supernova neutrinos · longo, prl 60:173,1988 krauss & tremaine, prl 60:176,1988 • proves...

Georg Raffelt, Max-Planck-Institut für Physik, München, Germany Neutrino Physics & Astrophysics, 17-21 Sept 2008, Beijing, China

Neutrinos and the starsNeutrinos and the starsSupernova NeutrinosSupernova Neutrinos

Georg Raffelt, MPI for PhysicsLectures at the Topical SeminarNeutrino Physics & Astrophysics17−21 Sept 2008, Beijing, China

Georg Raffelt, MPI for PhysicsLectures at the Topical SeminarNeutrino Physics & Astrophysics17−21 Sept 2008, Beijing, China


Sanduleak Sanduleak −−69 20269 202

Large Magellanic Cloud Large Magellanic Cloud Distance 50 kpcDistance 50 kpc(160.000 light years)(160.000 light years)

Tarantula NebulaTarantula Nebula


Sanduleak Sanduleak −−69 20269 202

Large Magellanic Cloud Large Magellanic Cloud Distance 50 kpcDistance 50 kpc(160.000 light years)(160.000 light years)

Tarantula NebulaTarantula Nebula

Supernova 1987ASupernova 1987A23 February 198723 February 1987


Supernova Neutrinos 20 Jahre nach SN 1987ASupernova Neutrinos 20 Jahre nach SN 1987A


Crab NebulaCrab Nebula


HeliumHelium--burning starburning star

HeliumHeliumBurningBurning

HydrogenHydrogenBurningBurning

MainMain--sequence starsequence star

Hydrogen BurningHydrogen Burning

Stellar Collapse and Supernova ExplosionStellar Collapse and Supernova Explosion


HeliumHelium--burning starburning star

HeliumHeliumBurningBurning

HydrogenHydrogenBurningBurning

MainMain--sequence starsequence star

Hydrogen BurningHydrogen Burning

Onion structureOnion structure

Degenerate iron core:Degenerate iron core:ρρ ≈≈ 101099 g cmg cm−−33

T T ≈≈ 101010 10 KKMMFeFe ≈≈ 1.5 M1.5 MsunsunRRFeFe ≈≈ 8000 km8000 km

Collapse (implosion)Collapse (implosion)



Collapse (implosion)Collapse (implosion)ExplosionExplosionNewborn Neutron StarNewborn Neutron Star

~ 50 km~ 50 km

ProtoProto--Neutron StarNeutron Starρρ ≈≈ ρρnucnuc == 33 ××10101414 g cmg cm−−33

T T ≈≈ 30 MeV30 MeV

NeutrinoNeutrinoCoolingCooling



Newborn Neutron StarNewborn Neutron Star

~ 50 km~ 50 km

ProtoProto--Neutron StarNeutron Starρρ ≈≈ ρρnucnuc == 33 ××10101414 g cmg cm−−33

T T ≈≈ 30 MeV30 MeV

NeutrinoNeutrinoCoolingCooling

Gravitational binding energyGravitational binding energy

EEbb ≈≈ 3 3 ×× 10105353 erg erg ≈≈ 17% M17% MSUN SUN cc22

This shows up as This shows up as 99% Neutrinos99% Neutrinos

1% Kinetic energy of explosion1% Kinetic energy of explosion(1% of this into cosmic rays) (1% of this into cosmic rays)

0.01% Photons, outshine host galaxy0.01% Photons, outshine host galaxy

Neutrino luminosityNeutrino luminosity

LLνν ≈≈ 3 3 ×× 10105353 erg / 3 secerg / 3 sec≈≈ 3 3 ×× 10101919 LLSUNSUN

While it lasts, outshines the entireWhile it lasts, outshines the entirevisible universevisible universe



Neutrino Signal of Supernova 1987ANeutrino Signal of Supernova 1987A

Within clock uncertainties,Within clock uncertainties,signals are contemporaneoussignals are contemporaneous

KamiokandeKamiokande--II (Japan)II (Japan)Water Cherenkov detectorWater Cherenkov detector2140 tons2140 tonsClock uncertainty Clock uncertainty ±±1 min1 min

IrvineIrvine--MichiganMichigan--Brookhaven (US)Brookhaven (US)Water Cherenkov detectorWater Cherenkov detector6800 tons6800 tonsClock uncertainty Clock uncertainty ±±50 ms50 ms

Baksan Scintillator TelescopeBaksan Scintillator Telescope(Soviet Union), 200 tons(Soviet Union), 200 tonsRandom event cluster ~ 0.7/dayRandom event cluster ~ 0.7/dayClock uncertainty Clock uncertainty +2/+2/--54 s54 s


SN 1987A Event No.9 in Kamiokande SN 1987A Event No.9 in Kamiokande

Kamiokande DetectorKamiokande Detector

Hirata et al., PRD 38 (1988) 448Hirata et al., PRD 38 (1988) 448


Thermonuclear vs. CoreThermonuclear vs. Core--Collapse SupernovaeCollapse Supernovae

Core collapse (Type II, Ib/c)Core collapse (Type II, Ib/c)Thermonuclear (Type Ia)Thermonuclear (Type Ia)

Chandrasekhar limit is reached Chandrasekhar limit is reached −− MMChCh ≈≈ 1.5 M1.5 Msunsun (2Y(2Yee))22

C O L L A P S E S E T S I NC O L L A P S E S E T S I N

Nuclear burning of C and O ignitesNuclear burning of C and O ignites→→ Nuclear deflagrationNuclear deflagration((““Fusion bombFusion bomb”” triggered by collapse)triggered by collapse)

Collapse to nuclear densityCollapse to nuclear densityBounce & shock Bounce & shock Implosion Implosion →→ ExplosionExplosion

Gain of nuclear binding energyGain of nuclear binding energy~ 1 MeV per nucleon ~ 1 MeV per nucleon

Gain of gravitational binding energyGain of gravitational binding energy~~ 100 MeV per nucleon100 MeV per nucleon99% into neutrinos 99% into neutrinos

Powered by gravityPowered by gravityPowered by nuclear binding energyPowered by nuclear binding energy

Comparable Comparable ““visiblevisible”” energy release of energy release of ~ 3 ~ 3 ×× 10105151ergerg

•• CarbonCarbon--oxygen white dwarfoxygen white dwarf(remnant of(remnant oflowlow--mass star)mass star)

•• Accretes matterAccretes matterfrom companionfrom companion

•• Degenerate iron coreDegenerate iron coreof evolved massive starof evolved massive star

•• Accretes matter Accretes matter by nuclear burningby nuclear burningat its surfaceat its surface



Explosion Mechanismfor Core-Collapse SNeExplosion Mechanismfor Core-Collapse SNe


Collapse and Prompt ExplosionCollapse and Prompt Explosion

Supernova explosion primarily a hydrodynamical phenomenonSupernova explosion primarily a hydrodynamical phenomenon

Movies by J.A.Font, Numerical Hydrodynamics in General RelativitMovies by J.A.Font, Numerical Hydrodynamics in General Relativityyhttp://www.livingreviews.orghttp://www.livingreviews.org

VelocityVelocity DensityDensity


Why No Prompt Explosion?Why No Prompt Explosion?

