Do White Dwarfs Need Axion Cooling?
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CollectiveNeutrino Neutrino Oscillations Collective Oscillations Georg G. Raffelt 3rd Schrödinger Lecture, Thursday 19 May 2011 Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Neutrino Oscillations in Matter Neutrinos in a medium suffer flavor-dependent refraction f W, Z n Lincoln Wolfenstein f n n Z n ๐e − ๐n 2 for ๐e ๐weak = 2๐บF × for ๐μ −๐n 2 Typical density of Earth: 5 g/cm3 Δ๐weak ≈ 2 × 10−13 eV = 0.2 peV Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Neutrino Oscillations in Matter 2-flavor neutrino evolution as an effective 2-level problem ๐๐ ๐ ๐๐ i =๐ป ๐ ๐ ๐ ๐ ๐๐ง Negative for ๐ With a 2๏ด2 Hamiltonian matrix ๐ป= 1 2๐ธ cos ๐ − sin ๐ sin ๐ cos ๐ ๐12 0 0 ๐22 cos ๐ sin ๐ Mass-squared matrix, rotated by mixing angle q relative to interaction basis, drives oscillations Δ๐2 2๐ธ ∼ 4 peV for 12 mass splitting 120 peV for 13 mass splitting Solar, reactor and supernova neutrinos: E ∼ 10 MeV Georg Raffelt, MPI Physics, Munich − sin ๐ ± 2๐บF cos ๐ ๐๐ − ๐๐ 2 0 0 − ๐๐ 2 Weak potential difference Δ๐weak = 2๐บF ๐๐ ∼ 0.2 peV for normal Earth matter, but large effect in SN core (nuclear density 3๏ด1014 g/cm3) Δ๐weak ∼ 10 eV 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Suppression of Oscillations in Supernova Core Effective mixing angle in matter tan 2๐m = sin 2๐ cos 2๐ − ๐๐ 2๐ธ 2๐บF Δ๐2 Supernova core 14 −3 ๐ = 3 × 10 g cm ๐๐ = 0.35 ๐๐ = 6 × 1037 cm−3 ๐ธ ∼ 100 MeV Solar mixing Δ๐2 ∼ 75 meV 2 sin 2๐ ∼ 0.94 Matter suppression effect • Inside a SN core, flavors are “de-mixed” • Very small oscillation amplitude • Trapped e-lepton number can only escape by diffusion ๐๐ 2๐ธ 2๐บ๐น Δ๐2 ∼ 2 × 1013 Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Snap Shots of Supernova Density Profiles astro-ph/0407132 • ๐๐ -๐๐,๐ conversions, driven by small mixing angle ๐13 and “atmospheric” mass 2 difference Δ๐13 • May reveal neutrino mass hierarchy H-resonance (13 splitting) L-resonance (12 splitting) Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Mikheev-Smirnov-Wolfenstein (MSW) effect Eigenvalue diagram of 2๏ด2 Hamiltonian matrix for 2-flavor oscillations Antineutrinos Neutrinos ๐๐ ๐22 2๐ธ Propagation through density gradient: adiabatic conversion ๐12 2๐ธ ๐๐ “Negative density” represents antineutrinos in the same diagram Georg Raffelt, MPI Physics, Munich Vacuum ๐๐ ๐๐ Density 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Stanislaw Mikheev († 23 April 2011) Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Citations of Wolfenstein’s Paper on Matter Effects Atm nu oscillations SNO, KamLAND 250 200 MSW effect SN 1987A 150 100 50 0 1978 1982 1986 1990 1994 1998 2002 2006 2010 Annual citations of Wolfenstein, PRD 17:2369, 1978 in the SPIRES data base (total of 3278 citations 1978–2010) Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Three-Flavor Neutrino Parameters Three mixing angles ๐12 , ๐13 , ๐23 (Euler angles for 3D rotation), ๐๐๐ = cos ๐๐๐ , a CP-violating “Dirac phase” ๐ฟ, and two “Majorana phases” ๐ผ2 and ๐ผ3 ๐๐ 1 ๐๐ = 0 ๐๐ 0 0 ๐23 −๐ 23 0 ๐ 23 ๐23 ๐13 0 ๐๐ฟ −๐ ๐ 13 39โ < ๐23 < 53โ Atmospheric/LBL-Beams Normal 3 m t 2 ๐13 < 11โ Reactor m t Sun e m t e Atmosphere 1 ๐12 −๐ 12 0 e 3 Georg Raffelt, MPI Physics, Munich m t ๐ 12 ๐12 0 0 0 1 33โ < ๐12 < 37โ Solar/KamLAND Δ๐2 72–80 meV2 v Atmosphere m t Sun e m t ๐ −๐๐ฟ ๐ 13 0v ๐13 Inverted 1 2 0 1 0 2180–2640 meV2 1 0 0 ๐ผ ๐ 22 ๐ 0 0 0 0 ๐ผ ๐ 23 ๐ ๐1 ๐2 ๐3 Relevant for 0n2b decay Tasks and Open Questions • Precision for q12 and q23 • How large is q13 ? • CP-violating phase d? • Mass ordering? (normal vs inverted) • Absolute masses? (hierarchical vs degenerate) • Dirac or Majorana? 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Three Phases of Neutrino Emission Prompt ne burst • Shock breakout No large ๐๐ detector • De-leptonization of available outer core layers Accretion Cooling • Shock stalls ~ 150 km fluxespowered and large • Large Neutrinos by ๐infalling differences ๐ -๐๐ฅ fluxmatter Cooling on neutrino Smaller fluxes and small time scale ๐๐diffusion -๐๐ฅ flux differences • Spherically symmetric model (10.8 Mโ) with Boltzmann neutrino transport • Explosion manually triggered by enhanced CC interaction rate Fischer et al. (Basel group), A&A 517:A80, 2010 [arxiv:0908.1871] Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Level-Crossing Diagram in a Supernova Envelope Normal mass hierarchy Vacuum Inverted mass hierarchy Vacuum Dighe & Smirnov, Identifying the neutrino mass spectrum from a supernova neutrino burst, astro-ph/9907423 Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Oscillation of Supernova Anti-Neutrinos Basel accretion phase model (10.8 ๐โ ) Original ๐๐ spectrum (no oscillations) Partial swap (Normal hierarchy) w/ Earth effects Detection spectrum by ๐๐ + ๐ → ๐ + ๐ + (water Cherenkov or scintillator detectors) Full swap ๐๐ ↔ ๐๐ฅ (Inverted Hier.) 8000 km path length in Earth assumed Detecting Earth effects requires good energy resolution (Large scintillator detector, e.g. LENA, or megaton water Cherenkov) Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Signature of Flavor Oscillations (Accretion Phase) 1-3-mixing scenarios Mass ordering A B C Normal (NH) Inverted (IH) Any (NH/IH) sin2 ๐13 MSW conversion ๐๐ survival prob. โณ 10−3 โฒ 10−5 adiabatic non-adiabatic 0 ๐๐ survival prob. cos 2 ๐12 ≈ 0.7 ๐๐ Earth effects Yes sin2 ๐12 ≈ 0.3 sin2 ๐12 ≈ 0.3 0 cos 2 ๐12 ≈ 0.7 No Yes May distinguish mass ordering Assuming collective effects are not important during accretion phase (Chakraborty et al., arXiv:1105.1130v1) Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Snap Shots of Supernova Density Profiles astro-ph/0407132 Equivalent neutrino density ∝ R-2 Accretion-phase luminosity ๐ฟ๐๐ ∼ 3 × 1052 erg s Corresponds to a neutrino number density of 3× 10 km 2 33 −3 10 cm ๐ H-resonance (13 splitting) L-resonance (12 splitting) Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Self-Induced Flavor Oscillations of SN Neutrinos Survival probability ๐๐ Normal Hierarchy atm Dm2 Survival probability ๐๐ Realistic nu-nu effect MSW effect q13 close to Chooz limit No nu-nu effect Realistic nu-nu effect Inverted Hierarchy Georg Raffelt, MPI Physics, Munich Collective oscillations (single-angle approximation) MSW No nu-nu effect 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Spectral Split Initial fluxes at neutrino sphere Figures from Fogli, Lisi, Marrone & Mirizzi, arXiv:0707.1998 After collective transformation Georg Raffelt, MPI Physics, Munich Explanations in Raffelt & Smirnov arXiv:0705.1830 and 0709.4641 Duan, Fuller, Carlson & Qian arXiv:0706.4293 and 0707.0290 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Collective Supernova Nu Oscillations since 2006 Two seminal papers in 2006 triggered a torrent of activities Duan, Fuller, Qian, astro-ph/0511275, Duan et al. astro-ph/0606616 Balantekin, Gava & Volpe, arXiv:0710.3112. Balantekin & Pehlivan, astro-ph/0607527. Blennow, Mirizzi & Serpico, arXiv:0810.2297. Cherry, Fuller, Carlson, Duan & Qian, arXiv:1006.2175. Chakraborty, Choubey, Dasgupta & Kar, arXiv:0805.3131. Chakraborty, Fischer, Mirizzi, Saviano, Tomàs, arXiv:1104.4031, 1105.1130. Choubey, Dasgupta, Dighe & Mirizzi, arXiv:1008.0308. Dasgupta & Dighe, arXiv:0712.3798. Dasgupta, Dighe & Mirizzi, arXiv:0802.1481. Dasgupta, Dighe, Mirizzi & Raffelt, arXiv:0801.1660, 0805.3300. Dasgupta, Mirizzi, Tamborra & Tomàs, arXiv:1002.2943. Dasgupta, Dighe, Raffelt & Smirnov, 0904.3542. Dasgupta, Raffelt, Tamborra, arXiv:1001.5396. Duan, Fuller, Carlson & Qian, astro-ph/0608050, 0703776, arXiv:0707.0290, 0710.1271. Duan, Fuller & Qian, arXiv:0706.4293, 0801.1363, 0808.2046, 1001.2799. Duan, Fuller & Carlson, arXiv:0803.3650. Duan & Kneller, arXiv:0904.0974. Duan & Friedland, arXiv:1006.2359. Duan, Friedland, McLaughlin & Surman, arXiv:1012.0532. Esteban-Pretel, Pastor, Tomàs, Raffelt & Sigl, arXiv:0706.2498, 0712.1137. Esteban-Pretel, Mirizzi, Pastor, Tomàs, Raffelt, Serpico & Sigl, arXiv:0807.0659. Fogli, Lisi, Marrone & Mirizzi, arXiv:0707.1998. Fogli, Lisi, Marrone & Tamborra, arXiv:0812.3031. Friedland, arXiv:1001.0996. Gava & Jean-Louis, arXiv:0907.3947. Gava & Volpe, arXiv:0807.3418. Galais, Kneller & Volpe, arXiv:1102.1471. Galais & Volpe, arXiv:1103.5302. Gava, Kneller, Volpe & McLaughlin, arXiv:0902.0317. Hannestad, Raffelt, Sigl & Wong, astro-ph/0608695. Wei Liao, arXiv:0904.0075, 0904.2855. Lunardini, Müller & Janka, arXiv:0712.3000. Mirizzi, Pozzorini, Raffelt & Serpico, arXiv:0907.3674. Mirizzi & Tomàs, arXiv:1012.1339. Pehlivan, Balantekin, Kajino, Yoshida, arXiv:1105.1182. Raffelt, arXiv:0810.1407, 1103.2891. Raffelt & Tamborra, arXiv:1006.0002. Raffelt & Sigl, hep-ph/0701182. Raffelt & Smirnov, arXiv:0705.1830, 0709.4641. Sawyer, hepph/0408265, 0503013, arXiv:0803.4319, 1011.4585. Wu & Qian, arXiv:1105.2068. Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Flavor-Off-Diagonal Refractive Index 2-flavor neutrino evolution as an effective 2-level problem ๐๐ ๐ ๐๐ i =๐ป ๐ ๐ ๐๐ก ๐๐ ๐ Effective mixing Hamiltonian ๐2 ๐ป= + 2๐บF 2๐ธ Mass term in flavor basis: causes vacuum oscillations ๐๐ ๐๐ − 2 0 Z n 0 ๐๐ − 2 + 2๐บF n ๐๐๐ ๐⟨๐๐ ๐๐ ๐⟨๐๐ ๐๐ ๐๐๐ Wolfenstein’s weak Flavor-off-diagonal potential, potential, causes MSW caused by flavor oscillations. “resonant” conversion (J.Pantaleone, PLB 287:128,1992) together with vacuum term Flavor oscillations feed back on the Hamiltonian: Nonlinear effects! Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Synchronizing Oscillations by Neutrino Interactions • Vacuum oscillation frequency depends on energy ๐ = Δ๐2 2๐ธ • Ensemble with broad spectrum quickly decoheres kinematically • n-n interactions “synchronize” the oscillations: ๐sync = ⟨Δ๐2 2๐ธ⟩ Average e-flavor component of polarization vector Time Pastor, Raffelt & Semikoz, hep-ph/0109035 Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Three Ways to Describe Flavor Oscillations Schrödinger equation in terms of “flavor spinor” ๐๐ ๐๐ Δ๐2 cos 2๐ i๐๐ก ๐ = ๐ป ๐ = ๐ ๐ 2๐ธ sin 2๐ Neutrino flavor density matrix ๐= ๐๐ ๐๐ ⟩ ๐๐ ๐๐ ⟩ ๐๐ ๐๐ ⟩ ๐๐ ๐๐ ⟩ sin 2๐ − cos 2๐ ๐๐ ๐๐ Equivalent commutator form of Schrödinger equation i๐๐ก ๐ = ๐ป, ๐ Expand 2๏ด2 Hermitean matrices in terms of Pauli matrices ๐ = Tr ๐ + 1 ๐ 2 ⋅ ๐ and ๐ป = Δ๐2 ๐ 2๐ธ ⋅ ๐ with ๐ = (sin 2๐, 0, cos 2๐) Equivalent spin-precession form of equation of motion ๐ = ๐๐ × ๐ with ๐ = Δ๐2 2๐ธ ๐ is “polarization vector” or “Bloch vector” Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Flavor Oscillation as Spin Precession Flavor direction ๐ง Mass direction ๐ ↑ Spin up ๐๐ ↓ Spin down ๐๐ 2๐ Twice the vacuum mixing angle Georg Raffelt, MPI Physics, Munich ๐ ๐ฆ Flavor polarization vector precesses around the mass direction with frequency ๐ = Δ๐2 2๐ธ ๐ฅ 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Adding Matter Schrödinger equation including matter i๐๐ก ๐๐ ๐๐ = Δ๐2 2๐ธ cos 2๐ sin 2๐ sin 2๐ + 2๐บ๐น − cos 2๐ ๐๐ − ๐๐ 2 0 0 − ๐๐ 2 ๐๐ ๐๐ Corresponding spin-precession equation ๐ = ๐๐ + ๐๐ × ๐ with ๐ = Δ๐2 2๐ธ and ๐ = 2๐บF ๐๐ ๐eff ๐ unit vector in mass direction ๐ = ๐๐ง unit vector in flavor direction ๐ง ๐eff = ๐๐ + ๐๐ ๐matter = 2๐บF ๐๐ ๐ 2๐matter ๐vac 2๐vac Georg Raffelt, MPI Physics, Munich ๐ฅ๐2 = ๐ 2๐ธ ๐ฅ 3rd Schrödinger Lecture, University Vienna, 19 May 2011 MSW Effect Adiabatically decreasing density: Precession cone follows ๐eff Large initial matter density: ๐matter • ๐ begins as flavor eigenstate • Ends as mass eigenstate ๐eff ๐vac Matter Density Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Adding Neutrino-Neutrino Interactions Precession equation for each ๐ mode with energy ๐ธ, i.e. ๐ = Δ๐2 2๐ธ ๐๐ = ๐๐ + ๐๐ + ๐๐ × ๐๐ with ๐ = 2๐บF ๐๐ and ๐ = 2๐บF ๐๐ ๐eff Total flavor spin of entire ensemble ๐= ๐ ๐๐ normalize |๐๐ญ=๐ | = 1 Individual spins do not remain aligned – feel “internal” field ๐๐๐ = ๐๐ ๐ง ๐ Synchronized oscillations for large neutrino density ๐ โซ ๐ฟ๐ ๐ precesses with ๐sync for large ๐ density Individual ๐๐ “trapped” on precession cones Precess around ๐ with frequency ∼ ๐ ๐ฅ Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Synchronized Oscillations by Nu-Nu Interactions For large neutrino density, individual modes precess around large common dipole moment Pastor, Raffelt & Semikoz, hep-ph/0109035 Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Two Spins Interacting with a Dipole Force Simplest system showing ๐-๐ effects: Isotropic neutrino gas with 2 energies ๐ธ1 and ๐ธ2 , no ordinary matter ๐1 = (๐1 ๐ + ๐๐) × ๐๐ with ๐ = ๐1 + ๐2 and ๐1,2 = Δ๐2 2๐ธ ๐2 = ๐2 ๐ + ๐๐ × ๐๐ Go to “co-rotating frame” around ๐ direction ๐1 = (๐c ๐ − ๐๐ + ๐๐) × ๐๐ ๐2 = (๐c ๐ + ๐๐ + ๐๐) × ๐๐ with ๐c = 1 2 ๐2 + ๐1 and ๐ = ๐ 1 2 ๐2 − ๐1 No interaction (๐ = 0) P1,2 precess in opposite directions Strong interactions (๐ → ∞) P1,2 stuck to each other (no motion in co-rotating frame, perfectly synchronized in lab frame) Georg Raffelt, MPI Physics, Munich Mass direction ๐1 ๐2 ๐ฆ ๐ฅ 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Two Spins with Opposite Initial Orientation No interaction (๐ = 0) Free precession in opposite directions Even for very small mixing angle, large-amplitude flavor oscillations ๐1 ๐2 ๐2 ๐ 1 −๐1๐ง , ๐2๐ง ๐ Time Strong interaction (๐ → ∞) Pendular motion Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Instability in Flavor Space Two-mode example in co-rotating frame, initially ๐1 = ↓, ๐2 = ↑ (flavor basis) ๐1 = [−๐๐ + ๐ (๐๐ + ๐๐ )] × ๐๐ ๐2 = [+๐๐ + ๐ (๐๐ + ๐๐ )] × ๐๐ 0 initially ๐ ๐ ๐1 ๐ = ๐1 + ๐2 ๐1 ๐2 ๐2 Matter effect transverse to mass and flavor directions Both ๐1 and ๐2 tilt around ๐ if ๐ is large ๐ฆ ๐ฅ • Initially aligned in flavor direction and ๐ = 0 • Free precession ±๐ Georg Raffelt, MPI Physics, Munich After a short time, transverse ๐ develops by free precession 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Collective Pair Annihilation Gas of equal abundances of ๐๐ and ๐๐ , inverted mass hierarchy Small effective mixing angle (e.g. made small by ordinary matter) Survival probability 1 ๐๐ ๐๐ ๐๐ ๐๐ 0.75 0.5 0.25 0 ๐๐ ๐๐ ๐๐ ๐๐ ๐๐ ๐๐ Time Dense neutrino gas unstable in flavor space: ๐๐ ๐๐ ↔ ๐๐ ๐๐ Complete pair conversion even for a small mixing angle Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Flavor Matrices of Occupation Numbers Neutrinos described by Dirac field ๐น ๐ก, ๐ฅ = ๐3๐ฉ 2๐ 3 † ๐๐ฉ ๐ก ๐ข๐ฉ + ๐−๐ฉ ๐ก ๐ฃ−๐ฉ ๐ i๐ฉ⋅๐ฑ in terms of the spinors in flavor space, providing spinor of flavor amplitudes † ๐ ๐1 ๐1 (๐ก, ๐ฉ) ๐1 ๐น1 1 (๐ก, ๐ฉ) ๐น = ๐น2 , ๐ = ๐2 , ๐ = ๐2 and ๐2 (๐ก, ๐ฉ) = ๐2† (๐ก, ๐ฉ) |0⟩ ๐3 ๐น3 ๐3 ๐3 (๐ก, ๐ฉ) ๐† (๐ก, ๐ฉ) 3 Measurable quantities are expectation values of field bi-linears ๐น † ๐น , therefore use “occupation number matrices” to describe the ensemble and its kinetic evolution (Boltzmann eqn for oscillations and collisions) (๐) ๐๐๐ = ๐๐† ๐๐ (๐) ๐๐๐ = ๐๐ ๐๐† = 1 − ⟨๐๐† ๐๐ ⟩ Drops out in commutators Describe ๐ with negative occupation numbers, reversed order of flavor indices (holes in Dirac sea) Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Flavor Pendulum Classical Hamiltonian for