-12
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65
The new particle table
Particle table ((arXiv:hep-ph/0404175v2)
pp /
)
2011-12
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66
Neutralinos as dark matter
• Supersymmetric partners of gauge bosons mix to
neutralino mass eigenstates
• Lightest neutralino χ 01 = χ = N11B + N12W3 + N13 H10 + N14 H 20
R-parity
parity quantum number
• R
3B + L+ 2 s
• baryon number B, lepton number L, spin s R ≡ ( −1)
• SM particles:
ti l R = 1 and
d sparticles:
ti l R = -1
1
p+ p→q+g+ X
q → q + χ10
g → qq + χ10
• In R
R-parity
parity conserving models Lightest Supersymmetric
Particle (LSP) is stable
• LSP = lightest neutralino fi dark matter candidate
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67
Expected abundance vs mass
Wch2
• variation of neutralino
2
density as function of Ω χ h
mass
• Allowed by collider and
direct search upper limits
on cross sections
Predictions of
Constrained Minimal
Supersymmetric extension of the
Standard Model with 7 free
parameters
W=[.05-0.5]
Ω [0.04
Ω=
[
– 1.0]]
• Expected mass range
50GeV – few TeV
2011-12
(
)
Neutralino
N
mass (GeV)
(G V)
Mliχ GeV
Dark Matter-Dark Energy
68
The difficult p
path to discoveryy
WIMP DETECTION
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 @ CERN
2011-12
Dark Matter-Dark Energy
71
Example from LHC
Probed masses up to ~ TeV
So signal was observed
H. Bachacou EPS2011
p + p → q + g → jets
j t + χ10 + χ10
2011-12
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72
χ + N → χ + N′
2011-12
experiment
σ ( χ p ) < 10−44 cm 2 = 10−8 pb
Dark Matter-Dark Energy
73
WIMPs in the Milky Way halo
• Assume galaxy with dark halo
gy densityy in ggalactic halo
• Energy
from rotation curves and
simulations
ρ χ ~ 0.3GeV cm3
• WIMP velocity in halo
O(galactic objects)
vχ ~ 270 km s −1
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Direct detection challenges
R∝N
ρχ
Mχ
σχp
• low rate Æ
large
g detector
• very small signal
Æ low threshold
• large background :
protect against
cosmic rays,
radioactivity, …
radioactivity
2011-12
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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 experiments
2011-12
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76
DAMA/LIBRA experiment
• In Gran Sasso underground laboratory
• Measure scintillation light from nuclear recoil in NaI crystals
• Observe modulation of 1 year (full curve) with phase of
152 5 days
152.5
• If interpreted as SUSY dark matter: M ~ 10-50 GeV/c2
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Combining different experiments
2011-12
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78
Noble liquids: XENON100
• 1400m under
d mountain in Gran Sasso tunnell ((Italy)
l ) : lower
l
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
produced during recoil of nucleon
• Double
D bl signal
i l helps
h l against
i fake
f k events
• Started data taking in 2009
2011-12
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79
2011-12
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80
XENON100
2011-12
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81
Combining different experiments
2011-12
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82
Indirect detection of WIMPs
• SSearch
h for
f signals
i l off annihilation
ihil i off WIMPs
WIMP in
i the
h Milky
Milk Way
W halo
h l
• Detect the produced antiparticles, gamma rays, neutrinos
• accumulation near galactic centre or in heavy objects like the Sun due
to gravitational attraction
2011-12
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83
Neutrino signals
• Expect WIMPs to accumulate in heavy objects like Sun
ρχ χ
velocity
distribution
Earth
Sun
σcΝ
νμ
ν int.
Gcapture
Gannihilation
2011-12
χχ →
qq
ll
W±, Z, H
Dark Matter-Dark Energy
Detector
μ
→ →νμ
84
Neutrino detection
3km
m ice la
ayer
South Pole station
Cherenkov light pattern
emitted by the muon is
registered by an array of
photomultiplier tubes (PMT)
Photomultiplier
p
tubes
µ
*
νμ
2011-12
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85
Signal and background
BG
signal
A few 10’000 atmospheric
neutrinos per year from
northern hemisphere
Max. a few neutrinos
per year from WIMPs
~1010 atmospheric
BG muons per year from
p
southern hemisphere
2011-12
Dark Matter-Dark Energy
86
IceCube search results
Sign
nal?
Num
mber off eventss
Neutralino 250 GeV to WW
Data
Background
2011-12
ψ(deg)
• Search for neutrinos from
WIMP annihilation in the Sun
• No significant signal found
• Rate is compatible with
atmospheric background
• Set upper limit on possible
flux
Dark Matter-Dark Energy
87
Combining the experimental searches
σ SD ( χ p ) ⎡⎣cm 2 ⎤⎦
Direct detection
experiments
2011-12
IceCube
Dark Matter-Dark Energy
SUSY models
allowed by
accelerator results
88
Summary
• Observation
Ob
ti off dark
d k matter
tt as gravitational
it ti
l effects
ff t
–
–
–
–
–
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
– Axions
• Weakly Interacting Massive Particles (WIMPs)
• Experimental WIMP searches
– Accelerators
– Direct detection experiments
– Indirect detection
• Dark energy
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