DissociatedDissociatedMaterialMaterial

(n, p, e, (n, p, e, νν))

•• 0.1 M0.1 Msunsun of iron has a of iron has a nuclear binding energynuclear binding energy≈≈ 1.7 1.7 ×× 10105151 ergerg

•• Comparable toComparable toexplosion energyexplosion energy

•• Shock wave forms Shock wave forms within the iron corewithin the iron core

•• Dissipates its energy Dissipates its energy by dissociating the by dissociating the remaining layer of iron remaining layer of iron


Neutrinos to the RescueNeutrinos to the Rescue

Picture adapted from Janka, astroPicture adapted from Janka, astro--ph/0008432ph/0008432

Neutrino heatingNeutrino heatingincreases pressureincreases pressurebehind shock frontbehind shock front


Supernova Delayed Explosion ScenarioSupernova Delayed Explosion Scenario


Standing Accretion Shock Instability (SASI)Standing Accretion Shock Instability (SASI)

Mezzacappa et al., http://www.phy.ornl.gov/tsi/pages/simulationsMezzacappa et al., http://www.phy.ornl.gov/tsi/pages/simulations.html.html


Gravitational Waves from CoreGravitational Waves from Core--Collapse SupernovaeCollapse Supernovae

MMüüller, Rampp, Buras, Janka, & Shoemaker,ller, Rampp, Buras, Janka, & Shoemaker,“Towards gravitational wave signals from“Towards gravitational wave signals fromrealistic core collapse supernova models,”realistic core collapse supernova models,”astroastro--ph/0309833ph/0309833

The gravitationalThe gravitational--wave signal from convectionwave signal from convectionis a generic and dominating featureis a generic and dominating feature

BounceBounce

ConvectionConvection

Asymmetric neutrino emissionAsymmetric neutrino emission


Supernova Neutrinos 20 Jahre nach SN 1987ASupernova Neutrinos 20 Jahre nach SN 1987ASome Particle-Physics

Lessons from SN 1987ASome Particle-Physics

Lessons from SN 1987A


Neutrino Mass Sensitivity by Signal DispersionNeutrino Mass Sensitivity by Signal Dispersion

TimeTime--ofof--flight delayflight delayof massive neutrinosof massive neutrinos

22

eV1m

EMeV10

kpc10D

ms1.5t ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=Δ ν

ν

22

eV1m

EMeV10

kpc10D

ms1.5t ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=Δ ν

ν

SN 1987ASN 1987A(50 kpc)(50 kpc) mmνν ≲≲ 20 eV20 eV

E E ≈≈ 20 MeV, 20 MeV, ΔΔt t ≈≈ 10 s10 sSimple estimate or detailed maximumSimple estimate or detailed maximumlikelihood analysis give similar resultslikelihood analysis give similar results

Future Future Galactic SNGalactic SNat 10 kpcat 10 kpc(Super(Super--K)K)

mmνν ~ 3 eV~ 3 eVRiseRise--time of signal ~ 10 mstime of signal ~ 10 ms(Totani, PRL 80:2040, 1998)(Totani, PRL 80:2040, 1998)

mmνν ~ 1 eV~ 1 eVFull signalFull signal(Nardi & Zuluaga, (Nardi & Zuluaga, NPB 731:140, 2005)NPB 731:140, 2005)

With lateWith lateblackblack--holeholeformationformation

mmνν ~ 2 eV~ 2 eVCutoff “infinitely” fastCutoff “infinitely” fast(Beacom et al., PRD 63:073011, 2001)(Beacom et al., PRD 63:073011, 2001)

mmνν ~ 1~ 1−−2 eV2 eVD D ≈≈ 750750 kpc, kpc, ΔΔt t ≈≈ 10 s10 sfew tens of eventsfew tens of events

Future SN inFuture SN inAndromedaAndromeda(Megatonne)(Megatonne)


Early Lightcurve of SN 1987AEarly Lightcurve of SN 1987A

Adapted fromAdapted fromArnett et al.,Arnett et al.,ARAA 27 (1989)ARAA 27 (1989)

ExpectedExpectedvisual visual brightnessbrightnessevolutionevolution

ExpectedExpectedbolometric bolometric brightnessbrightnessevolutionevolution

Neutrinos severalNeutrinos severalhours before light hours before light


Do Neutrinos Gravitate?Do Neutrinos Gravitate?

Neutrinos arrive a few hours earlier than photons Neutrinos arrive a few hours earlier than photons →→ Early warning (SNEWS)Early warning (SNEWS)SN 1987A: Transit time for photons and neutrinos equal to withinSN 1987A: Transit time for photons and neutrinos equal to within ~ 3h~ 3h

Equal within ~ 1 Equal within ~ 1 −− 4 4 ××1010−−33

Shapiro time delay for particles moving in a Shapiro time delay for particles moving in a gravitational potential gravitational potential

Longo, PRL 60:173,1988Longo, PRL 60:173,1988Krauss & Tremaine, PRL 60:176,1988Krauss & Tremaine, PRL 60:176,1988

•• Proves directly that neutrinos respond to gravity in the usual Proves directly that neutrinos respond to gravity in the usual waywaybecause for photons gravitational lensing already proves thisbecause for photons gravitational lensing already proves this pointpoint

•• Cosmological limits Cosmological limits ΔΔNNνν ≲≲ 1 much worse test of neutrino gravitation1 much worse test of neutrino gravitation•• Provides limits on parameters of certain nonProvides limits on parameters of certain non--GR theories of gravitationGR theories of gravitation•• Photons likely obscured for next galactic SN, so this result prPhotons likely obscured for next galactic SN, so this result probablyobably

unique to SN 1987A unique to SN 1987A

∫ months51dt)]t(r[U2t BAShapiro −≈−=Δ ∫ months51dt)]t(r[U2t BAShapiro −≈−=Δ


The EnergyThe Energy--Loss ArgumentLoss Argument

NeutrinoNeutrinospheresphere

NeutrinoNeutrinodiffusiondiffusion

LateLate--time signal most sensitive observabletime signal most sensitive observable

Emission of very weakly interactingEmission of very weakly interactingparticles would “steal” energy from theparticles would “steal” energy from theneutrino burst and shorten it.neutrino burst and shorten it.(Early neutrino burst powered by accretion,(Early neutrino burst powered by accretion,not sensitive to volume energy loss.)not sensitive to volume energy loss.)

Volume emissionVolume emissionof novel particlesof novel particles

SN 1987A neutrino signalSN 1987A neutrino signal


DirectDirectsearchsearch

Too muchToo muchcold dark mattercold dark matter

TeleTelescopescopeExperimentsExperiments

Globular clustersGlobular clusters(a(a--γγ--coupling)coupling)

Too manyToo manyeventsevents

Too muchToo muchenergy lossenergy loss

SN 1987A (aSN 1987A (a--NN--coupling)coupling)

Axion BoundsAxion Bounds

101033 101066 101099 10101212 [[GeVGeV]] ffaa

eVeVkeVkeV meVmeV μμeVeVmmaa

Too much hot dark matterToo much hot dark matter

CASTCAST ADMXADMX


Sterile NeutrinosSterile Neutrinos

To avoid complete energy loss in ~ 1 sTo avoid complete energy loss in ~ 1 s

sinsin22(2(2ΘΘeses) ) ≲≲ 3 3 ×× 1010−−1010

Average scattering rate in SN coreAverage scattering rate in SN coreinvolving ordinary leftinvolving ordinary left--handed neutrinoshanded neutrinos

110L s10 −≈Γ 110L s10 −≈Γ

Electron neutrino appears as sterile neutrinoElectron neutrino appears as sterile neutrinoin ½ sinin ½ sin22(2(2ΘΘeses) of all cases) of all cases

Les2

21

s )2(sin ΓΘ≈Γ Les2

21

s )2(sin ΓΘ≈Γ

1110es

221 s1s10)2(sin −− <Θ 1110

es2

21 s1s10)2(sin −− <Θ

ActiveActive--sterilesterilemixingmixing

sνsνee

ppWW

nn


Sterile Neutrino LimitsSterile Neutrino Limits

See also:See also:

