Dark Matter in Galaxy Clusters
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ESHEP School, Bansko (Bulgaria) - Sept 2015 Cosmology Lecture 2 Andrea De Simone Outline • LECTURE 1: The Universe around us. Dynamics. Energy Budget. The Standard Model of Cosmology: the 3 pillars (Expansion, Nucleosynthesis, CMB). • LECTURE 2: Dark Energy. Dark Matter as a thermal relic. Searches for WIMPs. • LECTURE 3: Shortcomings of Big Bang cosmology. Inflation. Baryogenesis A. De Simone 2 Outline • LECTURE 1: The Universe around us. Dynamics. Energy Budget. The Standard Model of Cosmology: the 3 pillars (Expansion, Nucleosynthesis, CMB) • LECTURE 2: Dark Energy. Dark Matter as a thermal relic. Searches for WIMPs. • LECTURE 3: Shortcomings of Big Bang cosmology. Inflation. Baryogenesis A. De Simone 3 Dark Energy 2 main sets of evidences for Dark Energy: 1. energy budget: fit to CMB anisotropy map provides many cosmological parameters: Ωtot ~ 1.0, Ωmatter ~ 0.3, Ωradiation ~ 0.0 ΩΛ ~ 0.7 2. distant SuperNovae (SN) (1998-Pelmutter, Schmidt, Riess - Nobel prize 2011) A. De Simone 4 20 20 Dark Energy luminosity distance dL =(1+z)r(z) depens on Ωmatter, ΩΛ ,Ωradiation , Ωk absolute (M) and apparent (m) magnitude are d related to distance: m M = 5 log L + K − 10pc ✓ ◆ FigureSN 5. ΛareCDM model: ʻstandard68.3%, 95.4%,and99 .7%candlesconfidence regions ofʼ the(known(Ωm, ΩΛ) plane from absolute SNe Ia combined with themagnitude). constraints from BAO and CMB. The left panel shows the SN Ia confidence region only including statistical errors while the right panel shows the SN Iaconfidenceregionwithboth statistical and systematic errors. Measure m measure dL measure Ωmatter, ΩΛ Figure 5. ΛCDM model: 68.3%, 95.4%,and99.7% confidence regions of the (Ωm, ΩΛ) plane from SNe Ia combined with the constraints from BAO and CMB. The left panel[arXiv:1105.3470] shows the SN Ia confidence region only including statistical errors while the right panel shows the SN Iaconfidenceregionwithboth statistical and systematic errors. new form of energy with negative pressure (w<0) results consistent with cosmological constant (vacuum energy with w=-1) Figure 6. wCDM model: 68.3%, 95.4%,and99.7% confidence regions in the (Ωm,w) plane from SNe Ia BAO and CMB. The left panel shows the SN Ia confidence region for statistical uncertainties only, whiletherightpanelshowstheconfidenceregionincludingbothstatistical and systematic uncertainties. We A.note thatDe CMB and Simone SN Ia constraints are orthogonal, making this combination of cosmological probes very powerful for investigating the nature of dark energy. 5 Figure 6. wCDM model: 68.3%, 95.4%,and99.7% confidence regions in the (Ωm,w) plane from SNe Ia BAO and CMB. The left panel shows the SN Ia confidence region for statistical uncertainties only, whiletherightpanelshowstheconfidenceregionincludingbothstatistical and systematic uncertainties. We note that CMB and SN Ia constraints are orthogonal, making this combination of cosmological probes very powerful for investigating the nature of dark energy. Dark Energy so WHAT IS DARK ENERGY? 4 ⌦⇤ 0.7= ⇢⇤ (meV) New physics at the meV scale? ' ) ' Some form of energy density which stays 3(1+w) ⇢ a− const. constant as the Universe expands: ⇤ / ⇠ at what scales do we expect new physics? Mweak~TeV, MPlanck~1022 GeV 123 4 60 4 ⇢ 10− M ⇢ 10− M ⇤ ⇠ Planck ⇤ ⇠ weak the “WRONGEST” estimate of particle physics (and biggest hierarchy problem...) SO WHAT? - maybe anthropic principle (we could only live in universes with small Λ) - maybe quantum gravity... A. De Simone 6 Evidences for Dark Matter Dark Matter Energy budget of the Universe Ordinary Matter Dark Energy 2 ⇢DM 3H 5 2 3 ⌦DM ⇢c 1.05 10− h GeV cm− ⌘ ⇢c ⌘ 8⇡GN ' ⇥ H0 2 ⇢DM h 1 1 0.67 ⌦DMh = =0.1196 0.0031 ⌘ 100 km s− Mpc− ' 2 ⇢c/h ±(Planck Coll.) Observational Evidences for Dark Matter: • Galaxy clusters • Galaxies • Cosmology (CMB and Large Scale Structure formation) Firmly established, but only gravitational interactions are probed A. De Simone 7 Dark Matter in Galaxy Clusters F. Zwicky (1933) measured proper motion of galaxies in Coma cluster (~1000 galaxies within radius ~ 1 Mpc) Virial Theorem: V +2 K =0 h i h i N 2 m2 average potential en. due to N2/2 V = G h i h i − 2 N R pairs of galaxies mv2 K = N h i average kinetic en. due to N galaxies h i 2 2R v2 M M 1933AcHPh...6..110Z Total mass M = N m h i = 300h h i⇠ GN ) L ⇠ L “should this be true, this surprising result 1933AcHPh...6..110Z would show that dark matter is of much greater density than luminous matter” Most of the matter is NOT LUMINOUS A. De Simone 8 Dark Matter in Galaxy Clusters - X-ray observations most ordinary mass in clusters is hot gas, emitting X-rays Pressure is due to