1. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Collective Supernova Neutrino Oscillations Georg Raffelt, MPI Physik, Munich, Germany JIGSAW 07, 12  23 Feb 2007, TIFR, Mumbai, India

2. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Sanduleak  69 202 Large Magellanic Cloud Distance 50 kpc (160.000 light years) Tarantula Nebula Supernova 1987A 23 February 1987 Supernova 1987A 23 February 1987 Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India

3. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Neutrino Signal of Supernova 1987A Within clock uncertainties, signals are contemporaneous Kamiokande-II (Japan) Water Cherenkov detector 2140 tons Clock uncertainty  1 min Irvine-Michigan-Brookhaven (US) Water Cherenkov detector 6800 tons Clock uncertainty  50 ms Baksan Scintillator Telescope (Soviet Union), 200 tons Random event cluster ~ 0.7/day Clock uncertainty +2/-54 s

4. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Flavor-Dependent Fluxes and Spectra Broad characteristics Duration a few seconds Duration a few seconds  E  ~ 10  20 MeV  E  ~ 10  20 MeV  E  increases with time  E  increases with time Hierarchy of energies Hierarchy of energies Approximate equipartition Approximate equipartition of energy between flavors of energy between flavors Livermore numerical model ApJ 496 (1998) 216 Prompt e deleptonizationburst e e x _ However, in traditional simulations transport of  and  schematic Incomplete microphysics Incomplete microphysics Crude numerics to couple Crude numerics to couple neutrino transport with neutrino transport with hydro code hydro code

5. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Flavor-Dependent Neutrino Fluxes vs. Equation of State Kitaura, Janka & Hillebrandt, “Explosions of O-Ne-Mg cores, the Crab supernova, and subluminous Type II-P supernovae”, astro-ph/0512065 Wolff & Hillebrandt nuclear EoS (stiff)Lattimer & Swesty nuclear EoS (soft)

6. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Level-Crossing Diagram in a SN Envelope Dighe & Smirnov, Identifying the neutrino mass spectrum from a supernova neutrino burst, astro-ph/9907423 Normal mass hierarchy Inverted mass hierarchy

7. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Self-Induced Flavor Oscillations of SN Neutrinos Survival probability e NormalHierarchy atm  m 2  13  close to Chooz limit InvertedHierarchy No nu-nu effect No MSWeffect MSWeffect Realistic Bipolarcollectiveoscillations(single-angle approximation) approximation) MSW Realistic nu-nu effect MSWeffect

8. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Matrices of Density in Flavor Space Neutrino quantum field Neutrino quantum field Spinors in flavor space Spinors in flavor space Quantum states (amplitudes) Variables for discussing neutrino flavor oscillations “Matrices of densities” (analogous to occupation numbers) “Quadratic” quantities, required for dealing with decoherence, collisions, Pauli-blocking, nu-nu-refraction, etc. Sufficient for “beam experiments,” but confusing “wave packet debates” for quantifying decoherence effects Destruction operators for (anti)neutrinos Neutrinos Anti-neutrinos

9. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India General Equations of Motion Usual matter effect with Vacuum oscillations Vacuum oscillations M is neutrino mass matrix M is neutrino mass matrix Note opposite sign between Note opposite sign between neutrinos and antineutrinos neutrinos and antineutrinos Nonlinear nu-nu effects are important when nu-nu interaction energy exceeds typical vacuum oscillation frequency (Do not compare with matter effect!)

10. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Two-Flavor Neutrino Oscillations in Vacuum “Magnetic field” in flavor space Polarization Polarization vector vector or different normalization  i Pauli matrices Neutrino flavor oscillation as a spin precession Neutrinos Spin 1/2 1/2Magneticmoment +  m 2 /2p Anti-neutrinos Spin 1/2 1/2Magneticmoment -  m 2 /2p x yz

11. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Synchronizing Oscillations by Neutrino Interactions Vacuum oscillation frequency of mode with momentum p ~ E Modified in a medium by the usual weak-interaction potential In an ensemble with a broad momentum distribution, the p-dependent oscillation frequency quickly leads to kinematical flavor decoherence In a dense neutrino gas, all modes go with the same frequency: “Synchronized flavor oscillations” or flavor oscillations” or“self-maintained coherence” coherence”

12. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Bipolar Oscillations of Neutrinos in a Box Dense gas of and Take equal densities with Assume only one energy with Small mixing angle, inverted hierarchy Survival probability of both and Time scale set by Time scale set by “Plateau phases” mean exponential “Plateau phases” mean exponential growth, increase by  log(  ) growth, increase by  log(  ) Reduced mixing angle by ordinary Reduced mixing angle by ordinary matter unimportant matter unimportantNote: This is no real “flavor conversion”, Rather a “collective pair conversion” Time scale proportional to

13. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Synchronized vs. Bipolar Oscillations Asymmetric system, initially consisting of unequal numbers with equal energies (equal oscillation frequency  ) and Free oscillations ≪ Bipolar oscillations ≪≪ Synchronized oscillations ≪

14. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Synchronized vs. Bipolar Oscillations Free oscillations ≪ Bipolar oscillations ≪≪ Synchronized oscillations ≪ Energy of the system: E pot always dominates E kin always dominates

15. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Synchronized vs. Bipolar Oscillations Free oscillations ≪ Bipolar oscillations ≪≪ Synchronized oscillations ≪ SupernovaCore R = 40  60 km R  200 km

16. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Equations of Motion for Two-Flavor Case Isotropic neutrinos, ignore matter, only one neutrino energy Sum Diff. Neglect first term for  Length S = 2 approximately conserved Tilt angle of S relative to B-direction Pendulum in flavour space Inverted (unstable) for inverted hierarchy Inverted (unstable) for inverted hierarchy Stable (harmonic oscillator) otherwise Stable (harmonic oscillator) otherwise

17. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Impact of Ordinary Matter Matter has identical effect Matter has identical effect on nus and anti-nus on nus and anti-nus In rotating frame (frequency ) In rotating frame (frequency ) no matter effect, rotating B-field no matter effect, rotating B-field For inverted hierarchy: For inverted hierarchy: “driven” inverted harmonic “driven” inverted harmonic oscillator, exponentially growing oscillator, exponentially growing amplitude amplitude Exponentially growing phase, scales with Analytic solution in: Hannestad, Raffelt, Sigl & Wong, Self-induced conversion in dense neutrino gases: Pendulum in flavour space astro-ph/0608695

18. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Asymmetric System as a Pendulum with Spin Neutrinos and anti-neutrinos New variables Essentially particle number ( ) Lepton number ( ) Equations of motion Conserved quantities Spherical pendulum Energy Angular momentum along force direction Angular momentum along pendulum Interpretation as pendulum with spin Pendulum orientation Angular momentum Moment of inertia Spin Equations of motion once more Precession (synchronized oscillations) Pendulum (bipolar oscillations) NO FREE LUNCH Net flavor lepton number along mass Net flavor lepton number along mass direction is conserved direction is conserved “Bipolar conversions” are PAIR conversions, “Bipolar conversions” are PAIR conversions, no net flavor-lepton number violation no net flavor-lepton number violation True flavor conversion only caused by True flavor conversion only caused by vacuum flavor oscillation effect vacuum flavor oscillation effect No unusual enhancement No unusual enhancement (unlike MSW effect) (unlike MSW effect)

19. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Pendulum in Flavor Space Mass direction in flavor space Precession (synchronized oscillation) Nutation(bipolar oscillation) oscillation) Spin (Lepton Asymmetry) Very asymmetric system Very asymmetric system - Large spin - Large spin - Almost pure precession - Almost pure precession - Fully synchronized oscillations - Fully synchronized oscillations Perfectly symmetric system Perfectly symmetric system - No spin - No spin - Simple spherical pendulum - Simple spherical pendulum - Fully bipolar oscillation - Fully bipolar oscillation Polarization vector for neutrinos plus antineutrinos ≫

20. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Toy Supernova in “Single-Angle” Approximation Bipolar Oscillations Assume 80% anti-neutrinos Assume 80% anti-neutrinos Vacuum oscillation frequency Vacuum oscillation frequency  = 0.3 km  1  = 0.3 km  1 Neutrino-neutrino interaction Neutrino-neutrino interaction energy at nu sphere (r = 10 km) energy at nu sphere (r = 10 km)  = 0.3  10 5 km  1  = 0.3  10 5 km  1 Falls off approximately as r  4 Falls off approximately as r  4 (geometric flux dilution and nus (geometric flux dilution and nus become more co-linear) become more co-linear) Decline of oscillation amplitude explained in pendulum analogy by inreasing moment of inertia (Hannestad, Raffelt, Sigl & Wong astro-ph/0608695) astro-ph/0608695)

21. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Nonlinear Neutrino Conversion in Supernovae Survival probability e NormalHierarchy atm  m 2  13  close to Chooz limit InvertedHierarchy Duan, Fuller, Carlson, Qian: “Simulation of Coherent Non-Linear Neutrino Duan, Fuller, Carlson, Qian: “Simulation of Coherent Non-Linear Neutrino Flavor Transformation in the Supernova Environment. 1. Correlated Flavor Transformation in the Supernova Environment. 1. Correlated Neutrino Trajectories”, astro-ph/0606616. See also: astro-ph/0608050 Neutrino Trajectories”, astro-ph/0606616. See also: astro-ph/0608050

22. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Flux Term as a Source of Decoherence General two-flavor expression Axial symmetry around some direction, e.g., supernova radial direction Density (isotropic) term Responsible for usual collective phenomena (“self-maintained coherence”) coherence”) Flux term Responsible for kinematical decoherence (“self-induced decoherence”) decoherence”) Raffelt & Sigl, Self-induced decoherence in dense neutrino gases hep-ph/0701182

23. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Kinematical Decoherence - Symmetric Case InvertedHierarchy Isotropic (single angle) Large flux (“half isotropic”) NormalHierarchy

24. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Inverted Hierarchy - Asymmetric Case (  = 0.8) Single angle Multi angle Polarizationvectors Length Length z-component z-component Energycomponents

25. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Inverted Hierarchy - Asymmetric Case (  = 0.6) Single angle Multi angle Polarizationvectors Length Length z-component z-component Energycomponents

26. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Normal Hierarchy - Asymmetric Case (  = 0.8) Single angle Multi angle Polarizationvectors Length Length z-component z-component Energycomponents

27. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Normal Hierarchy - Asymmetric Case (  = 0.9) Single angle Multi angle Polarizationvectors Length Length z-component z-component Energycomponents

28. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Nonlinear Neutrino Conversion in Supernovae Survival probability e NormalHierarchy atm  m 2  13  close to Chooz limit InvertedHierarchy Duan, Fuller, Carlson, Qian: “Simulation of Coherent Non-Linear Neutrino Duan, Fuller, Carlson, Qian: “Simulation of Coherent Non-Linear Neutrino Flavor Transformation in the Supernova Environment. 1. Correlated Flavor Transformation in the Supernova Environment. 1. Correlated Neutrino Trajectories”, astro-ph/0606616. See also: astro-ph/0608050 Neutrino Trajectories”, astro-ph/0606616. See also: astro-ph/0608050

29. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Different Oscillation Modes in Supernovae Center Neutrinosphere ~15 0 R [km] ~10 4 ~200 Bipolar oscillations for inverted hierarchy Fluxes H-Resonance (atm) Freestreaming ≫ ≪ Matter effect important Matter effect important Usually suppresses mixing angle Usually suppresses mixing angle MSW Neutrino-neutrino collective effects strong ~10 5 L-Resonance (sol) MSW Synchronisedoscillations Little effect because of matter-suppressed mixing angle ~80 Importance of bipolar oscillations in this SN region first noted by Duan, Fuller & Qian astro-ph/0511275

30. Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India Papers on collective neutrino oscillations 1992 Flavor off-diagonal refractive index 1992-1998 Numerical & analytic studies, but not much impact (nobody really understood) 2001-2002 Flavor equilibration of cosmological neutrinos with chemical potential before BBN epoch 1994-2004 SN neutrino oscillations and r-process nucleosynthesis (everybody missed the main point) point) 2006-2007 “Bipolar” oscillations crucial for SN neutrinos Pantaleone, PLB 287(1992) 128 Samuel, Kostolecký & Pantaleone in various combinations: PLB 315:46 & 318:127 (1993), 385:159 (1996) PRD 48:1462 (1993), 49:1740 (1994), 52:621 & 3184 (1995), 53:5382 (1996), 58:073002 (1998) Pastor, Raffelt & Semikoz, hep-ph/0109035 Lunardini & Smirnov, hep-ph/0012056 Dolgov et al., hep-ph/0201287 Wong, hep-ph/0203180 Abazajian, Beacom & Bell, astro-ph/0203442 Pantaleone, astro-ph/9405008 Qian & Fuller, astro-ph/9406073 Sigl, astro-ph/9410094 Pastor & Raffelt, astro-ph/0207281 Balantekin & Yüksel, astro-ph/0411159 Duan, Fuller & Qian, astro-ph/0511275 Duan, Fuller, Carlson & Qian, astro-ph/0606616 Hannestad, Raffelt, Sigl & Wong, astro-ph/0608695 Raffelt & Sigl, hep-ph/0701182