MaalampiMaalampi & & PeltoniemiPeltoniemi::Effects of the 17Effects of the 17--keVkeVneutrino in supernovae neutrino in supernovae PLB 269:357,1991PLB 269:357,1991

HidakaHidaka & & FullerFuller::Dark matter sterileDark matter sterileneutrinos in stellarneutrinos in stellarcollapse: alteration ofcollapse: alteration ofenergy/lepton numberenergy/lepton numbertransport and atransport and amechanism formechanism forsupernova explosionsupernova explosionenhancementenhancementPRD 74:125015,2006 PRD 74:125015,2006


Supernova 1987A Limit on Large Extra DimensionsSupernova 1987A Limit on Large Extra Dimensions

Cullen & Perelstein, hepCullen & Perelstein, hep--ph/9904422ph/9904422Hanhart et al., nuclHanhart et al., nucl--th/0007016th/0007016

SN 1987A energySN 1987A energy--loss argument:loss argument:

R R << 1 1 mmm, M m, M > > 9 TeV 9 TeV (n (n = = 2)2)

R R << 1 nm, M 1 nm, M >> 0.7 TeV (n 0.7 TeV (n == 3)3)

Originally the most restrictiveOriginally the most restrictivelimit on such theories, exceptlimit on such theories, exceptfor cosmological argumentsfor cosmological arguments

SN core emits large flux of SN core emits large flux of KK gravity modes byKK gravity modes bynucleonnucleon--nucleon bremsstrahlungnucleon bremsstrahlung

Large multiplicity of modesLarge multiplicity of modes

RT ~ 10RT ~ 101111

for R ~ 1 mm, T ~ 30 MeVfor R ~ 1 mm, T ~ 30 MeV

2PlMRate −∝ 2PlMRate −∝

n2Pl

n

2Pl

n

M

T

M

)RT(Rate +∝∝ n2

Pl

n

2Pl

n

M

T

M

)RT(Rate +∝∝


Supernova Neutrinos 20 Jahre nach SN 1987ASupernova Neutrinos 20 Jahre nach SN 1987ANeutrinos from the

Next Galactic SupernovaNeutrinos from the

Next Galactic Supernova


Local Group of GalaxiesLocal Group of Galaxies

250250

6060

3030

Events in a detector withEvents in a detector with30 x Super30 x Super--K fiducial volume,K fiducial volume,e.g. Hypere.g. Hyper--KamiokandeKamiokande


CoreCore--Collapse SN Rate in the Milky WayCollapse SN Rate in the Milky Way

Gamma rays fromGamma rays from2626Al (Milky Way)Al (Milky Way)

Historical galacticHistorical galacticSNe (all types)SNe (all types)

SN statistics inSN statistics inexternal galaxiesexternal galaxies

No galacticNo galacticneutrino burstneutrino burst

CoreCore--collapse SNe per centurycollapse SNe per century00 11 22 33 44 55 66 77 88 99 1010

van den Bergh & McClure (1994)van den Bergh & McClure (1994)

Cappellaro & Turatto (2000)Cappellaro & Turatto (2000)

Diehl et al. (2006)Diehl et al. (2006)

Tammann et al. (1994)Tammann et al. (1994)Strom (1994)Strom (1994)

90 90 %% CL (25 y obserservation)CL (25 y obserservation) Alekseev et al. (1993)Alekseev et al. (1993)

References: van den Bergh & McClure, ApJ 425 (1994) 205. CappellReferences: van den Bergh & McClure, ApJ 425 (1994) 205. Cappellaro & Turatto, astroaro & Turatto, astro--ph/0012455. Diehl et al., Nature 439 (2006) 45. Strom, Astron. Aph/0012455. Diehl et al., Nature 439 (2006) 45. Strom, Astron. Astrophys. 288 (1994) L1. strophys. 288 (1994) L1. Tammann et al., ApJ 92 (1994) 487. Alekeseev et al., JETP 77 (19Tammann et al., ApJ 92 (1994) 487. Alekeseev et al., JETP 77 (1993) 339 and my update.93) 339 and my update.


Nearby Galaxies with Many Observed SupernovaeNearby Galaxies with Many Observed Supernovae

M83 (NGC 5236, Southern Pinwheel)M83 (NGC 5236, Southern Pinwheel)D = 4.5 MpcD = 4.5 Mpc

Observed Supernovae: Observed Supernovae: 1923A,1923A, 1945B,1945B, 1950B,1950B, 1957D,1957D, 1968L,1968L,1983N 1983N

NGC 6946 NGC 6946 D = (5.5 ± 1) MpcD = (5.5 ± 1) Mpc

Observed Supernovae:Observed Supernovae:1917A,1917A, 1939C,1939C, 1948B,1948B, 1968D,1968D, 1969P,1969P,1980K,1980K, 2002hh,2002hh, 2004et,2004et, 2008S2008S


Large Detectors for Supernova NeutrinosLarge Detectors for Supernova Neutrinos

SuperSuper--Kamiokande (10Kamiokande (1044))KamLAND (400)KamLAND (400)

MiniBooNEMiniBooNE(200)(200)

In brackets eventsIn brackets eventsfor a “fiducial SN”for a “fiducial SN”at distance 10 kpcat distance 10 kpc

LVD (400)LVD (400)Borexino (100)Borexino (100)

IceCube (10IceCube (1066))

BaksanBaksan(100)(100)


SSuperuperNNova ova EEarly arly WWarning arning SSystem (SNEWS)ystem (SNEWS)

Neutrino observation can alert astronomersNeutrino observation can alert astronomersseveral hours in advance to a supernova.several hours in advance to a supernova.To avoid false alarms, require alarm from atTo avoid false alarms, require alarm from atleast two experiments.least two experiments.

CoincidenceCoincidenceServer Server @ BNL@ BNL

SuperSuper--KK

AlertAlert

Others ?Others ?

LVDLVD

IceCubeIceCube

http://snews.bnl.govhttp://snews.bnl.govastroastro--ph/0406214ph/0406214

Supernova 1987ASupernova 1987AEarly Light CurveEarly Light Curve


Simulated Supernova Signal at SuperSimulated Supernova Signal at Super--KamiokandeKamiokande

Simulation for SuperSimulation for Super--Kamiokande SN signal at 10 kpc,Kamiokande SN signal at 10 kpc,based on a numerical Livermore modelbased on a numerical Livermore model

[Totani, Sato, Dalhed & Wilson, ApJ 496 (1998) 216][Totani, Sato, Dalhed & Wilson, ApJ 496 (1998) 216]

AccretionAccretionPhasePhase

KelvinKelvin--HelmholtzHelmholtzCooling PhaseCooling Phase


Supernova Pointing with NeutrinosSupernova Pointing with Neutrinos

•• Beacom & Vogel: Can a supernova be located by its neutrinos?Beacom & Vogel: Can a supernova be located by its neutrinos?[astro[astro--ph/9811350] ph/9811350]

•• Tomàs, Semikoz, Raffelt, Kachelriess & Dighe: Supernova pointinTomàs, Semikoz, Raffelt, Kachelriess & Dighe: Supernova pointing withg withlowlow-- and highand high--energy neutrino detectors [hepenergy neutrino detectors [hep--ph/0307050]ph/0307050]

ee ν→ν ee ν→ν

+→ν nepe+→ν nepe

SKSK

SK SK ×× 3030

Neutron tagging efficiencyNeutron tagging efficiency

90 90 %%NoneNone

7.8º7.8º 3.2º3.2º

1.4º1.4º 0.6º0.6º

9595%% CL halfCL half--cone opening anglecone opening angle


IceCube as a Supernova Neutrino DetectorIceCube as a Supernova Neutrino Detector

Each optical module (OM) picks upEach optical module (OM) picks upCherenkov light from its neighborhood.Cherenkov light from its neighborhood.SN appears as “correlated noise”.SN appears as “correlated noise”.

