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, 2 nd 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 H t 2 2 8 R t G N R t 3 ρtot t Cosmological redshift Rt 0 1 z z t0 0 Rt Closure parameter Energy density evolves with time t c t t Ω k =0 2 2 3 4 2 0 Ω t0 1 0 1 Ω t0 1 H t H z t z z m r Λ k 2012-13 Dark Matter 4

Dark matter : Why and how much? 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 luminous 1% dark energy 76% dark baryonic 4% rad t matter Neutrino HDM <1% cold dark matter 18% 0 t 0 10 5 0.24 2 2 3 4 0 0 1 0 1 0 H t H t z t z t m r 2012-13 Dark Matter 5

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 2012-13 Dark Matter 6

Velocities of galaxies in clusters and M/L ratio Galaxy rotation curves Gravitational lensing Bullet Cluster PART 1 GRAVITATIONAL EFFECTS OF DARK MATTER 2012-13 Dark Matter 7

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 M MMW Mcluster 1 10 500 L L L MW cluster Rotation curves of stars in galaxies large missing mass up to large distance from centre 2012-13 Dark Matter 8

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 COMA cluster v 1000 galaxies 20Mpc diameter 100 Mpc(330 Mly) from Earth Optical (Sloan Digital Sky Survey) + IR(Spitzer Space Telescope NASA 2012-13 Dark Matter 9

Dark matter in galaxy clusters 2 Mass from velocity of galaxies around centre of mass of cluster using virial theorem 10 M ( velocities) 10 M M M L KE v 1 2 GPE M 500 7 10 L cluster sun L L M L COMA M L SUN Proposed explanation: missing dark = invisible mass Missing mass has no interaction with electromagnetic radiation 2012-13 Dark Matter 10

Galaxy rotation curves Stars orbiting in spiral galaxies gravitational force = centrifugal force mv r 2 mm r 2 r G Star inside hub v r Star far away from hub v 1 r 2012-13 Dark Matter 11

NGC 1560 galaxy 2012-13 Dark Matter 12

Universal features Large number of rotation curves of spiral galaxies measured by Vera Rubin up to 110kpc from centre Show a universal behaviour 2012-13 Dark Matter 13

Dark matter halo Galaxies are embedded in dark matter halo Halo extends to far outside visible region HALO DISK 2012-13 Dark Matter 14

DM Density (GeV cm -3 ) 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 Milky Way halo m od els Solar system Dark Matter Distance from centre (kpc) 2012-13 15

Gravitational lensing Gavitational lensing by galaxy clusters effect larger than expected from visible matter only 2012-13 Dark Matter 16

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 2012-13 Dark Matter 17

Lens geometries and images 2012-13 Dark Matter 18

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 2012-13 Dark Matter 19

Strong lensing: Different lensing effects 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 2012-13 Dark Matter 20

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 2012-13 Dark Matter 21

Bullet cluster in X-rays X rays from hot gas and dust - Chandra observatory mass map contours from weak lensing of many galaxies 2012-13 Dark Matter 22

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 2012-13 Dark Matter 23

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 2012-13 Dark Matter 24

Baryons MACHOs = Massive Compact Halo Objects Standard neutrinos Axions WIMPs = Weakly Interacting Massive Particles Part 3 PART 2 THE NATURE OF DARK MATTER 2012-13 Dark Matter 25

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 2012-13 Dark Matter 26

Total baryon content Visible baryons Neutral and ionised hydrogen dark baryons Mini black holes MACHOs BARYONIC MATTER 2012-13 Dark Matter 27

Baryon content of universe Ω B =.044 measurement of light element abundances and of He mass fraction Y And of CMB anisotropies Interpreted in Big Bang Nucleosynthesis model He mass fraction D/H abundance N B N 6.1 0.6 10 10 Ω B = 0.044 ± 0.005 2012-13 Dark Matter 28

