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). - PowerPoint PPT Presentation
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India
xx__ However, in traditionalHowever, in traditional
simulations transport simulations transport
of of and and schematic schematic
• Incomplete microphysicsIncomplete microphysics
• Crude numerics to coupleCrude numerics to couple neutrino transport withneutrino transport with hydro codehydro code
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India
Flavor-Dependent Neutrino Fluxes vs. Equation Flavor-Dependent Neutrino Fluxes vs. Equation of Stateof State
Kitaura, Janka & Hillebrandt, “Explosions of O-Ne-Mg cores, the CrabKitaura, Janka & Hillebrandt, “Explosions of O-Ne-Mg cores, the Crabsupernova, and subluminous Type II-P supernovae”, astro-ph/0512065supernova, and subluminous Type II-P supernovae”, astro-ph/0512065
Wolff & Hillebrandt nuclear EoS (stiff)
ee
,, ,
Lattimer & Swesty nuclear EoS (soft)
ee
,, ,
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India
Level-Crossing Diagram in a SN EnvelopeLevel-Crossing Diagram in a SN Envelope
Dighe & Smirnov, Identifying the neutrino mass spectrum from a supernovaDighe & Smirnov, Identifying the neutrino mass spectrum from a supernovaneutrino burst, astro-ph/9907423neutrino burst, astro-ph/9907423
Normal mass hierarchyNormal mass hierarchy Inverted mass hierarchyInverted mass hierarchy
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India
Self-Induced Flavor Oscillations of SN Self-Induced Flavor Oscillations of SN NeutrinosNeutrinos
Survival probability Survival probability eeSurvival probability Survival probability ee
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India
General Equations of MotionGeneral Equations of Motion
pqqqp3
3
FpFp
2
pt ),)(cos1(2
qdG2],L[G2,
p2M
i
pqqqp3
3
FpFp
2
pt ),)(cos1(2
qdG2],L[G2,
p2M
i
pqqqp3
3
FpFp
2
pt ),)(cos1(2
qdG2],L[G2,
p2M
i
pqqqp3
3
FpFp
2
pt ),)(cos1(2
qdG2],L[G2,
p2M
i
Usual matter effect withUsual matter effect with
nn00
0nn0
00nn
Lee
nn00
0nn0
00nn
Lee
• Vacuum oscillationsVacuum oscillations M is neutrino mass M is neutrino mass matrixmatrix
• Note opposite sign Note opposite sign betweenbetween neutrinos and neutrinos and antineutrinosantineutrinosNonlinear nu-nu effects are importantNonlinear nu-nu effects are importantwhen nu-nu interaction energy exceedswhen nu-nu interaction energy exceedstypical vacuum oscillation frequencytypical vacuum oscillation frequency(Do not compare with matter effect!)(Do not compare with matter effect!)
cos1nG2E2
mF
2
osc
cos1nG2E2
mF
2
osc
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India
Two-Flavor Neutrino Oscillations in VacuumTwo-Flavor Neutrino Oscillations in Vacuum
““Magnetic field”Magnetic field”in flavor spacein flavor space 2
Bp2
mm
p4
mmp
21
22
21
220
p
2B
p2
mm
p4
mmp
21
22
21
220
p
2cos
0
2sin
B
2cos
0
2sin
B
PolarizationPolarization vectorvector 2
Pf ppp
2
Pf ppp
2
P1f ppp
2
P1f ppp
or differentor differentnormalizationnormalization
ii Pauli Pauli
matricesmatrices
Neutrino flavor oscillation as a spin precessionNeutrino flavor oscillation as a spin precession
NeutrinosNeutrinos
p
2
pt PBp2
mP
p
2
pt PBp2
mP
SpinSpin 1/21/2
MagneticMagneticmomentmoment
++mm22/2p/2p
Anti-neutrinosAnti-neutrinos
p
2
pt PBp2
mP
p
2
pt PBp2
mP
SpinSpin 1/21/2
MagneticMagneticmomentmoment
--mm22/2p/2p
BB
pPpP
22
xxyy
zz
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India
Synchronizing Oscillations by Neutrino Synchronizing Oscillations by Neutrino InteractionsInteractions
Vacuum oscillation frequency Vacuum oscillation frequency of mode with momentum p ~ Eof mode with momentum p ~ E p2
m2
osc
p2
m2
osc
Modified in a medium by theModified in a medium by theusual weak-interaction potentialusual weak-interaction potential
In an ensemble withIn an ensemble witha broad momentuma broad momentumdistribution, thedistribution, thep-dependent oscillationp-dependent oscillationfrequency quickly leadsfrequency quickly leadsto kinematicalto kinematicalflavor decoherenceflavor decoherence
In a dense neutrino gas,In a dense neutrino gas,all modes go with theall modes go with thesame frequency:same frequency:““SynchronizedSynchronized flavor oscillations” orflavor oscillations” or““self-maintainedself-maintained coherence”coherence”
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India
Bipolar Oscillations of Neutrinos in a BoxBipolar Oscillations of Neutrinos in a Box
Dense gas of and Dense gas of and
Take equal densities withTake equal densities with
ee ee
eenG2nG2 FF eenG2nG2 FF
Assume only one energy withAssume only one energy with
1012 E2m 1012 E2m
Small mixing angle, inverted hierarchySmall mixing angle, inverted hierarchy
01.0 01.0
Survival probability of both and Survival probability of both and ee ee