•• About 300About 300CherenkovCherenkovphotons photons per OMper OMfrom a SNfrom a SNat 10 kpcat 10 kpc

•• NoiseNoiseper OMper OM< 500 Hz< 500 Hz

•• Total ofTotal of4800 OMs4800 OMsin IceCubein IceCube

IceCube SN signal at 10 kpc, basedIceCube SN signal at 10 kpc, basedon a numerical Livermore modelon a numerical Livermore model[Dighe, Keil & Raffelt, hep[Dighe, Keil & Raffelt, hep--ph/0303210]ph/0303210]

Method first discussed byMethod first discussed byHalzenHalzen, , JacobsenJacobsen & & ZasZasastroastro--ph/9512080ph/9512080


LAGUNA LAGUNA -- Approved FP7 Design StudyApproved FP7 Design Study

LLarge arge AApparati for pparati for GGrand rand UUnification and nification and NNeutrino eutrino AAstrophysicsstrophysics(see also arXiv:(see also arXiv:0705.01160705.0116))



Neutrinos FromAll Cosmic Supernovae

Neutrinos FromAll Cosmic Supernovae


Diffuse Background Flux of SN NeutrinosDiffuse Background Flux of SN Neutrinos

1 SNu ~ 4 L1 SNu ~ 4 Lνν / L/ Lγγ,B,BAverage neutrinoAverage neutrinoluminosity of galaxiesluminosity of galaxies~ photon luminosity~ photon luminosity

1 SNu 1 SNu == 1 SN / 101 SN / 101010 LLsun,Bsun,B / 100 years/ 100 years

LLsun,Bsun,B == 0.54 L0.54 Lsunsun == 2 2 ×× 10103333 erg/serg/s

EEνν ~ 3 ~ 3 ×× 10105353 erg per coreerg per core--collapse SNcollapse SN

For galaxies, averageFor galaxies, averagenuclear & gravitationalnuclear & gravitationalenergy release comparableenergy release comparable

•• Photons come fromPhotons come from nuclear energynuclear energy

•• Neutrinos from Neutrinos from gravitational energygravitational energy

PresentPresent--day SN rate of ~ 1 SNu, extrapolated to the entire universe,day SN rate of ~ 1 SNu, extrapolated to the entire universe,

corresponds to corresponds to ννee flux of ~ 1 cmflux of ~ 1 cm−−22 ss−−11

Realistic flux is dominated by much larger early starRealistic flux is dominated by much larger early star--formation rateformation rate•• Upper limit ~ 54 cmUpper limit ~ 54 cm−−22 ss−−11

[Kaplinghat et al., astro[Kaplinghat et al., astro--ph/9912391]ph/9912391]•• “Realistic estimate” ~ 10 cm“Realistic estimate” ~ 10 cm−−22 ss−−11

[Hartmann & Woosley, Astropart. Phys. 7 (1997) 137][Hartmann & Woosley, Astropart. Phys. 7 (1997) 137]Measurement would tell us about early history of star formationMeasurement would tell us about early history of star formation


Experimental Limits on Relic Supernova NeutrinosExperimental Limits on Relic Supernova Neutrinos

Cline, astroCline, astro--ph/0103138ph/0103138

UpperUpper--limit flux oflimit flux ofKaplinghat et al., Kaplinghat et al., astroastro--ph/9912391ph/9912391Integrated 54 cmIntegrated 54 cm--22 ss--11

SuperSuper--K upper limitK upper limit29 cm29 cm--22 ss--1 1 for for Kaplinghat et al. spectrumKaplinghat et al. spectrum[hep[hep--ex/0209028]ex/0209028]


DSNB Measurement with Neutron TaggingDSNB Measurement with Neutron Tagging

Beacom & Vagins, hepBeacom & Vagins, hep--ph/0309300 ph/0309300 [Phys. Rev. Lett., 93:171101, 2004] [Phys. Rev. Lett., 93:171101, 2004]

Pushing the boundaries of neutrinoPushing the boundaries of neutrinoastronomy to cosmological distancesastronomy to cosmological distances

Future largeFuture large--scale scintillatorscale scintillatordetectors (e.g. LENA with 50 kt)detectors (e.g. LENA with 50 kt)

•• Inverse beta decay reaction taggedInverse beta decay reaction tagged•• Location with smaller reactor fluxLocation with smaller reactor flux

(e.g. Pyh(e.g. Pyhääsalmi in Finland) couldsalmi in Finland) couldallow for lower thresholdallow for lower threshold



Oscillations of Supernova Neutrinos

Oscillations of Supernova Neutrinos


Structure of Supernova Neutrino SignalStructure of Supernova Neutrino Signal

1.1. Collapse (infall phase)Collapse (infall phase)2.2. Shock break outShock break out3.3. Matter accretionMatter accretion4.4. KelvinKelvin--Helmholtz coolingHelmholtz cooling

Traps Traps neutrinosneutrinosand and leptonleptonnumbernumberof outerof outercore core layerslayers


Neutronization Burst as a Standard CandleNeutronization Burst as a Standard Candle

Different MassDifferent Mass Neutrino TransportNeutrino Transport Nuclear EoSNuclear EoS

KachelriessKachelriess,,TomàsTomàs, , BurasBuras,,JankaJanka, , MarekMarek& & RamppRampp,,astroastro--phph/0412082/0412082

If mixingIf mixingscenario isscenario isknown,known,perhaps bestperhaps bestmethod tomethod todeterminedetermineSN distance,SN distance,especially ifespecially ifobscuredobscured

(better than(better than55--10%)10%)


FlavorFlavor--Dependent Fluxes and SpectraDependent Fluxes and Spectra

Broad characteristicsBroad characteristics•• Duration a few secondsDuration a few seconds•• ⟨⟨EEνν⟩⟩ ~ ~ 1010−−20 MeV20 MeV•• ⟨⟨EEνν⟩⟩ increases with timeincreases with time•• Hierarchy of energiesHierarchy of energies

•• Approximate equipartitionApproximate equipartitionof energy between flavorsof energy between flavors

xee EEE ννν << xee EEE ννν <<

Livermore numerical modelLivermore numerical modelApJ 496 (1998) 216ApJ 496 (1998) 216

Prompt Prompt ννeedeleptonizationdeleptonizationburstburst

ννee

ννee

ννxx__

However, in traditionalHowever, in traditionalsimulations transport simulations transport of of ννμμ and and ννττ schematicschematic

•• Incomplete microphysicsIncomplete microphysics

•• Crude numerics to coupleCrude numerics to coupleneutrino transport withneutrino transport withhydro codehydro code


FlavorFlavor--Dependent Neutrino Fluxes vs. Equation of StateDependent Neutrino Fluxes vs. Equation of State

Kitaura, Janka & Hillebrandt, “Explosions of OKitaura, Janka & Hillebrandt, “Explosions of O--NeNe--Mg cores, the CrabMg cores, the Crabsupernova, and subluminous Type IIsupernova, and subluminous Type II--P supernovae”, astroP supernovae”, astro--ph/0512065ph/0512065

Wolff & Hillebrandt nuclear EoS (stiff) Lattimer & Swesty nuclear EoS (soft)


LevelLevel--Crossing Diagram in a SN EnvelopeCrossing Diagram in a SN Envelope

Dighe & Smirnov, Identifying the neutrino mass spectrum from a sDighe & Smirnov, Identifying the neutrino mass spectrum from a supernovaupernovaneutrino burst, astroneutrino burst, astro--ph/9907423ph/9907423