two spins interacting with a dipole force ๐ ๐ 2 ๐ป = ๐๐ ⋅ ๐2 − ๐1 + ๐ 2 Angular-momentum Poisson brackets ๐๐ , ๐๐ = ๐๐๐๐ ๐๐ Lagrangian top (spherical pendulum with spin), moment of inertia ๐ผ ๐2 ๐ป = ๐๐ ⋅ ๐ + 2๐ผ Total angular momentum ๐, radius vector ๐, fulfilling ๐๐ , ๐๐ = ๐๐๐๐ ๐๐ , Total angular momentum ๐๐ , ๐๐ = 0 ๐๐ , ๐๐ = ๐๐๐๐ ๐๐ ๐ = ๐1 + ๐2 Pendulum EoMs Precession equations of motion ๐ = ๐ผ −1 ๐ × ๐ and ๐ = ๐๐ × ๐ ๐1,2 = (โ๐๐ + ๐๐) × ๐1,2 EoMs and Hamiltonians identical (up to a constant) with the identification ๐ ๐ ๐ = ๐2 − ๐1 − ๐ and ๐ = ๐ผ −1 Constants of motion: ๐12 , ๐22 , ๐ ⋅ ๐, ๐ ⋅ ๐, ๐2 and ๐ป Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Pendulum in Flavor Space Precession (synchronized oscillation) Polarization vector for neutrinos plus antineutrinos Nutation (pendular oscillation) • Very asymmetric system - Large spin - Almost pure precession - Fully synchronized oscillations • Perfectly symmetric system - No spin - Plane pendulum Spin (Lepton asymmetry) Mass direction in flavor space Hannestad, Raffelt, Sigl, Wong: astro-ph/0608695] Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Flavor Conversion in a Toy Supernova astro-ph/0608695 • Two modes with ๐ = ±0.3 km−1 • Assume 80% anti-neutrinos • Sharp onset radius • Oscillation amplitude declining • Neutrino-neutrino interaction energy at nu sphere (๐ = 10 km) ๐ = 0.3 × 105 km−1 • Falls off approximately as ๐ −4 (geometric flux dilution and nus become more co-linear) Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Neutrino Conversion and Flavor Pendulum 1 2 Sleeping top 1 Georg Raffelt, MPI Physics, Munich 3 Precession and nutation Ground state 2 3 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Fermi-Dirac Spectrum Fermi-Dirac energy spectrum ๐๐ ๐๐ธ ∝ ๐ธ2 ๐ ๐ธ ๐−๐ +1 ๐ degeneracy parameter, −๐ for ๐ ๐๐ Same spectrum in terms of w = T/E • Antineutrinos E ๏ฎ -E • and dN/dE negative (flavor isospin convention) ๐ > 0: ๐๐ = ↑ and ๐๐ = ↓ ๐ < 0: ๐๐ = ↓ and ๐๐ = ↑ ๐๐ ๐ = 0.2 infrared ๐๐ Georg Raffelt, MPI Physics, Munich ๐๐ infrared High-E tail 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Flavor Pendulum Single “positive” crossing (potential energy at a maximum) Single “negative” crossing (potential energy at a minimum) Dasgupta, Dighe, Raffelt & Smirnov, arXiv:0904.3542 For movies see http://www.mppmu.mpg.de/supernova/multisplits Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 General Stability Condition Spin-precession equations of motion for modes with ๐ = Δ๐2 2๐ธ ๐๐ = ๐๐ × ๐๐ Small-amplitude expansion: x-y-component described as complex number S (off-diagnonal r element), linearized EoMs −i๐๐ = ๐๐๐ − ๐ ๐๐′ ๐๐′ ๐๐′ Fourier transform ๐๐ = ๐น๐ ๐ ๐Ω๐ก , with Ω = ๐พ + ๐๐ a complex frequency ๐ − Ω ๐น๐ = ๐ ๐๐′ ๐๐′ ๐๐′ Eigenfunction is ๐น๐ ∝ ๐ − Ω ๐๐ −1 ๐ = ๐๐ ๐−Ω −1 and eigenvalue Ω = ๐พ + ๐๐ is solution of Instability occurs for ๐ = Im Ω ≠ 0 Exponential run-away solutions become pendulum for large amplitude. Banerjee, Dighe & Raffelt, work in