dark matter and dark energy components chapter 7 lecture 3

Dark Matter and Dark Energy components

chapter 7

Lecture 3

The early universechapters 5 to 8

Particle Astrophysics , D. Perkins, 2nd edition, Oxford

5. The expanding universe6. Nucleosynthesis and baryogenesis7. Dark matter and dark energy components8. Development of structure in early universe

exercises

Slides + book http://w3.iihe.ac.be/~cdeclerc/astroparticles

Dark Matter lect3 3

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– Alternatives to dark matter

• Part 2: Nature of the dark matter :– Baryons and MACHO’s, primordial black holes– Standard neutrinos– Axions

• Part 3: Weakly Interacting Massive Particles (WIMPs)• Part 4: Experimental WIMP searches (partly today)• Part 5: Dark energy (next lecture)2014-15

Dark Matter lect3 4

Previously

• Universe is flat k=0• Dynamics given by Friedman equation

• Cosmological redshift

• Closure parameter

• Energy density evolves with time

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0

01 0R t

z z tR t

c

tt

t

Ωk=0

Dark Matter lect3 5

Dark matter : Why and how much?

2014-15

luminous1%

dark baryonic4%

NeutrinoHDM<1%

cold dark matter~24%

dark energy~70%

• 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

50

0

10

0.30rad

matter

t

t

2 3 420 0 0 01 1m rH t H t z t z t

Planck, 2013

Dark Matter lect3 6

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

2014-15

Dark Matter lect3 7

PART 1GRAVITATIONAL EFFECTS OF DARK MATTER

Velocities of galaxies in clusters and M/L ratioGalaxy rotation curvesGravitational lensingBullet Cluster

2014-15

Dark Matter lect3 8

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, γ-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

2014-15

L is much smaller than expected

from value of M

Dark Matter lect3 9

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 TelescopeNASA

COMA cluster

1000 galaxies 20Mpc diameter

100 Mpc(330 Mly) from Earth

v

Dark Matter lect3 10

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

radiation2014-15

L should be largerMost of the mass M does not emit light


Galaxy rotation curves

• Stars orbiting in spiral galaxies • gravitational force = centrifugal force

• Star inside hub• Star far away from hub

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2

2

Mmmv

r r

r G


NGC 1560 galaxy

2014-15

optical

HI 21cm radio emission from gas


Universal features

• Large number of rotation curves of spiral galaxies measured by Vera Rubin – up to 110kpc from centre

• Show a universal behaviour

2014-15


Dark matter halo • Galaxies are embedded in dark matter halo

• Halo extends to far outside visible region

2014-15

HALO

DISK

15

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 simulations

Dark Matter lect3

Solar system

DM

Den

sity

(GeV

cm

-3)

Distance from centre (kpc)

2014-15

Milky Way halo models

Dark Matter lect3 162014-15


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

2014-15


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

2014-15

Distorted images of remote quasar

Lens = cluster Abell 2218


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

2014-15


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 1E0657-558

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

2014-15


Another example

• Abell 1689 cluster• Blue = reconstructed dark matter map

2014-15


Alternative theories

• MOND theory proposed by Milgrom in 1983• Modification of Newtonian Dynamics over (inter)-galactic

distances• Far away from centre of cluster or galaxy the acceleration

of an object becomes small -> no need for hidden mass• Explains rotation curves• Does not explain Bullet Cluster

2014-15


PART 2THE NATURE OF DARK MATTER

BaryonsMACHOs = Massive Compact Halo Objects

Primordial black holes

Standard neutrinosAxionsWIMPs = Weakly Interacting Massive Particles →Part 3

2014-15


What are we looking for?• Particles with mass – interact gravitationally• Particles which are not observed in radio, visible, X-rays, γ-rays, .. :

neutral and possibly weakly interacting

• Candidates: • Dark baryonic matter: baryons, MACHOs, primordial black holes• 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