Baryon budget of universe From BB nucleosynthesis and CMB fluctuations: Related to history of universe at z=10 9 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 baryons lum 0.05 0.01 Inter Gallactic Matter = gas of hydrogen in clusters of galaxies Absorption of Ly emission from distant quasars yields neutral hydrogen fraction in inter gallactic regions Most hydrogen is ionised and invisible in absorption spectra form dark baryonic matter 2012-13 Dark Matter 29

Mini black holes Negligible contribution from mini black holes BHs must have M BH < 10 5 M Heavier BH would yield lensing effects which are not observed BH 10 7 2012-13 Dark Matter 30

Massive Astrophysical Compact Halo Objects Dark stars in the halo of the Milky Way Observed through microlensing of large number of stars MACHOS 2012-13 Dark Matter 31

Microlensing Light of source is amplified by gravitational lens When lens is small (star, planet) multiple images of source cannot be distinguished : addition of images = amplification But : amplification effect varies with time as lens passes in front of source - period T Efficient for observation of e.g. faint stars Period T 2012-13 Dark Matter 32

Microlensing - MACHOs Amplification of signal by addition of multiple images of source Amplification varies with time of passage of lens in front of source 2 2 x x t A 1 / x 1 2 4 Typical time T : days to months depends on distance & velocity MACHO = dark astronomical object seen in microlensing M 0.001-0.1M x T 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 2012-13 Dark Matter 33

Optical depth experimental challenge Optical depth = probability that one source undergoes gravitational lensing For = N L M = Mass density of lenses along line of sight Optical depth depends on distance to source D S 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: 7x10 6 bright stars monitored in ~7 years one candidate MACHO found less than 8% of halo mass are MACHOs 2012-13 Dark Matter 34 2 G DS c per source 10 2 3 7

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 2012-13 Dark Matter 35

Meebrengen naar examen To do 2012-13 Dark Matter 36

STANDARD NEUTRINOS AS DARK MATTER 2012-13 Dark Matter 37

Standard neutrinos Standard Model of Particle Physics measured at LEP N fermion families 3 types of light left-handed neutrinos with M ν <45GeV/c2 Fit of observed light element abundances to BBN model (lecture 2) N neutrino species 2.984 0.009 3.5 Neutrinos have only weak and gravitational interactions 2012-13 Dark Matter 38

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 weak interactions e e i e,, Neutrinos freeze-out at kt ~ 3MeV and t ~ 1s When interaction rate W << H expansion rate i i Lecture 2 2012-13 Dark Matter 39

Cosmic Neutrino Background Relic neutrino density and temperature today for given species ( e,, ) (lecture 2) 3 N N N 113 cm 11 1 3 4 T t0 T t0 1.95K mev 11-3 Total density today for all flavours N 340 cm High density, of order of CMB but difficult to detect! At freeze-out : relativistic p FO m 3 2012-13 Dark Matter 40

Neutrino mass If all critical density today is built up of neutrinos 1 c e,, m c 2 47 ev m ν < 16 ev c 2 Measure end of electron energy spectrum in tritium beta decay 3 3 1H 2He e e m ev c 2 2012-13 Dark Matter 41

Count rate Neutrino mass 3 3 1H 2He e e m 0.0eV m 1.0eV m ev c 2 Electron energy (kev) 2012-13 Dark Matter 42

Neutrinos as hot dark matter Relic neutrinos are numerous have very small mass < ev Were relativistic when decoupling from other matter at kt~3mev can only be Hot Dark Matter HDM Relativistic particles prevent formation of large-scale structures through free streaming they iron away the structures HDM should be limited From simulations of structures: maximum 30% of DM is hot 2012-13 Dark Matter 43

simulations Hot dark matter warm dark matter cold dark matter See eg work of Carlos Frenk http://star-www.dur.ac.uk/~csf/ Observations 2dF galaxy survey 2012-13 Dark Matter 44

Postulated to solve strong CP problem Could be cold dark matter particle AXIONS 2012-13 Dark Matter 45

