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Collective Supernova Neutrino Oscillations Georg Raffelt, MPI Physik, Munich, Germany

Collective Supernova Neutrino Oscillations Georg Raffelt, MPI Physik, Munich, Germany JIGSAW 07, 12 - 23 Feb 2007, TIFR, Mumbai, India. Sanduleak - 69 202. Supernova 1987A 23 February 1987. Tarantula Nebula. Large Magellanic Cloud Distance 50 kpc (160.000 light years).

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Collective Supernova Neutrino Oscillations Georg Raffelt, MPI Physik, Munich, Germany

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  1. Collective Supernova Neutrino Oscillations GeorgRaffelt,MPIPhysik,Munich,Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India

  2. Sanduleak -69 202 Supernova 1987A23 February 1987 Tarantula Nebula Large Magellanic Cloud Distance 50 kpc (160.000 light years) Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India

  3. Neutrino Signal of Supernova 1987A 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 Within clock uncertainties, signals are contemporaneous

  4. Flavor-Dependent Fluxes and Spectra Prompt ne deleptonization burst nx _ ne ne Livermore numerical model ApJ 496 (1998) 216 • Broad characteristics • Duration a few seconds • En ~ 10-20 MeV • En increases with time • Hierarchy of energies • Approximate equipartition • of energy between flavors • However, in traditional • simulations transport • of nm and nt schematic • Incomplete microphysics • Crude numerics to couple • neutrino transport with • hydro code

  5. Flavor-Dependent Neutrino Fluxes vs. Equation of State Wolff & Hillebrandt nuclear EoS (stiff) Lattimer & Swesty nuclear EoS (soft) Kitaura, Janka & Hillebrandt, “Explosions of O-Ne-Mg cores, the Crab supernova, and subluminous Type II-P supernovae”, astro-ph/0512065

  6. Level-Crossing Diagram in a SN Envelope Normal mass hierarchy Inverted mass hierarchy Dighe & Smirnov, Identifying the neutrino mass spectrum from a supernova neutrino burst, astro-ph/9907423

  7. Self-Induced Flavor Oscillations of SN Neutrinos Survival probability ne Survival probability ne Normal Hierarchy atm Dm2 Q13close to Chooz limit MSW effect MSW effect Realistic nu-nu effect No nu-nu effect Inverted Hierarchy Bipolar collective oscillations (single-angle approximation) MSW effect MSW Realistic nu-nu effect No nu-nu effect

  8. Matrices of Density in Flavor Space Neutrino quantum field Spinors in flavor space Destruction operators for (anti)neutrinos Variables for discussing neutrino flavor oscillations Quantum states (amplitudes) “Matrices of densities” (analogous to occupation numbers) Neutrinos Anti- neutrinos Sufficient for “beam experiments,” but confusing “wave packet debates” for quantifying decoherence effects “Quadratic” quantities, required for dealing with decoherence, collisions, Pauli-blocking, nu-nu-refraction, etc.

  9. General Equations of Motion Usual matter effect with Nonlinear nu-nu effects are important when nu-nu interaction energy exceeds typical vacuum oscillation frequency (Do not compare with matter effect!) • Vacuum oscillations • M is neutrino mass matrix • Note opposite sign between • neutrinos and antineutrinos

  10. Two-Flavor Neutrino Oscillations in Vacuum Polarization vector si Pauli matrices or different normalization “Magnetic field” in flavor space Neutrinos Anti-neutrinos z Spin 1/2 Magnetic moment +Dm2/2p Spin 1/2 Magnetic moment -Dm2/2p y x Neutrino flavor oscillation as a spin precession

  11. 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 “self-maintained coherence”

  12. Bipolar Oscillations of Neutrinos in a Box Survival probability of both and Dense gas of and Take equal densities with Assume only one energy with Small mixing angle, inverted hierarchy • Time scale set by • “Plateau phases” mean exponential • growth, increase by -log(q) • Reduced mixing angle by ordinary • matter unimportant Note: This is no real “flavor conversion”, Rather a “collective pair conversion” Time scale proportional to

  13. Synchronized vs. Bipolar Oscillations Synchronized oscillations Bipolar oscillations Free oscillations ≪ ≪ ≪ ≪ Asymmetric system, initially consisting of unequalnumbers with equal energies (equal oscillation frequency w) and

  14. Synchronized vs. Bipolar Oscillations Synchronized oscillations Bipolar oscillations Free oscillations ≪ ≪ ≪ ≪ Energy of the system: Ekin always dominates Epot always dominates

  15. Synchronized vs. Bipolar Oscillations Synchronized oscillations Bipolar oscillations Free oscillations ≪ ≪ ≪ ≪ Supernova Core R = 40-60 km R  200 km

  16. Equations of Motion for Two-Flavor Case Isotropic neutrinos, ignore matter, only one neutrino energy Sum Neglect first term for w ≪m Diff. Length S = 2 approximately conserved Tilt angle of S relative to B-direction • Pendulum in flavour space • Inverted (unstable) for inverted hierarchy • Stable (harmonic oscillator) otherwise