electrons: P (r)=ne(r)Te(r) Law of hydrostatic equilibrium: accel dV G M(R) G M(R) dP = dm = ⇢ (R) N = ⇢ (R) N dR − Area − b Area R2 − b R2 R where M(R)=4⇡ ⇢(r)r2dr ⇢b(r)=µne(r)mb Z0 dP G M(R) = µn (R)m N dR − e b R2 EXTRACT THE MASS from X-ray luminosity from temperature maps and spatial distributions More matter than just baryons! A. De Simone 9 Dark Matter in Galaxy Clusters - Gravitational Lensing General Relativity at work! Abell NGC 2218 - “Bullet” Cluster Two colliding clusters of galaxies A. De Simone 10 1991MNRAS.249..523B Dark Matter in Galaxies Rotation curves G M(R) R v(R)= N ,M(R)=4⇡ ⇢(r)r2dr R r Z0 1/2 Expectation: v(r) R− at large R / Observations: v(r) const. at large R ' More matter than visible! and distributed differently (in the halo) halo disk 2 MDM R requires ⇢DM 1/r / / gas A. De Simone 11 Dark Matter in Cosmology CMB Recall that CMB temperature maps give accurate information about cosmological parameters (H0, Ωtot, ΩB etc...) (see 1st lecture) Formation of Large-Scale Structures different DM types give different scenarios: Hot DM ``top-down'': large structures fragment into smaller pieces. Cold DM ``bottom-up'': smaller objects merge into bigger structures hierarchically. cosmological observations (CMB and galaxy observations) + numerical simulations exclude HDM. A. De Simone 12 Problems of Cold DM (?) “cusp-core problem” 1 1.5 Numerical simulations predict “cuspy” density profiles ⇢ r − ÷ − (small r) ⇠ Observations favor more constant densities “missing satellite problem” Numerical simulations predict large number (100-1000) of sub-haloes Only ~ 10 observed NOT CLEAR SITUATION Some propose Wark Dark Matter It may simply be that Numerical Simulations are not accurate enough (baryons not included) and small sub-haloes are invisible. A. De Simone 13 Alternatives to Dark Matter (?) explanation of flat rotation curves with modification of gravity (rather than DM)? MOND (MOdified Newtonian Dynamics) GN M(R)m ma (a>a ) 11 2 = 2 ⇤ (critical acceleration a 10 − m/s ) R2 ma /a (a<a ) ⇤ ⇠ ⇢ ⇤ ⇤ 1/2 [GN M(R)/R] (Newton) v(R)= 1/4 [GN M(R)a ] (MOND) ⇢ ⇤ (flat) MOND IS FALSE! 1. evidence for DM is much more than rotation curves 2. bullet cluster contradicts MOND 3. some galaxies do not have a flat rotation curve A. De Simone 14 Key Properties of Particle DM • stable (or with lifetime at least longer than the age of the Universe) • no electric charge, no color charge • non-collisional • not hot • DM is in a fluid limit (not a collection of discrete compact objects) MAssive Compact Halo Objects (MACHOs) are astrophysical objects with macroscopic mass (large planets or small dead stars). MACHOs searches exclude 7 10− M . M . 10M (using gravitational lensing) A small window for primordial black holes still open 13 7 10− M . M . 10− M A. De Simone 15 Key Properties of Particle DM • DM is classical (non-relativistic) today confined on galactic scales ~ 1 kpc, with densities ~ 1 GeV cm-3 and velocities ~ 100 km/s. For bosons: De Broglie wavelength λ = h/p must be less than 1 kpc h 2⇡ 1 14 22 m (2 10− cm GeV) 10− eV & 1 3 21 1kpc v ' 10− c 3 10 cm · · ' · 3 · (v=100 km/s) For fermions: DM quantum occupation number must be <1 (Pauli) 3 1/4 ⇢(r ) 3 m h ⇢(r ) λ . 1= ⇢(r ) . = m & 1keV m ) λ3 ) v3 ' (Gunn-Tremaine bound) 3 4 ( ⇢ ( r )=0 . 4 GeV cm − (0 . 04 eV) ) ' A. De Simone 16 Candidates for Dark Matter (an incomplete list) WIMP non-WIMP neutralino axion minimal DM gravitino heavy neutrino sterile neutrino inert Higgs doublet techni-baryon, LKP topological defects LTP primordial black holes ... ... WIMP = Weakly Interacting Massive Particle (or... the “Holy Grail” of DM physics) A. De Simone 17 Candidates for Dark Matter (an incomplete list) WIMP non-WIMP neutralino axion minimal DM gravitino heavy neutrino sterile neutrino inert Higgs doublet techni-baryon, LKP topological defects LTP primordial black holes ... ... WIMP = Weakly Interacting Massive Particle (or... the “Holy Grail” of DM physics) A. De Simone 18 Thermal Production28 Chapter 4. What is Dark Matter? Assume: 102 • X is stable 108 • X is in thermal eq. at T >> mX 104 eq QUALITATIVE ANALYSIS Y Y 6 Y - initially, in thermal equilibrium 10 109 χχ SM SM abundance 8 $ 10 equilibrium DM - Universe cools, less and less X Y smaller ⇤ of Out / 10 10 ⇥ χχ SM SM Y bigger ⇤ ! Yeq - Universe expands, reaction slows down 1012 1010 1 2 ⇥ 3 2 3 and X abundance “freezes out” of the 10 1 10 10 10 1 10 10 10 expansion z ⇥ M T z ⇥ M T / χχ / SM SM ⇤ ! Figure 4.4: Sample of DM freeze-out. Left:sampleoftheevolutionoftheDMabundanceY = n/s as function of z = T/M. Right:sampleoftheevolutionofthenon-equilibriumabundance Y Yeq,comparedtotheanalyticapproximationofeq.(4.48)(dashed,validforz zf )andof − ⇧ A.