Normal mass hierarchyNormal mass hierarchy Inverted mass hierarchyInverted mass hierarchy


Spectra Emerging from SupernovaeSpectra Emerging from Supernovae

Primary fluxesPrimary fluxes

for for

for for

for for

0eF0eF0eF0eF0xF0xF

eνeν

eνeν

ττμμ νννν ,,, ττμμ νννν ,,,

After leaving theAfter leaving thesupernova envelope,supernova envelope,the fluxes arethe fluxes arepartially swappedpartially swapped

0x

0e

0e F)p1(FpF −+= 0

x0e

0e F)p1(FpF −+=

0x

0e

0e F)p1(FpF −+= 0

x0e

0e F)p1(FpF −+=

0e

0e

0xx4

1 F4

p1F

4p1

F4

pp2F

−+

−+

++=∑ 0

e0e

0xx4

1 F4

p1F

4p1

F4

pp2F

−+

−+

++=∑

NormalNormal

InvertedInverted

sinsin22(2(2ΘΘ1313))

≲≲ 1010−−55

≳≳ 1010−−33

AnyAny

Mass orderingMass ordering

sinsin22((ΘΘ1212)) ≈≈ 0.30.3

00 coscos22((ΘΘ1212)) ≈≈ 0.70.7

sinsin22((ΘΘ1212)) ≈≈ 0.30.3 coscos22((ΘΘ1212)) ≈≈ 0.70.7

00

CaseCase

AA

BB

CC

Survival probabilitySurvival probability

)for(p eν )for(p eν )for(p eν )for(p eν


Oscillation of Supernova AntiOscillation of Supernova Anti--NeutrinosNeutrinos

Measured Measured spectrum at a detector like spectrum at a detector like SuperSuper--Kamiokande Kamiokande

eνeν Assumed flux parametersAssumed flux parameters

Flux ratioFlux ratio 1:8.0:e =νν μ 1:8.0:e =νν μ

MeV15)(E e =ν MeV15)(E e =ν

MeV18)(E x =ν MeV18)(E x =ν

Mixing parametersMixing parameters22

sun meV60m =Δ 22sun meV60m =Δ

9.0)2(sin2 =θ 9.0)2(sin2 =θ

ΠΠ(Dighe, Kachelriess, Keil, Raffelt, Semikoz, Tomàs),(Dighe, Kachelriess, Keil, Raffelt, Semikoz, Tomàs),hephep--ph/0303210, hepph/0303210, hep--ph/0304150, hepph/0304150, hep--ph/0307050, hepph/0307050, hep--ph/0311172 ph/0311172

No oscillationsNo oscillations

Oscillations in SN envelopeOscillations in SN envelope

Earth effects includedEarth effects included


One detector observes SN shadowed by EarthOne detector observes SN shadowed by Earth

ModelModel--Independent Strategies for Observing Earth EffectsIndependent Strategies for Observing Earth Effects

Case 1:Case 1:•• Another detectorAnother detector

observes SN directlyobserves SN directly•• Identify Earth effectsIdentify Earth effects

by comparing signalsby comparing signals

Dighe, Keil & Raffelt, “Identifying Earth matterDighe, Keil & Raffelt, “Identifying Earth mattereffects on supernova neutrinos at a single detector”effects on supernova neutrinos at a single detector”[hep[hep--ph/0304150]ph/0304150]

Case2: Identify “wiggles” in signal of single detectorCase2: Identify “wiggles” in signal of single detectorProblem: Smearing by limited energy resolutionProblem: Smearing by limited energy resolution

Water CherenkovWater CherenkovNeed megaton detectorNeed megaton detectorwith ~ 10with ~ 105 5 eventsevents

Scintillator detectorScintillator detector~ 2000 events~ 2000 events

may be enoughmay be enough

If 13If 13--mixing angle ismixing angle isknown to be “large”,known to be “large”,e.g.e.g. fromfrom DoubleDouble Chooz,Chooz,observed “wiggles” inobserved “wiggles” inenergy spectrum signifyenergy spectrum signifynormal mass hierarchynormal mass hierarchy


Supernova Shock Propagation and Neutrino OscillationsSupernova Shock Propagation and Neutrino Oscillations

Schirato & Fuller:Schirato & Fuller:Connection betweenConnection betweensupernova shocks,supernova shocks,flavor transformation,flavor transformation,and the neutrino signaland the neutrino signal[astro[astro--ph/0205390]ph/0205390]

R. Tomàs, M. Kachelriess,R. Tomàs, M. Kachelriess,G. Raffelt, A. Dighe,G. Raffelt, A. Dighe,H.H.--T. Janka & L. Scheck: T. Janka & L. Scheck: Neutrino signatures ofNeutrino signatures ofsupernova forward andsupernova forward andreverse shock propagationreverse shock propagation[[astroastro--ph/0407132ph/0407132] ]

ResonanceResonancedensity fordensity for

2atmmΔ 2atmmΔ


ShockShock--Wave Propagation in IceCubeWave Propagation in IceCube

ChoubeyChoubey, , HarriesHarries & & RossRoss, “Probing neutrino oscillations from supernovae shock, “Probing neutrino oscillations from supernovae shockwaves via the IceCube detector”, astrowaves via the IceCube detector”, astro--ph/0604300ph/0604300

Normal HierarchyNormal Hierarchy

Inverted HierarchyInverted HierarchyNo shockwaveNo shockwave

Inverted HierarchyInverted HierarchyForward shockForward shock

Inverted HierarchyInverted HierarchyForward & reverse shockForward & reverse shock

,8.0)(Flux)(Flux

x

e =νν ,8.0

)(Flux)(Flux

x

e =νν

MeV18E,MeV15E xe == νν MeV18E,MeV15E xe == νν



Collective Supernova Neutrino OscillationsCollective Supernova Neutrino Oscillations


Neutrino Density Streaming off a Supernova CoreNeutrino Density Streaming off a Supernova Core

Typical luminosity in oneTypical luminosity in oneneutrino speciesneutrino species

Corresponds to a neutrinoCorresponds to a neutrinonumber density ofnumber density of

CurrentCurrent--current structurecurrent structureof weak interactionof weak interactioncauses suppression ofcauses suppression ofeffective potential foreffective potential forcollinearcollinear--moving particlesmoving particles

NuNu--nu refractive effectnu refractive effectdecreases asdecreases as

Appears to be negligibleAppears to be negligible

serg52103L ×=ν serg52103L ×=ν

2335

Rkm

cm103n ⎟⎠⎞

⎜⎝⎛×= −

ν2

335R

kmcm103n ⎟

⎠⎞

⎜⎝⎛×= −

ν

Equivalent Neutrino density ∝ R −2

Nu-nu refraction ∝R −4

)cos1(GV Fweak θ−∝ )cos1(GV Fweak θ−∝

4RV −∝νν4RV −∝νν


Collective Effects in Neutrino Flavor OscillationsCollective Effects in Neutrino Flavor Oscillations

Collapsed supernova core or accretion torus ofCollapsed supernova core or accretion torus ofmerging neutron stars:merging neutron stars:

•• Neutrino flux very dense: Up to 10Neutrino flux very dense: Up to 103535 cmcm−−3 3

•• NeutrinoNeutrino--neutrino interaction energy neutrino interaction energy much larger than vacuum oscillation frequencymuch larger than vacuum oscillation frequency

•• Large “matter effect” of neutrinos on eachLarge “matter effect” of neutrinos on eachotherother

•• NonNon--linear oscillation effectslinear oscillation effects

•• Assume 80% antiAssume 80% anti--neutrinosneutrinos•• Vacuum oscillation frequencyVacuum oscillation frequency