  17. Impact of Ordinary Matter • Matter has identical effect • on nus and anti-nus • In rotating frame (frequency l) • no matter effect, rotating B-field • For inverted hierarchy: • “driven” inverted harmonic • oscillator, exponentially growing • 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. Asymmetric System as a Pendulum with Spin Neutrinos and anti-neutrinos Interpretation as pendulum with spin Pendulum orientation Angular momentum New variables • NO FREE LUNCH • Net flavor lepton number along mass • direction is conserved • “Bipolar conversions” are PAIR conversions, • no net flavor-lepton number violation • True flavor conversion only caused by • vacuum flavor oscillation effect • No unusual enhancement • (unlike MSW effect) Essentially particle number ( ) Moment of inertia Lepton number ( ) Spin Equations of motion Equations of motion once more Conserved quantities Spherical pendulum Pendulum (bipolar oscillations) Energy Angular momentum along force direction Angular momentum along pendulum Precession (synchronized oscillations)

  19. Pendulum in Flavor Space Polarization vector for neutrinos plus antineutrinos Precession (synchronized oscillation) Nutation (bipolar oscillation) Spin (Lepton Asymmetry) • Very asymmetric system • - Large spin • - Almost pure precession • - Fully synchronized oscillations • Perfectly symmetric system • - No spin • - Simple spherical pendulum • - Fully bipolar oscillation ≫ Mass direction in flavor space

  20. Toy Supernova in “Single-Angle” Approximation • Assume 80% anti-neutrinos • Vacuum oscillation frequency • w = 0.3 km-1 • Neutrino-neutrino interaction • energy at nu sphere (r = 10 km) • m = 0.3105 km-1 • Falls off approximately as r-4 • (geometric flux dilution and nus • become more co-linear) Bipolar Oscillations Decline of oscillation amplitude explained in pendulum analogy by inreasing moment of inertia (Hannestad, Raffelt, Sigl & Wong astro-ph/0608695)

  21. Nonlinear Neutrino Conversion in Supernovae Survival probability ne Survival probability ne Normal Hierarchy atm Dm2 Q13close to Chooz limit Inverted Hierarchy Duan, Fuller, Carlson, Qian: “Simulation of Coherent Non-Linear Neutrino Flavor Transformation in the Supernova Environment. 1. Correlated Neutrino Trajectories”, astro-ph/0606616. See also: astro-ph/0608050

  22. 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”) Flux term Responsible for kinematical decoherence (“self-induced decoherence”) Raffelt & Sigl, Self-induced decoherence in dense neutrino gases hep-ph/0701182

  23. Kinematical Decoherence - Symmetric Case Isotropic (single angle) Large flux (“half isotropic”) Normal Hierarchy Inverted Hierarchy

  24. Inverted Hierarchy - Asymmetric Case (a = 0.8) Single angle Multi angle • Polarization • vectors • Length • z-component Energy components

  25. Inverted Hierarchy - Asymmetric Case (a = 0.6) Single angle Multi angle • Polarization • vectors • Length • z-component Energy components

  26. Normal Hierarchy - Asymmetric Case (a = 0.8) Single angle Multi angle • Polarization • vectors • Length • z-component Energy components

  27. Normal Hierarchy - Asymmetric Case (a = 0.9) Single angle Multi angle • Polarization • vectors • Length • z-component Energy components

  28. Nonlinear Neutrino Conversion in Supernovae Survival probability ne Survival probability ne Normal Hierarchy atm Dm2 Q13close to Chooz limit Inverted Hierarchy Duan, Fuller, Carlson, Qian: “Simulation of Coherent Non-Linear Neutrino Flavor Transformation in the Supernova Environment. 1. Correlated Neutrino Trajectories”, astro-ph/0606616. See also: astro-ph/0608050

  29. Different Oscillation Modes in Supernovae Center Synchronised oscillations Little effect because of matter-suppressed mixing angle 0 ≫ Neutrino sphere ≪ ~15 Neutrino-neutrino collectiveeffectsstrong Fluxes Free streaming ~80 Bipolar oscillations for inverted hierarchy Matter effect important Usually suppresses mixing angle ~200 Importance of bipolar oscillations in this SN region first noted by Duan, Fuller & Qian astro-ph/0511275 H-Resonance (atm) MSW ~104 L-Resonance (sol) MSW ~105 R [km]

  30. Papers on collective neutrino oscillations 1992 Flavor off-diagonal refractive index Pantaleone, PLB 287(1992) 128 1992-1998 Numerical&analytic studies, but not much impact (nobody really understood) 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) 2001-2002 Flavor equilibration of cosmological neutrinos with chemical potential before BBN epoch 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 1994-2004 SN neutrino oscillations and r-process nucleosynthesis (everybody missed the main point) Pantaleone, astro-ph/9405008 Qian & Fuller, astro-ph/9406073 Sigl, astro-ph/9410094 Pastor & Raffelt, astro-ph/0207281 Balantekin & Yüksel, astro-ph/0411159 2006-2007 “Bipolar” oscillations crucial for SN neutrinos 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

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