Dark Matter and Dark Energy components chapter 7 · chapter 7 Lecture 3 See also Dark Matter awareness week December 2010 ... –Rotation curves galaxies, mass/light ratios in galaxies

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)

2012-13 Dark Matter 3

Previously

• Universe is flat k=0

• Dynamics given by Friedman equation

• Cosmological redshift

• Closure parameter

• Energy density evolves with time


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?


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


PART 1 GRAVITATIONAL EFFECTS OF DARK MATTER

Velocities of galaxies in clusters and M/L ratio

Galaxy rotation curves

Gravitational lensing

Bullet Cluster


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


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


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


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


2

2

Mmmv

r r

r G

v r

1v

r

NGC 1560 galaxy


Universal features

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

• Show a universal behaviour


Dark matter halo • Galaxies are embedded in dark matter halo

• Halo extends to far outside visible region


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


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


Lens geometries and images


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


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


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


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


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


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


PART 2 THE NATURE OF DARK MATTER

Baryons

MACHOs = Massive Compact Halo Objects

Standard neutrinos

Axions

WIMPs = Weakly Interacting Massive Particles →Part 3


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


BARYONIC MATTER

Total baryon content

Visible baryons

Neutral and ionised hydrogen – dark baryons

Mini black holes

MACHOs


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


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


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


710BH

MACHOS

Massive Astrophysical Compact Halo Objects

Dark stars in the halo of the Milky Way

Observed through microlensing of large number of stars


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


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


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


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


Blue filter

red filter

To do

• Meebrengen naar examen


STANDARD NEUTRINOS AS DARK MATTER


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


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


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


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


2

, ,

47e

m c eV 2

νm <16eV c1c

2m eV c

3 3

1 2 eH He e

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

Neutrino mass


3 3

1 2 eH He e

1.0m eV

0.0m eV

Electron energy (keV)

Co

un

t ra

te

2m eV c

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



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


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


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


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


production decayA

6 3 210 10Am eV c1 A

cA

2 3

64

A AA

G m

Axions were not yet observed


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


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


0.05 0.01 00.18 .24CDMmatter 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 : 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


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


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


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


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


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


P=M/T (time ->)

Nu

mb

er 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

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


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


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



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


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


The new particle table

Particle table (arXiv:hep-ph/0404175v2)


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


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



three complementary strategies

production at accelerators

• Controlled production in laboratory: particle accelerators

• LHC @ CERN


Example from LHC


H. Bachacou EPS2011

0 01 1p p q g jets

Probed masses up to ~ TeV So signal was observed


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


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)


Documents

Dark Matter and Dark Energy components chapter 7 · chapter 7 Lecture 3 See also Dark Matter awareness week December 2010 ... –Rotation curves galaxies, mass/light ratios in galaxies