ωω = 0.3 km= 0.3 km−−11

•• NeutrinoNeutrino--neutrino interaction neutrino interaction energy at nu sphere (r = 10 km)energy at nu sphere (r = 10 km)μμ = 0.3= 0.3××101055 kmkm−−11

•• Falls off approximately as Falls off approximately as rr−−44

(geometric flux dilution and nus(geometric flux dilution and nusbecome more cobecome more co--linear)linear)


Survival probability Survival probability ννeeSurvival probability Survival probability ννee

NormalNormalHierarchyHierarchy

atm atm ΔΔmm22

ΘΘ1313 closecloseto Choozto Choozlimitlimit

InvertedInvertedHierarchyHierarchy

NoNonunu--nu effectnu effect

NoNonunu--nu effectnu effect

SelfSelf--Induced Flavor Oscillations of SN NeutrinosInduced Flavor Oscillations of SN Neutrinos

RealisticRealisticnunu--nu effectnu effect

BipolarBipolarcollectivecollectiveoscillationsoscillations(single(single--angleangleapproximation)approximation)

MSWMSW

RealisticRealisticnunu--nu effectnu effect

MSWMSWeffecteffect


Mass Hierarchy at Extremely Small ThetaMass Hierarchy at Extremely Small Theta--1313

Dasgupta, Dighe & Mirizzi, arXiv:0802.1481Dasgupta, Dighe & Mirizzi, arXiv:0802.1481

Ratio of spectra inRatio of spectra intwo water Cherenkovtwo water Cherenkovdetectors (0.4 Mton),detectors (0.4 Mton),one shadowed by theone shadowed by theEarth, the other notEarth, the other not

Using Earth matter effects to diagnose transformationsUsing Earth matter effects to diagnose transformations


Collective SN neutrino oscillations 2006Collective SN neutrino oscillations 2006--2008 (I)2008 (I)

“Bipolar” collective transformations“Bipolar” collective transformationsimportant, even for dense matterimportant, even for dense matter

•• Duan, Fuller & Qian Duan, Fuller & Qian astroastro--ph/0511275ph/0511275

Numerical simulationsNumerical simulations•• Including multiIncluding multi--angle effectsangle effects•• Discovery of “spectral splits”Discovery of “spectral splits”

•• Duan, Fuller, Carlson & QianDuan, Fuller, Carlson & Qianastroastro--ph/0606616, 0608050ph/0606616, 0608050

•• Pendulum in flavor spacePendulum in flavor space•• Collective pair annihilationCollective pair annihilation•• Pure precession modePure precession mode

•• Hannestad, Raffelt, Sigl & WongHannestad, Raffelt, Sigl & Wongastroastro--ph/0608695ph/0608695

•• Duan, Fuller, Carlson & QianDuan, Fuller, Carlson & Qianastroastro--ph/0703776ph/0703776

SelfSelf--maintained coherencemaintained coherencevs. selfvs. self--induced decoherenceinduced decoherencecaused by multicaused by multi--angle effectsangle effects

•• Sawyer, hepSawyer, hep--ph/0408265, 0503013 ph/0408265, 0503013 •• Raffelt & Sigl, Raffelt & Sigl, hephep--ph/0701182ph/0701182•• EstebanEsteban--Pretel, Pastor, Tomàs,Pretel, Pastor, Tomàs,

Raffelt & Sigl, arXiv:0706.2498Raffelt & Sigl, arXiv:0706.2498

Theory of “spectral splits”Theory of “spectral splits”in terms of adiabatic evolution inin terms of adiabatic evolution inrotating framerotating frame

•• Raffelt & Smirnov,Raffelt & Smirnov,arXiv:0705.1830, 0709.4641 arXiv:0705.1830, 0709.4641

•• Duan, Fuller, Carlson & QianDuan, Fuller, Carlson & QianarXiv:0706.4293, 0707.0290 arXiv:0706.4293, 0707.0290

Independent numerical simulationsIndependent numerical simulations •• FogliFogli, , LisiLisi, , MarroneMarrone & M& MirizziirizziarXiv:0707.1998 arXiv:0707.1998


Collective SN neutrino oscillations 2006Collective SN neutrino oscillations 2006--2008 (II)2008 (II)

SecondSecond--order muorder mu--tau refractive effecttau refractive effectimportant in threeimportant in three--flavor contextflavor context

•• EstebanEsteban--Pretel, Pastor, Tomàs,Pretel, Pastor, Tomàs,Raffelt & Sigl, arXiv:0712.1137Raffelt & Sigl, arXiv:0712.1137

ThreeThree--flavor effects in Oflavor effects in O--NeNe--Mg SNeMg SNeon neutronization burston neutronization burst(MSW(MSW--prepared spectral double split)prepared spectral double split)

•• Duan, Fuller, Carlson & Qian,Duan, Fuller, Carlson & Qian,arXiv:0710.1271arXiv:0710.1271

•• Dasgupta, Dighe, Mirrizzi & Raffelt,Dasgupta, Dighe, Mirrizzi & Raffelt,arXiv:arXiv:0801.16600801.1660

Theory of threeTheory of three--flavor collectiveflavor collectiveoscillationsoscillations

•• Dasgupta & Dighe,Dasgupta & Dighe,arXiv:0712.3798arXiv:0712.3798

Identifying the neutrino mass hierarchyIdentifying the neutrino mass hierarchyat extremely small Thetaat extremely small Theta--1313

•• Dasgupta, Dighe & Mirizzi,Dasgupta, Dighe & Mirizzi,arXiv:0802.1481 arXiv:0802.1481

But for high density, conversionsBut for high density, conversionssuppressed by geometric effectsuppressed by geometric effect

•• EstebanEsteban--Pretel, Mirizzi, Pastor,Pretel, Mirizzi, Pastor,Tomàs, Raffelt, Serpico & Sigl,Tomàs, Raffelt, Serpico & Sigl,arXiv:0807.0659arXiv:0807.0659

Collective oscillations along flux linesCollective oscillations along flux linesfor nonfor non--spherical geometryspherical geometry

•• Dasgupta, Dighe, Mirizzi & Raffelt,Dasgupta, Dighe, Mirizzi & Raffelt,arXiv:0805.3300arXiv:0805.3300


Neutrino Oscillations in a Neutrino Background Neutrino Oscillations in a Neutrino Background

νννν

ff

ZZνννν

W, ZW, Z

ff

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

−+=⎟⎟

⎠

⎞⎜⎜⎝

⎛∂∂

μμ νν

νν e

n21

n21

eF

2e

n0

0nnG2

E2M

ti ⎟⎟

⎠

⎞⎜⎜⎝

⎛

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

−+=⎟⎟

⎠

⎞⎜⎜⎝

⎛∂∂

μμ νν

νν e

n21

n21

eF

2e

n0

0nnG2

E2M

ti

Neutrinos in a mediumNeutrinos in a mediumsuffer flavorsuffer flavor--dependentdependentrefractionrefraction(Wolfenstein,(Wolfenstein,PRD 17:2369, 1978) PRD 17:2369, 1978)

νννν

νν

ZZ

⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

++=⎟⎟

⎠

⎞⎜⎜⎝

⎛∂∂

μνννν

νννν

μ νν

νν

μμ

μμ eF

2en2nn

nnn2G2

E2M

ti

ee

ee⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

++=⎟⎟

⎠

⎞⎜⎜⎝

⎛∂∂

μνννν

νννν

μ νν

νν

μμ

μμ eF

2en2nn

nnn2G2

E2M

ti

ee

ee

If neutrinos form theIf neutrinos form thebackground, thebackground, therefractive index hasrefractive index has“offdiagonal elements”“offdiagonal elements”(Pantaleone,(Pantaleone,PLB 287:128, 1992)PLB 287:128, 1992)

•• One can not operationally distinguish betweenOne can not operationally distinguish between“beam” and “background”“beam” and “background”

•• Problem is fundamentally nonlinearProblem is fundamentally nonlinear


Matrices of Density in Flavor SpaceMatrices of Density in Flavor Space

Neutrino quantum fieldNeutrino quantum field

Spinors in flavor spaceSpinors in flavor space

Quantum states (amplitudes)Quantum states (amplitudes)

Variables for discussing neutrino flavor oscillationsVariables for discussing neutrino flavor oscillations

“Matrices of densities” “Matrices of densities” (analogous to occupation numbers)(analogous to occupation numbers)

“Quadratic” quantities, required for“Quadratic” quantities, required fordealing with decoherence, collisions,dealing with decoherence, collisions,PauliPauli--blocking, nublocking, nu--nunu--refraction, etc.refraction, etc.