2014-15


BARYONIC MATTER

Total baryon contentVisible baryonsNeutral and ionised hydrogen – dark baryonsMini black holesMACHOs

2014-15


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

2014-15

106.047 0.074 10BN

N

2BΩ h =0.02207 0.00027

He mass fraction

D/H abundance

ΩBh2=.022

PDG 2013


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 Lyα 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

2014-15

0.01lum

0.05baryons


Lyα forest and neutral hydrogen gas

2014-15

Hydrogen atomsAbsorb UV light

Emission of UV light by quasarλ= 1216 ÅLyman α transition in H

Measurement of absorption spectra yields amount of neutral H


tiny black holes

• Primordial black holes could make up dark matter if created early enough in history of universe and survive inflation

• PBH of 1011kg could have lifetime = age of universe• Emit Hawking radiation in form of γ–rays -> signal expected• If present in Milky Way halo they would be detected by

gravitational microlensing (see MACHO’s, next part)• no events were observed

• -> contribution to DM negligible

2014-15


MACHOS

Massive Astrophysical Compact Halo ObjectsDark stars in the halo of the Milky WayObserved through microlensing of large number of stars

2014-15


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

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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 2014-15

2 2

1 / 12 4

x xx x

T

At


Optical depth – experimental challenge

• Optical depth τ = probability that one source undergoes gravitational lensing

• For ρ = 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 MACHOs2014-15

2

23

Gc

SD

7per source 10


schema

2014-15


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

2014-15

Blue filter

red filter


STANDARD NEUTRINOS AS DARK MATTER

2014-15


Standard neutrinos

• Standard Model of Particle Physics – measured at LEP

→ 3 types of light neutrinos with Mν<45GeV/c2

• Fit of observed light element abundances to BBN model (lecture 2)

• Neutrinos have only weak andgravitational interactions

2014-15

2.984 0.009fermion familiesN

3.5neutrino speciesN


Relic standard 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

2014-15

sweak interaction , ,i ie e i e

Lecture 2


Cosmic Neutrino Background

• Relic neutrino density and temperature today• for given species (νe, νμ, ντ ) (lecture 2)

• Total density today for all flavours• High density, of order of CMB – but difficult to detect!• At freeze-out : relativistic

2014-15

0T t 1.95K meV

-3113N cmN

3340N cm


Neutrino mass

• If all critical density today is built up of neutrinos

• Direct mass measurement: Measure end of electron energy spectrum in beta decay

2014-15

2

, ,

47e

m c eV

2νm <16eV c1

c

2m eV c

3 31 2 eH He e

Coun

t rat

e

Electron energy (keV)

http://upload.wikimedia.org/wikipedia/commons/6/64/KATRIN_Spectrum.svg


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

2014-15


Simulations and data: majority must be CDMHot dark matter warm dark matter cold dark matter

Observations2dF galaxy survey

See eg work of Carlos Frenkhttp://star-www.dur.ac.uk/~csf/

simulations


AXIONS

Postulated to solve ‘strong CP’ problemCould be cold dark matter particle

2014-15


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

2014-15

experiment 25. . . 10 .e d m e cm

QCD quark gauge standard L L L L

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 very light and weakly interacting• Is a pseudo-scalar with spin 0- ; Behaves like π0

• Decay rate to photons

2014-15

1010~ 0.6A

A

GeVm meV

f

2 3

64A A

A

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 photons in magnetic field

• CAST experiment @ CERN: axions from Sun• If axion density = critical density today then

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production decayA

6 3 210 10Am eV c 1 A

cA

2 3

64A A

A

G m


Axions were not yet observed

2014-15

Axion mass (eV)

Axio

n-γ

coup

ling

(GeV

-1)

Combination of mass and coupling below CAST limit are still allowed by experimentCAST has best sensitivity

Axion model predictionsSome are excluded by CAST limits


PART 3WIMPS AS DARK MATTER

Which candidatesShort recall of SuperSymmetryExpected abundances of neutralinos todayExpected mass range

Weakly Interacting Massive Particles

2014-15


luminous1%

dark baryonic4%

NeutrinoHDM<1%

cold dark matter~24%

dark energy~70%

summary up to now• Standard neutrinos can be Hot

DM• Most of baryonic matter is dark

– MACHO? PBH?