progress Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Stability of Fermi-Dirac Spectrum ๐ ๐ 2๐ ๐พ Banerjee, Dighe & Raffelt, work in progress Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Stability of Schematic Double Peak ๐ ๐ Spectrum is unstable in the range 1 1 < ๐ < 2 2 ๐+1 ๐−1 where ๐ = ๐๐ ๐๐ . With ๐ = 0.7, system is unstable for 0.296 < ๐ < 37.5 Otherwise the system is stuck. Banerjee, Dighe & Raffelt, work in progress Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Decreasing Neutrino Density Certain initial neutrino density Four times smaller initial neutrino density Dasgupta, Dighe, Raffelt & Smirnov, arXiv:0904.3542 For movies see http://www.mppmu.mpg.de/supernova/multisplits Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Spectral Split Initial fluxes at neutrino sphere Figures from Fogli, Lisi, Marrone & Mirizzi, arXiv:0707.1998 After collective transformation Georg Raffelt, MPI Physics, Munich Explanations in Raffelt & Smirnov arXiv:0705.1830 and 0709.4641 Duan, Fuller, Carlson & Qian arXiv:0706.4293 and 0707.0290 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Multiple Spectral Splits Inverted Hierarchy ๐๐ ๐๐ ๐๐ ๐๐ Normal Hierarchy Dasgupta, Dighe, Raffelt & Smirnov, arXiv:0904.3542 Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Multiple Spectral Splits in the w Variable ๐๐ฅ ๐๐ ๐๐ ๐๐ฅ anti-neutrinos Georg Raffelt, MPI Physics, Munich neutrinos • Given is the flux spectrum f(E) for each flavor • Use ๐ = Δ๐2 2๐ธ to label modes • Label anti-neutrinos with −๐ • Define “spectrum” as ๐๐๐ ๐ธ − ๐๐๐ฅ (๐ธ) ๐ ๐ ∝ ๐๐๐ฅ ๐ธ − ๐๐๐ (๐ธ) • Swaps develop around every “postive” spectral crossing • Each swap flanked by two splits Dasgupta, Dighe, Raffelt & Smirnov, arXiv:0904.3542 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Supernova Cooling-Phase Example Normal Hierarchy Inverted Hierarchy Dasgupta, Dighe, Raffelt & Smirnov, arXiv:0904.3542 For movies see http://www.mppmu.mpg.de/supernova/multisplits Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Multi-Angle Decoherence Precession eqns for modes with vacuum oscillation frequency ๐ = Δ๐2 2๐ธ (negative for ๐), and velocity ๐ฏ (direction of motion), homogeneous system ๐๐,๐ฏ = ๐๐ × ๐๐,๐ฏ + ๐ 1 − cos ๐๐ฏ๐ฏ′ ๐๐′ ,๐ฏ′ × ๐๐,๐ฏ ๐′ ,๐ฏ ′ Axial symmetry around some direction (e.g. SN radial direction), measure velocities against that direction: ๐ฃ = cos ๐ ๐๐,๐ฃ = ๐๐ × ๐๐,๐ฃ + ๐ ๐′ ,๐ฃ ′ ๐๐′ ,๐ฃ ′ × ๐๐,๐ฃ − ๐ ๐′ ,๐ฃ ′ ๐ ๐ฃ ′ ๐๐′ ,๐ฃ ′ × ๐ฃ๐๐,๐ฃ ๐ (Flux) • Flux term vanishes in isotropic gas • Can grow exponentially even with only a small initial seed fluctuation • Symmetric ๐๐ system decoheres in both hierarchies Raffelt & Sigl, Self-induced decoherence in dense neutrino gases, hep-ph/0701182 Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Multi-Angle Decoherence Homogeneous ensemble of ๐๐ ๐๐ (symmetric distribution) Normal hierarchy isotropic half-isotropic Inverted hierarchy isotropic half-isotropic Raffelt & Sigl, Self-induced decoherence in dense neutrino gases, hep-ph/0701182 Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Multi-Angle Decoherence of Supernova Neutrinos Small asymmetry Large asymmetry Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Critical Asymmetry for Multi-Angle Decoherence Required ๐๐ ๐๐ asymmetry to suppress multi-angle decoherence Effective ๐ flux Esteban-Pretel, Pastor, Tomàs, Raffelt & Sigl: Decoherence in supernova neutrino transformations suppressed by deleptonization, astro-ph/0706.2498 Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Multi-Angle Matter Effect Precession equation in a homogeneous ensemble ๐๐ก ๐๐,๐ฏ = ๐๐ + ๐๐ + ๐๐ × ๐๐,๐ฏ , where ๐ = 2๐บF ๐๐ and ๐ = 2๐บF ๐๐ Matter term is “achromatic”, disappears in a rotating frame Neutrinos streaming from a SN core, evolution along radial direction (๐ฏ ⋅ ๐๐ ) ๐๐,๐ฏ = ๐๐ + ๐๐ + ๐๐ × ๐๐,๐ฏ Projected on the radial direction, oscillation pattern compressed: Accrues vacuum and matter phase faster than on radial trajectory Matter effect can suppress collective conversion unless ๐๐ โณ ๐๐ Esteban-Pretel, Mirizzi, Pastor, Tomàs, Raffelt, Serpico & Sigl, arXiv:0807.0659 Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Multi-Angle Matter Effect in Basel (10.8 Msun) Model Schematic single-energy, multi-angle simulations with realistic density profile no matter 500 1000 1500 Distance [km] 500 1000 1500 Distance [km] 500 1000 1500 Distance [km] Chakraborty, Fischer, Mirizzi, Saviano & Tomàs, arXiv:1105.1130 Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Signature of Flavor Oscillations (Accretion Phase) 1-3-mixing scenarios Mass ordering A B C Normal (NH) Inverted (IH) Any (NH/IH) sin2 ๐13 MSW conversion ๐๐ survival prob. โณ 10−3 โฒ 10−5 adiabatic non-adiabatic 0 ๐๐ survival prob. cos 2 ๐12 ≈ 0.7 ๐๐ Earth effects Yes sin2 ๐12 ≈ 0.3 sin2 ๐12 ≈ 0.3 0 cos 2 ๐12 ≈ 0.7 No Yes May distinguish mass ordering Assuming collective effects are not important during accretion phase (Chakraborty et al., arXiv:1105.1130v1) Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Coalescing Neutron Stars and Short Gamma-Ray Bursts Gamma rays + − ๐ ๐ plasma • Annihilation rate strongly suppressed if ๐๐ ๐๐ pairs transform to ๐๐ฅ ๐๐ฅ pairs • Collective effects important? ๐๐ ๐๐ Density of torus relatively small: • ๐๐ and ๐๐ not efficiently produced • Large ๐๐ ๐๐ pair abundance Accretion disk or torus 100-200 km Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Oscillation Along Streamlines ๐๐ survival probability for a disk-like source (coalescing neutron stars) • No neutrino-neutrino interactions: Oscillations along trajectories like a “beam” • Self-maintained coherence: Oscillation along “flux lines” of overall neutrino flux. Dasgupta, Dighe, Mirizzi & Raffelt, arXiv:0805.3300 Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011 Looking forward to the next galactic supernova of May theoretical take anext long work time to do! Looking Lots forward to No the problem galactic supernova Georg Raffelt, MPI Physics, Munich 3rd Schrödinger Lecture, University Vienna, 19 May 2011
