Lecture 16 Relic Neutrinos

Lecture 16 Relic Neutrinos AS 4022 Cosmology

Below Threshold: k T m c2 k T m c 2 Photons in the tail of the blackbody photon spectrum have enough energy to create pairs. dnγ dE 2 3 / 2 n g mc m c 2 /k T e nγ 2 k T n /nγ 3k T AS 4022 Cosmology 2mc2 E mc2 /k T

Below Threshold: k T m c2 2 4 1/ 2 E (p c m c 2 2 ) k T m c 2 E mc 2 p2 mc 2 y2 kT kT 2mkT kT Particle density: g n 3 / (2π h) 2 4 π p dp 4π g 3 (2 m k T ) exp( E /k T ) (2π h/ ) Energy density: ε mc2 n Pressure : P n k T ε mc2 s ε P : Entropy 1 n k kT kT AS 4022 Cosmology m c 2 3/2 kT e 2 y 2 ye 0 π 1/ 2 4 dy

Freeze-Out ( Decoupling ) Particle-antiparticle pairs stay in equilibrium with photons by Pair creations: γ γ A A and Annihilations: A A γ γ Creation rate dies below threshold, when kT mc2. Annihilation rate dies during freeze-out, when collision time expansion time. 1 n σv σ v dt Relic number density: AS 4022 Cosmology n H σv 1 H 2 2 1 T mc2 H 10 2 t 10 K MeV

Freeze-Out ( Decoupling ) Particle density evolution : ( 2 n 3H n σ v n 2 n LTE Neutrino mass and cross section are small. Neutrinos decouple while relativistic. Relic neutrinos are Hot Dark Matter. n /nγ Relic density: n ) νe νe 47 3H σv 2 σ Weak 10 m ( k T /1MeV) n LTE Particles with larger cross section stay in LTE longer before freezing out. e e σ e 6 10 29 m2 2 m c /k T AS 4022 Cosmology “Survival of the weakest” 2

WIMPS as Cold Dark Matter WIMP Weakly Interacting Massive Particle: σ Weak 10 43 cm2 ( k T /1MeV) σ Thompson 6 10 25 cm2 2 Freeze-out when kT mc2: 2 2 H 1s k T mc 1 s t MeV MeV 2 Number density at freeze-out : n H 1 σv σv t 2 kT m n0 mc Ω ρc ρ c c 2 σ v 1s MeV Number density today : AS 4022 T0 3 n n0 n 3 T (1 z) Cosmology (2 10 4 eV) 2 k T0 3 k T 3 (5200eV cm 3 ) σ v/c (3 1010 cm) (106 eV) 5 10 38 cm2 σ v/c 2

Neutrino Decoupling Annihilation of pairs releases energy. Interactions share this out among remaining (lighter) particles. Neutrino interactions are weak (no EM charge). Decouple from LTE just above the corresponding lepton threshold: Tτ 1013.3 K Tµ 1012.1 K Te 10 9.7 K Neutrinos take no share of the e e- annihilation energy. Entropy conserved: s geff T 3 1/ 3 Tγ (before) 4 1/ 3 g(after) 11 Tγ (after) g(before) g(γ ) 2 4 g(γ e e ) 2 7 (2 2) 11 8 Relic neutrino temp lower than photon temp: AS 4022 Cosmology 1/ 3 Tν 4 1.945 K Tγ 11 2.725 K

Relic Neutrinos Today: Neutrino temp lower than photon temp: 4 1/ 3 Tν Tγ 1.95 K 11 3 neutrino types ( e µ τ ) and anti-neutrinos. Neutrinos are left-handed fermions: g(ν) 1 x (7/8) . Neutrino contribution to radiation energy density today: 4 4 /3 g(ν ) T (ν ) ε( 3(ν ν )) 1 7 4 6 6 0.68 ε(γ ) g(γ ) T (γ ) 2 8 11 Although not detected, the 1.95K neutrino background makes a significant contribution to the radiation energy density today. Ωγ 5 10 5 zM γ ΩM Ωγ 6000 Ων 3 10 5 ΩR 8 10 5 AS 4022 Cosmology zM R ΩM ΩR 3500

Relic Neutrinos as Dark Matter Number density of relic neutrinos : 3 Tν 3 4 411 113 n ν ν nγ 3 4 Tγ 4 11 cm cm3 ( ) If neutrino mass is mυ k T0 10-3.6 eV then non-relativistic (Cold) Dark Matter today. Neutrino mass needed to account for Dark Matter : 2 m Ω h i ν Ων h 2 93.5 eV 11.9 eV 0.26 0.7 m i Experimental limits on neutrino masses: ν e 2.2 eV ν µ 0.17 MeV ν τ 15 MeV AS 4022 Cosmology

Neutrino Masses Neutrino oscillations neutrino mass: each type ( e µ τ ) is a mix of 3 mass states ( m1 m2 m3 ) travel time depends on mass interference,oscillation between types Solar neutrino problem solved: 2/3 of solar neutrinos change type enroute to Earth. Neutrinos from cosmic ray showers change type enroute thru the Earth. Oscillation wavelength depends on energy difference: 2 2 1/ 2 m 2c 2 mc m 2c 3 2 2 2 4 1/ 2 E ( p c m c ) pc 1 2 pc 1 pc 2 p 2p 2p 2 1 2 E1 E 2 m m2 Δ ( m12 ) 2 2 Experimental limits: Δ ( m12 ) 8.0 10 5 eV 2 2 Δ ( m23 ) 2.5 10 3 eV 2 AS 4022 Cosmology

Relic Neutrinos as Dark Matter Number density of relic neutrinos : If neutrino mass is m υ k T 0 10-3.6 eV then non-relativistic (Cold) Dark Matter today. Neutrino mass needed to account for Dark Matter : Ω ν h 2 m i 93.5 eV m i 11.9 eV Ω ν 0.26 h 0.7 2 n(ν ν) 3 4 T ν T γ