Sufficient for “beam experiments”Sufficient for “beam experiments”

( )( ) ( ) xpi

p†

p3

3evp,tbup,ta

2

pd)x,t(

rrrr

rrr

⋅− ⎥

⎦

⎤⎢⎣

⎡−+⎮

⌡

⌠

π=Ψ

( )( ) ( ) xpi

p†

p3

3evp,tbup,ta

2

pd)x,t(

rrrr

rrr

⋅− ⎥

⎦

⎤⎢⎣

⎡−+⎮

⌡

⌠

π=Ψ

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

ΨΨΨ

=Ψ

3

2

1

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

ΨΨΨ

=Ψ

3

2

1

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

3

2

1

aaa

a⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

3

2

1

aaa

a⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

3

2

1

bbb

b⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

3

2

1

bbb

bDestructionDestructionoperators foroperators for(anti)neutrinos(anti)neutrinos

( )( )( )

( )( )( )

0a

p,tap,ta

p,tp,tp,t

†

p,t3

2

1

3

2

1

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

=ννν

r

r

r

r

r

r( )( )( )

( )( )( )

0a

p,tap,ta

p,tp,tp,t

†

p,t3

2

1

3

2

1

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

=ννν

r

r

r

r

r

rNeutrinosNeutrinos

AntiAnti--neutrinosneutrinos

( ) ( ) ( )p,tap,tap,t i†jij

rrr=ρ ( ) ( ) ( )p,tap,tap,t i

†jij

rrr=ρ

( ) ( ) ( )p,tbp,tbp,t j†iij

rrr=ρ ( ) ( ) ( )p,tbp,tbp,t j

†iij

rrr=ρ


General Equations of MotionGeneral Equations of Motion

( )]),)[(cos1(

2

qdG2],L[G2,

p2M

i pqqqp3

3FpFp

2pt

rrrrrrrrv

ρρρθπ

ρρρ −−⎮⌡

⌠++

⎥⎥⎦

⎤

⎢⎢⎣

⎡+=∂

( )]),)[(cos1(

2

qdG2],L[G2,

p2M

i pqqqp3

3FpFp

2pt

rrrrrrrrv

ρρρθπ

ρρρ −−⎮⌡

⌠++

⎥⎥⎦

⎤

⎢⎢⎣

⎡+=∂νν

( )]),)[(cos1(

2

qdG2],L[G2,

p2M

i pqqqp3

3FpFp

2pt

rrrrrrrrv

ρρρθπ

ρρρ −−⎮⌡

⌠++

⎥⎥⎦

⎤

⎢⎢⎣

⎡−=∂

( )]),)[(cos1(

2

qdG2],L[G2,

p2M

i pqqqp3

3FpFp

2pt

rrrrrrrrv

ρρρθπ

ρρρ −−⎮⌡

⌠++

⎥⎥⎦

⎤

⎢⎢⎣

⎡−=∂νν

Usual matter effect withUsual matter effect with

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

−−

−=

ττ

μμnn00

0nn000nn

Lee

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

−−

−=

ττ

μμnn00

0nn000nn

Lee

•• Vacuum oscillationsVacuum oscillationsM is neutrino mass matrixM is neutrino mass matrix

•• Note opposite sign betweenNote opposite sign betweenneutrinos and antineutrinosneutrinos and antineutrinos

Nonlinear nuNonlinear nu--nu effects are importantnu effects are importantwhen nuwhen nu--nu interaction energy exceedsnu interaction energy exceedstypical vacuum oscillation frequencytypical vacuum oscillation frequency(Do not compare with matter effect!)(Do not compare with matter effect!)

θ−=μ<Δ

=ω ν cos1nG2E2

mF

2osc θ−=μ<

Δ=ω ν cos1nG2

E2m

F2

osc


Oscillations of Neutrinos plus Antineutrinos in a BoxOscillations of Neutrinos plus Antineutrinos in a Box

Equal and densities, single energy E, withEqual and densities, single energy E, witheνeν eνeνE2

mnG2

2F e

Δωμ ν =>=

E2m

nG22

F eΔ

ωμ ν =>= ≫≫

P)PP(PBPt ×−+×+=∂ μω P)PP(PBPt ×−+×+=∂ μω

EqualEqualself termsself terms

P)PP(PBPt ×−+×−=∂ μω P)PP(PBPt ×−+×−=∂ μω

)(ν)(ν

)(ν)(ν43421 43421 4434421 4434421

Opposite vacuumOpposite vacuumoscillationsoscillations

ωμκ = ωμκ =

PPPP

BBω+ ω+

ω− ω−

PP

PP

BB

“Pendulum in flavor space”“Pendulum in flavor space”•• Inverted mass hierarchyInverted mass hierarchy

→→ Inverted pendulumInverted pendulum→→ UnstableUnstable eveneven forfor smallsmall mixingmixing angleangle

•• Normal mass hierarchyNormal mass hierarchy→→ SmallSmall--amplitude oscillationsamplitude oscillations


Flavor Conversion Without Flavor Mixing?Flavor Conversion Without Flavor Mixing?

•• This is no real “flavor conversion”,This is no real “flavor conversion”,rather a “coherent pair conversion”rather a “coherent pair conversion”

•• Occurs anyway at second order GOccurs anyway at second order GFF•• Coherent “speedCoherent “speed--up effect” (Sawyer)up effect” (Sawyer)

Equal Equal ννee and and ννee densities in a boxdensities in a box(inverted hierarchy)(inverted hierarchy)

Inverted pendulum:Inverted pendulum:

•• Time to fall dependsTime to fall dependslogarithmically onlogarithmically onsmall initial angle small initial angle ΘΘ

•• Stays up forever onlyStays up forever onlyfor for ΘΘ = 0= 0

•• Unstable by quantumUnstable by quantumuncertainty relationuncertainty relation(“How long can a pencil(“How long can a pencilstand on its tip?”)stand on its tip?”)