• 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

2014-15

0.05 0.01 00.24 .30CDMmatter Baryons HDM


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 :• Weakly Interacting Massive Particles : WIMPs• 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


Weakly interacting and massive• Massive neutrinos:

– The 3 standard neutrinos have very low masses – contribute to Hot DM

– Massive non-standard neutrinos : 4th generation of leptons 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• New particles from models with extra space dimensions• …….

MSSM


SuperSymmetry in short

• 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 candidate

217

19

1010

10W

PL

M GeV

M GeV

Q fermion boson Q boson fermion


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 • If R-parity is conserved there is a stable Lightest SUSY

Particle: neutralino

• Neutralino could be dark matter particle• Is searched for at LHC


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 σ depends on model parameters : e.g. weak interactions

AnnihilationW T N T χv

Could be neutralino or other weakly interacting

massive particle

WIMP velocity at FO

TFO


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

1

* 221.66

PL

g TH T

M

2

~ 25FO

cP FO

k

M

T

FO FOW T H T

GF = Fermi constant

2

PM

T

c

k

2

~25FO

M ckT


P=M/T (time ->)

Num

ber d

ensi

ty N

(T)

today

Increasing <σAv>

Depends on model

P~25


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

T

0N2FO PLT M

A FOv H T FON T

0 T L

FO

P

P

M

3

30

FOR T

RT

T FON T0N


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 ≈0.3c

35 210X cm O pb 1

25

3 10

10~

FO

t cm sv

2 31

2 2FOkT

M v 1

23~ 0.3v

c FOP

WIMP miracle


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

2014-15

MWIMP (eV)

Ω

HDM neutrinos

CDM WIMPs


PART 4: EXPERIMENTAL WIMP SEARCHES

Direct dark matter detectionIndirect detectionSearches at colliders

The difficult path to discovery

2014-15


Where should we look?

• Search for WIMPs in the Milky Way halo Indirect detection: expect WIMPs from the halo to annihilate with

each other to known particlesDirect detection: expect WIMPs from the halo to interact in a

detector on Earth

2014-15

Dark matter halo

Luminous disk

Solar system

© ESO


three complementary strategies


DIRECT DETECTION EXPERIMENTS

2014-15


Principle of direct detection

• Earth moves in WIMP ‘wind’ from halo• Elastic collision of WIMP with nucleus in

detector

• recoil energy

• Velocity of WIMPs ~ velocity of galactic objects

2014-15

N N

N

N

m m

m m

µ

1 3~ 220 ~ 10km s c χv

Xe


Cross section and event rates

• Event rate depends on density of WIMPs in solar system

• Rate depends on scattering cross section – present upper limit

2014-15

Rm

N χpσ

3~ 0.3GeV cm

DM

Den

sity

(GeV

cm

-3)

Distance from centre (kpc)

Rate depends on number N of nuclei in target

44 2 810 10cm pb σ χp Weak interactions!


• low rate large detector

• very small signal low threshold

• large background : protect against cosmic rays, radioactivity, …

2014-15

Direct detection challenges

pRM

N


Annual modulation• Annual modulations due to movement of solar system in

galactic WIMP halo• Observed by DAMA/LIBRA – not confirmed by other

experiments

2014-15

pRM

N

0 cosmR R R t

Earth against the wind in JuneMaximum rate

In direction of the wind in DecemberMinimum rate


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• If interpreted as SUSY dark matter: M ~ 10-50 GeV/c2

2014-15


From event rate to cross section

2014-15

R NM

χpσ

Other experiments see no signal and put upper limits on the cross section

Some experiments claim to see a signal at this mass and with this cross section

Expected cross sections for models with supersymmetry

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