)1P()(prob z21
ee )1P()(prob z21
ee
• Time scale set byTime scale set by
• “ “Plateau phases” mean exponentialPlateau phases” mean exponential growth, increase by growth, increase by log(log())
• Reduced mixing angle by ordinaryReduced mixing angle by ordinary matter unimportantmatter unimportant
2 2 Note:Note:This is no real “flavor conversion”,This is no real “flavor conversion”,Rather a “collective pair conversion” Rather a “collective pair conversion”
ee ee
Time scale Time scale proportional to proportional to FGFG
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India
Synchronized vs. Bipolar OscillationsSynchronized vs. Bipolar Oscillations
Asymmetric system, Asymmetric system, initially consisting of initially consisting of unequalunequal numbersnumbers with equal energies (equal oscillation frequency with equal energies (equal oscillation frequency ) and ) and
NO FREE LUNCHNO FREE LUNCH• Net flavor lepton number along massNet flavor lepton number along mass direction is conserveddirection is conserved• “ “Bipolar conversions” are PAIR Bipolar conversions” are PAIR conversions,conversions, no net flavor-lepton number violationno net flavor-lepton number violation• True flavor conversion only caused byTrue flavor conversion only caused by vacuum flavor oscillation effectvacuum flavor oscillation effect• No unusual enhancementNo unusual enhancement (unlike MSW effect)(unlike MSW effect)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India
Pendulum in Flavor SpacePendulum in Flavor Space
Mass directionMass directionin flavor spacein flavor space
• Neutrino-neutrino interaction Neutrino-neutrino interaction energy at nu sphere (r = 10 km)energy at nu sphere (r = 10 km)
= 0.3= 0.3101055 km km11
• Falls off approximately as Falls off approximately as rr44
(geometric flux dilution and nus(geometric flux dilution and nus become more co-linear)become more co-linear)
Decline of oscillation amplitudeDecline of oscillation amplitudeexplained in pendulum analogyexplained in pendulum analogyby inreasing moment of inertiaby inreasing moment of inertia(Hannestad, Raffelt, Sigl & Wong(Hannestad, Raffelt, Sigl & Wong astro-ph/0608695)astro-ph/0608695)
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India
Nonlinear Neutrino Conversion in SupernovaeNonlinear Neutrino Conversion in Supernovae
Survival probability Survival probability eeSurvival probability Survival probability ee
NormalNormalHierarchyHierarchy
atm atm mm22
1313closeclose
to Choozto Choozlimitlimit
InvertedInvertedHierarchyHierarchy
Duan, Fuller, Carlson, Qian: “Simulation of Coherent Non-Linear NeutrinoDuan, Fuller, Carlson, Qian: “Simulation of Coherent Non-Linear Neutrino Flavor Transformation in the Supernova Environment. 1. CorrelatedFlavor Transformation in the Supernova Environment. 1. Correlated Neutrino Trajectories”, astro-ph/0606616. See also: astro-ph/0608050Neutrino Trajectories”, astro-ph/0606616. See also: astro-ph/0608050
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India
Flux Term as a Source of DecoherenceFlux Term as a Source of Decoherence
pqqqp3
3
Fp
2
pt P)PP)(cos1(2
qdG2PB
p2m
P
pqqqp3
3
Fp
2
pt P)PP)(cos1(2
qdG2PB
p2m
P
ppqqq3
3
pqq3
3
Fp
2
pt Pcos)PP(cos2
qdP)PP(
2
qdG2PB
p2m
P
ppqqq3
3
pqq3
3
Fp
2
pt Pcos)PP(cos2
qdP)PP(
2
qdG2PB
p2m
P
General two-flavor expressionGeneral two-flavor expression
Axial symmetry around some direction, e.g., supernova radial directionAxial symmetry around some direction, e.g., supernova radial direction
p0 PD
p0 PD
pp1 cosPD
pp1 cosPD
Density (isotropic) termDensity (isotropic) termResponsible for usualResponsible for usualcollective phenomenacollective phenomena(“self-maintained(“self-maintained coherence”)coherence”)
Little effect because ofLittle effect because ofmatter-suppressedmatter-suppressedmixing anglemixing angle
~80~80
Importance of bipolarImportance of bipolaroscillations in this SNoscillations in this SNregion first noted byregion first noted byDuan, Fuller & QianDuan, Fuller & Qianastro-ph/0511275 astro-ph/0511275
Georg Raffelt, Max-Planck-Institut für Physik, München, Germany JIGSAW 07, 12-23 Feb 2007, TIFR, Mumbai, India
Papers on collective neutrino oscillationsPapers on collective neutrino oscillations
1992 Flavor off-diagonal1992 Flavor off-diagonalrefractive indexrefractive index
1992-19981992-1998NumericalNumerical && analytic studies,analytic studies,but not much impactbut not much impact(nobody really understood)(nobody really understood)
1994-20041994-2004SN neutrino oscillations and SN neutrino oscillations and r-process nucleosynthesisr-process nucleosynthesis(everybody missed the main(everybody missed the main point)point)
2006-20072006-2007““Bipolar” oscillationsBipolar” oscillationscrucial for SN neutrinos crucial for SN neutrinos