Dark Matter and Dark Energy components chapter 7

Name: Dark Matter and Dark Energy components chapter 7
Uploaded: 2017-07-16T10:14:58+00:00
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Description: Dark Matter and Dark Energy components chapter 7

Dark Matter and Dark Energy components chapter 7
Lecture 3

The early universe chapters 5 to 8 Particle Astrophysics , D
The early universe chapters 5 to 8 Particle Astrophysics , D. Perkins, 2nd edition, Oxford The expanding universe Nucleosynthesis and baryogenesis Dark matter and dark energy components Development of structure in early universe exercises Slides + book

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) Dark Matter lect3

Previously Universe is flat k=0 Dynamics given by Friedman equation
Cosmological redshift Closure parameter Energy density evolves with time Ωk=0 Dark Matter lect3

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 Planck, 2013 Dark Matter lect3

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 Dark Matter lect3

Part 1 Gravitational effects of dark matter
Velocities of galaxies in clusters and M/L ratio Galaxy rotation curves Gravitational lensing Bullet Cluster Part 1 Gravitational effects of dark matter Dark Matter lect3

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 L is much smaller than expected from value of M Dark Matter lect3

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 v COMA cluster 1000 galaxies 20Mpc diameter 100 Mpc(330 Mly) from Earth Optical (Sloan Digital Sky Survey) + IR(Spitzer Space Telescope NASA Dark Matter lect3

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 L should be larger Most of the mass M does not emit light Dark Matter lect3

Galaxy rotation curves
Stars orbiting in spiral galaxies gravitational force = centrifugal force Star inside hub Star far away from hub Dark Matter lect3

HI 21cm radio emission from gas
NGC 1560 galaxy optical HI 21cm radio emission from gas Dark Matter lect3

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 lect3

Dark matter halo Galaxies are embedded in dark matter halo
Halo extends to far outside visible region HALO DISK Dark Matter lect3

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 Milky Way halo models DM Density (GeV cm-3) Solar system Dark Matter lect3 Distance from centre (kpc)

Dark Matter lect3

Gravitational lensing
Gavitational lensing by galaxy clusters -> effect larger than expected from visible matter only Dark Matter lect3

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 Dark Matter lect3

Lens geometries and images
Dark Matter lect3

Observation of gravitational lenses
First observation in 1979: effect on twin quasars Q Mass of ‘lens’ can be deduced from distortion of image only possible for massive lenses : galaxy clusters Distorted images of remote quasar Lens = cluster Abell 2218 Dark Matter lect3

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 Dark Matter lect3

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 1E Dark Matter lect3

Bullet cluster in X-rays
X rays from hot gas and dust - Chandra observatory mass map contours from weak lensing of many galaxies Dark Matter lect3

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 Dark Matter lect3

Another example Abell 1689 cluster Blue = reconstructed
dark matter map Dark Matter lect3

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 Dark Matter lect3

Dark Matter lect3

Part 2 The nature of dark matter
Baryons MACHOs = Massive Compact Halo Objects Primordial black holes Standard neutrinos Axions WIMPs = Weakly Interacting Massive Particles →Part 3 Part 2 The nature of dark matter Dark Matter lect3

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 Dark Matter lect3

Baryonic matter Total baryon content Visible baryons
Neutral and ionised hydrogen – dark baryons Mini black holes MACHOs Baryonic matter Dark Matter lect3

Baryon content of universe
ΩBh2=.022 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 PDG 2013 Dark Matter lect3

Baryon budget of universe
From BB nucleosynthesis and CMB fluctuations: Related to history of universe at z= 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 Dark Matter lect3

Lyα forest and neutral hydrogen gas
Hydrogen atoms Absorb UV light Emission of UV light by quasar λ= 1216 Å Lyman α transition in H Measurement of absorption spectra yields amount of neutral H Dark Matter lect3