Strong CP problem QCD lagrangian for strong interactions L L L L 2 QCD quark gauge standard Term L θ is generally neglected gt S F a 2 F F 16 violates P and T symmetry violates CP symmetry Violation of T symmetry would yield a non-zero neutron electric dipole moment predicted 15 16 e. d. m. 10 e. cm L a Experimental upper limits experiment 25 e. d. m. 10 e. cm 10 10 2012-13 Dark Matter 46

Strong CP problem Solution by Peccei-Quinn : introduce higher global U(1) symmetry, which is broken at an energy scale f a This extra term cancels the L θ term L With broken symmetry comes a boson field φ a = axion with mass Axion is light and weakly interacting m Is a pseudo-scalar with spin 0- ; Behaves like π 0 Decay rate to photons A f A A ~ 0.6meV A 2 gt S 16 10 10 GeV f 2012-13 Dark Matter 47 F 2 A G F a F 2 3 A 64 m a A

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 production A decay CAST experiment @ CERN: axions from Sun If axion density = critical density today then A G 2 3 A 64 m A 1 A A c ma 10 10 ev c 6 3 2 2012-13 Dark Matter 48

Axion-γ coupling (GeV -1 ) Axions were not yet observed Axion model predictions Some are excluded by CAST limits Combination of mass and coupling below CAST limit are still allowed by experiment CAST has best sensitivity Axion mass (ev) 2012-13 Dark Matter 49

Weakly Interacting Massive Particles PART 3 WIMPS AS DARK MATTER 2012-13 Dark Matter 50

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 luminous 1% dark baryonic 4% Neutrino HDM <1% cold dark matter 18% Need to search for candidates for non-baryonic cold dark matter in particle physics beyond the SM dark energy 76% matter Baryons HDM CDM 0.05 0.01 0.18 0.24 2012-13 Dark Matter 51

Non-baryonic CDM candidates Axions To reach density of order ρ c their mass must be very small m c No experimental evidence yet Most popular candidate for CDM : WIMPs A 2 6 3 10 10 ev 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 ) 2012-13 Dark Matter 52

Weakly interacting and massive Massive neutrinos: The 3 standard neutrinos have very low masses contribute to Hot DM Massive standard neutrinos up to M Z /2 = 45GeV/c 2 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/c 2 Stable particle survived from primordial era of universe Other SUSY candidates: sneutrinos, gravitinos, axinos New particles from models with extra space dimensions. MSSM 2012-13 Dark Matter 53

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 Expected mass range 1) 4 M s < M ~ s ~ M 2 2 2 W 2 2 2) 4 M s > MW ~ ~ t 0 1 ~ v 1 1 s M 2 2012-13 Dark Matter 54

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 HDM neutrinos CDM WIMPs 1) 4 M s < M ~ s ~ M 2 2 2 W 2 2 2) 4 M s > MW ~ ~ t 0 1 ~ v 1 1 s M 2 M WIMP (ev) 2012-13 Dark Matter 55

WIMP annihilation rate at freeze-out WIMP with mass M must be non-relativistic at freeze-out gas in thermal equilibrium kt N T Mc 2 MT 2 Boltzman gas 3 Mc2 2 e f kt f,... number density Could be neutralino or other weakly interacting massive particle T FO Annihilation rate W T N T Annihilationv χ WIMP velocity at FO Cross section depends on model parameters : weak interactions 2012-13 Dark Matter 56

Freeze-out temperature assume that couplings are of order of weak interactions G F = Fermi constant v G M F 2 Rewrite expansion rate H T 1.66 g M 1 * 2 2 PL T Freeze-out condition W T FO H T FO Mc2 2 3 kt 2 2 2 T MT e GF M ~ f M PL f = constants 100 Set P M c kt 2 solve for P P FO M kt c FO 2 ~ 25 kt FO M c ~ 25 2 2012-13 Dark Matter 57

Number density N(T) Depends on model Increasing <σ A v> P~25 today P=M/T (time ->) 2012-13 Dark Matter 58