μμνν↔νν ee μμνν↔νν ee

Not clear (to me) if coherentNot clear (to me) if coherenttransformations can be triggeredtransformations can be triggeredby quantum fluctuations aloneby quantum fluctuations alone(mixing angle (mixing angle ΘΘ = 0)= 0)

__


Supernova Neutrino ConversionSupernova Neutrino Conversion

NeutrinosNeutrinosin a boxin a box

NeutrinosNeutrinosstreamingstreamingoff a off a supernovasupernovacorecore

Permanent pendularPermanent pendularoscillationsoscillations

Complete conversionComplete conversion

•• NuNu--nu interaction energynu interaction energydecreasesdecreases

•• Pendulum’s moment ofPendulum’s moment ofinertia inertia μμ−−11 increasesincreases

•• Conservation of angular Conservation of angular momentummomentum→→ kinetic energy decreaseskinetic energy decreases→→ amplitude decreases amplitude decreases ∝∝ μμ1/21/2

ν=μ nG2 F ν=μ nG2 FEnvelope declinesEnvelope declinesas as ∝∝ μμ1/21/2 ∝∝ rr−−22


Flavor Conversion in Toy SupernovaFlavor Conversion in Toy Supernova

PendularOscillations

•• Assume 80% antiAssume 80% anti--neutrinosneutrinos•• Vacuum oscillation frequencyVacuum oscillation frequency

ωω = 0.3 km= 0.3 km−−11

•• NeutrinoNeutrino--neutrino interaction neutrino interaction energy at nu sphere (r = 10 km)energy at nu sphere (r = 10 km)μμ = 0.3= 0.3××101055 kmkm−−11

•• Falls off approximately as Falls off approximately as rr−−44

(geometric flux dilution and nus(geometric flux dilution and nusbecome more cobecome more co--linear)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 & Wongastroastro--ph/0608695)ph/0608695)


Synchronized vs. Pendular OscillationsSynchronized vs. Pendular Oscillations

•• Ensemble of unequal densities (antineutrino frEnsemble of unequal densities (antineutrino fraction action αα < 1< 1) ) •• Equal energies (equal oscillation frequency Equal energies (equal oscillation frequency ωω = = ΔΔmm22/2E/2E))•• Interaction energy Interaction energy

ee nn νν α= ee nn νν α=

enG2 F ν=μ enG2 F ν=μ

Free oscillationsFree oscillations

ω<μ ω<μ ≪≪

PrPr

PrPr

ω+ ω+

ω− ω−

BrBr

Pendular oscillationsPendular oscillations

ωα−

α+<μ<ω 2)1(

1 ωα−

α+<μ<ω 2)1(

1≪≪ ≪≪

PrPr

PrPr

ωμα+=κ )1( ωμα+=κ )1(

BrBr

Synchronized oscillationsSynchronized oscillations

μ<ωα−

α+2)1(

1 μ<ωα−

α+2)1(

1≪≪

PrPr

PrPr

ωα−α+

=ω11

synch ωα−α+

=ω11

synch

BrBr


Synchronized vs. Pendular OscillationsSynchronized vs. Pendular Oscillations

Free oscillationsFree oscillations

ω<μ ω<μ ≪≪

PrPr

PrPr

ω+ ω+

ω− ω−

BrBr

Pendular oscillationsPendular oscillations

ωα−

α+<μ<ω 2)1(

1 ωα−

α+<μ<ω 2)1(

1≪≪ ≪≪

PrPr

PrPr

ωμα+=κ )1( ωμα+=κ )1(

BrBr

Synchronized oscillationsSynchronized oscillations

μ<ωα−

α+2)1(

1 μ<ωα−

α+2)1(

1≪≪

PrPr

PrPr

ωα−α+

=ω11

synch ωα−α+

=ω11

synch

BrBr

SupernovaSupernovaCoreCore R = 40R = 40−−60 km60 km R R ≈≈ 200 km200 km


Pendulum in Flavor SpacePendulum in Flavor Space

Mass directionMass directionin flavor spacein flavor space

PrecessionPrecession(synchronized oscillation)(synchronized oscillation)

NutationNutation(pendular(pendularoscillation)oscillation)

SpinSpin(Lepton Asymmetry)(Lepton Asymmetry)

•• Very asymmetric systemVery asymmetric system-- Large spin Large spin -- Almost pure precession Almost pure precession -- Fully synchronized oscillationsFully synchronized oscillations

•• Perfectly symmetric systemPerfectly symmetric system-- No spinNo spin-- Simple spherical pendulumSimple spherical pendulum-- Fully pendular oscillationFully pendular oscillation

[Hannestad, Raffelt, Sigl, Wong:[Hannestad, Raffelt, Sigl, Wong:astroastro--ph/0608695]ph/0608695]

νν > nn νν > nn

Polarization vectorPolarization vectorfor neutrinos plusfor neutrinos plusantineutrinos antineutrinos

νν = nn νν = nn

≫≫


MultiMulti--Energy and MultiEnergy and Multi--Angle EffectsAngle Effects

( ) pqqpq3

3Fpp

2pt P)PP)(cos1(

2

qdG2PLPB

p2m

P ×−−⎮⌡

⌠+×+×+=∂ θ

πλ

Δ( ) pqqpq3

3Fpp

2pt P)PP)(cos1(

2

qdG2PLPB

p2m

P ×−−⎮⌡

⌠+×+×+=∂ θ

πλ

Δ

( ) pqqpq3

3Fpp

2pt P)PP)(cos1(

2

qdG2PLPB

p2m

P ×−−⎮⌡

⌠+×+×−=∂ θ

πλ

Δ( ) pqqpq3

3Fpp

2pt P)PP)(cos1(

2

qdG2PLPB

p2m

P ×−−⎮⌡

⌠+×+×−=∂ θ

πλ

Δ

)(ν)(ν

)(ν)(ν

•• Different modes oscillateDifferent modes oscillatewith different frequencieswith different frequencies→→ kinematical decoherencekinematical decoherence

•• SelfSelf--maintained coherencemaintained coherenceby nuby nu--nu interactionsnu interactions

•• Can lead to “spectral split”Can lead to “spectral split”

Isotropic matter backgroundIsotropic matter backgroundaffects all modes the sameaffects all modes the same

MultiMulti--angle effects for nonangle effects for non--isotropicisotropicnu distribution (streaming from SN):nu distribution (streaming from SN):Different modes should oscillateDifferent modes should oscillatedifferently differently →→ kinematical decoherencekinematical decoherenceHowever, nuHowever, nu--nu interaction can lead tonu interaction can lead to

•• “Angular synchronization”“Angular synchronization”(quasi(quasi--single angle behavior)single angle behavior)

•• SelfSelf--accelerated multiaccelerated multi--angleangledecoherencedecoherence


Spectral Split (Stepwise Spectral Swapping)Spectral Split (Stepwise Spectral Swapping)

FogliFogli, , LisiLisi, , MarroneMarrone & M& Mirizziirizzi, arXiv:0707.1998, arXiv:0707.1998

Initial fluxesInitial fluxesat nu sphereat nu sphere

AfterAftercollectivecollectivetranstrans--formationformation

For explanation seeFor explanation see

Raffelt & SmirnovRaffelt & SmirnovarXiv:0705.1830arXiv:0705.1830

0709.46410709.4641

Duan, Fuller,Duan, Fuller,Carlson & QianCarlson & QianarXiv:0706.4293arXiv:0706.4293

0707.02900707.0290


Spectral split in terms of the Spectral split in terms of the ωω variablevariable

initialν

initialν

finalν

finalν

Collective conversion of thermal spectra of Collective conversion of thermal spectra of ννee and and ννee as in a supernovaas in a supernova__

Energy spectrumEnergy spectrum Spectrum in terms of Spectrum in terms of ωω == ΔΔmm22/2E/2E

Flavor lepton number conservation:Flavor lepton number conservation:Equal integralsEqual integrals

Raffelt & Smirnov, arXiv:Raffelt & Smirnov, arXiv:0709.46410709.4641

initialνinitialν

finalν finalν


SN 1006SN 1006

Looking forward to the next galactic supernovaLooking forward to the next galactic supernova

http://antwrp.gsfc.nasa.gov/apod/ap060430.htmlhttp://antwrp.gsfc.nasa.gov/apod/ap060430.html

May take a long timeMay take a long timeNo problemNo problemLots of theoretical work to do!Lots of theoretical work to do!

supernova neutrinos · longo, prl 60:173,1988 krauss & tremaine, prl 60:176,1988 • proves...

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