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 Dark Matter lect3

MACHOs Massive Astrophysical Compact Halo Objects
Dark stars in the halo of the Milky Way Observed through microlensing of large number of stars MACHOs Dark Matter lect3

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 Dark Matter lect3

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 ≈ M 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 Dark Matter lect3

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 MACHOs Dark Matter lect3

schema Dark Matter lect3

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 Dark Matter lect3

Dark Matter lect3

Standard Neutrinos as dark matter
Dark Matter lect3

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 and gravitational interactions Dark Matter lect3

Relic standard neutrinos
Lecture 2 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 Dark Matter lect3

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 Dark Matter lect3

Neutrino mass If all critical density today is built up of neutrinos
Direct mass measurement: Measure end of electron energy spectrum in beta decay Count rate Electron energy (keV) Dark Matter lect3

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 Dark Matter lect3

Simulations and data: majority must be CDM
Hot dark matter warm dark matter cold dark matter See eg work of Carlos Frenk simulations Observations 2dF galaxy survey Dark Matter lect3

Dark Matter lect3

Axions Postulated to solve ‘strong CP’ problem
Could be cold dark matter particle Axions Dark Matter lect3

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 Dark Matter lect3

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 Dark Matter lect3

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 CERN: axions from Sun If axion density = critical density today then Dark Matter lect3

Axions were not yet observed
Axion model predictions Some are excluded by CAST limits Axion-γ coupling (GeV-1) Axion mass (eV) Combination of mass and coupling below CAST limit are still allowed by experiment CAST has best sensitivity Dark Matter lect3

Part 3 WIMPs as dark matter
Which candidates Short recall of SuperSymmetry Expected abundances of neutralinos today Expected mass range Weakly Interacting Massive Particles Part 3 WIMPs as dark matter Dark Matter lect3

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 Dark Matter lect3

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 …) Dark Matter lect3

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 Dark Matter lect3

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 Dark Matter lect3

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 Dark Matter lect3

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 Could be neutralino or other weakly interacting massive particle TFO WIMP velocity at FO Dark Matter lect3

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 GF = Fermi constant Dark Matter lect3

Increasing <σAv>
Depends on model Increasing <σAv> today Number density N(T) P~25 P=M/T (time ->) Dark Matter lect3

Relic abundance today Ω(T0) - 1
At freeze-out annihilation rate ~ expansion rate WIMP number density today for T0 = 2.73K Energy density today Dark Matter lect3

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 WIMP miracle Dark Matter lect3

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 Ω MWIMP (eV) Dark Matter lect3

Dark Matter lect3

Part 4: experimental WIMP searches
Direct dark matter detection Indirect detection Searches at colliders The difficult path to discovery Part 4: experimental WIMP searches Dark Matter lect3

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 particles Direct detection: expect WIMPs from the halo to interact in a detector on Earth Dark matter halo Luminous disk Solar system © ESO Dark Matter lect3

three complementary strategies
Dark Matter lect3

Direct detection experiments
Dark Matter lect3

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 Xe Dark Matter lect3

Cross section and event rates
Event rate depends on density of WIMPs in solar system Rate depends on scattering cross section – present upper limit Rate depends on number N of nuclei in target DM Density (GeV cm-3) Distance from centre (kpc) Weak interactions! Dark Matter lect3

Direct detection challenges
low rate  large detector very small signal  low threshold large background : protect against cosmic rays, radioactivity, … Dark Matter lect3

Annual modulation Annual modulations due to movement of solar system in galactic WIMP halo Observed by DAMA/LIBRA – not confirmed by other experiments Earth against the wind in June Maximum rate In direction of the wind in December Minimum rate Dark Matter lect3

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 days If interpreted as SUSY dark matter: M ~ GeV/c2 Dark Matter lect3

From event rate to cross section
Some experiments claim to see a signal at this mass and with this cross section Other experiments see no signal and put upper limits on the cross section Expected cross sections for models with supersymmetry Dark Matter lect3

Dark Matter lect3

Dark Matter and Dark Energy components chapter 7

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