Relic abundance today Ω(T 0 ) - 1 At freeze-out annihilation rate expansion rate N T FO WIMP number density today for T 0 = 2.73K A v H T FO N T 0 N T FO 3 R T FO R 3 T 0 N T 0 T T 0 FO 3 A v T 2 FO M PL Energy density today T 0 M N T 0 M P F O PL T 3 0 A v P M FO PL T 0 T 0 6 10 v A 31 GeV s 1 t 0 c 10 v 25 FO c 3 ms 1 2012-13 Dark Matter 59

Relic abundance today Ω(t 0 ) - 2 Relic abundance of WIMPs today For 1 WIMP miracle t 0 ~ 10 v 25 FO cm s 3 1 35 2 X 10 cm O pb 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 1 M v 2 2 2 3 kt FO v c 1 2 ~ 3 0.3 P FO v FO 0.3 c 2012-13 Dark Matter 60

Neutralino is good candidate for cold dark matter SUSY = extension of standard model at high energy SUPERSYMMETRY : POPULAR CANDIDATES 2012-13 Dark Matter 61

What are we looking for? Particle with charge = 0 With mass in [GeV-TeV] domain Only interacting through gravitational and weak interactions Stable Decoupled from radiation before BBN era Has not yet been observed in laboratory = accelerators 2012-13 Dark Matter 62

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 Planck scale M M W PL 10 10 2 19 GeV GeV 10 17 Solves problems of Standard Model, like the hierarchy problem: = divergence of radiative corrections to Higgs mass Provides a dark matter canndidate 2012-13 Dark Matter 63

SuperSymmetric particles Need to introduce new particles: supersymmetric particles Associate to all SM particles a superpartner with spin 1/2 (fermion boson) sparticles minimal SUSY: minimal supersymmetric extension of the SM reasonable assumptions to reduce nb of parameters Parameters = masses, couplings - must be determined from experiment Searches at colliders: so particles seen yet M accessible range production sensitivity 2012-13 Dark Matter 64

The new particle table Particle table (arxiv:hep-ph/0404175v2) 2012-13 Dark Matter 65

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 N B N W N H N H 1 0 0 0 11 12 3 13 1 14 2 R 3 2 1 B L s In R-parity conserving models Lightest Supersymmetric Particle (LSP) is stable LSP = lightest neutralino dark matter candidate 2012-13 Dark Matter 66

Expected abundance vs mass variation of neutralino density as function of mass Allowed by collider and direct search upper limits on cross sections h 2 2 h =[.05-0.5] Ω= [0.04 1.0] Expected mass range 50GeV few TeV Neutralino mass (GeV) 2012-13 Dark Matter 67 M GeV

The difficult path to discovery PART 5: WIMP DETECTION 2012-13 Dark Matter 68

three complementary strategies 2012-13 Dark Matter 69

production at accelerators Controlled production in laboratory: particle accelerators LHC @ CERN 2012-13 Dark Matter 70

Example from LHC Probed masses up to ~ TeV So signal was observed H. Bachacou EPS2011 p p q g jets 0 0 1 1 2012-13 Dark Matter 71

N N Very small effects experiment 44 2 8 p 10 cm 10 pb 2012-13 Dark Matter 72

Indirect detection of WIMPs Search for signals of annihilation of WIMPs in the Milky Way halo Detect the produced antiparticles, gamma rays, neutrinos accumulation near galactic centre or in heavy objects like the Sun due to gravitational attraction 2012-13 Dark Matter 73

Overview Part 1: Observation of dark matter as gravitational effects Rotation curves galaxies, mass/light ratios in galaxies Velocities of galaxies in clusters Gravitational lensing Bullet cluster Part 2: Nature of the dark matter : Baryons and MACHO s Standard neutrinos Axions Part 3: Weakly Interacting Massive Particles (WIMPs) Part 4: Experimental WIMP searches (lecture 4) Part 5: Dark energy (lecture 4) 2012-13 Dark Matter 74