Neutrino Oscillations in Core-Collapse Supernovae

Meng-Ru Wu, Technische Universität Darmstadt
Supernovae and Gamma-Ray Bursts 201310/14/2013-11/15/2013

Neutrino Oscillations in Core-Collapse Supernovae- Core-collapse supernovae & neutrinos- Active-active neutrino oscillations- Active-sterile neutrino oscillations

Supernova explosion – the death of massive stars

The Tarantula Nebulaand supernova 1987ain the LMC(From NASA website)(From AAO website)energy of the emitted light ~ 1049-1050 ergs
peak luminosity may be as bright as an entire galaxy!
- produce elements after BBN- star formation & galaxy formation- galactic chemical enrichment

Neutrinos in supernovae
Over 99 percent of gravitational energy iscarried away by ~1058 different kind ofneutrinos in a time scale of 10 seconds.

3GM 2NS
53
E G≈≈3×10 ergs !
5 R NS(H.-Th. Janka, et al, PTEP 01A309 (2012))→ Delayed neutrino-heating mechanism for explosion→ Neutrino-driven winds as a site of heavy element formation→ Neutrino-induced nucleosynthesis in supernova envelopes

Neutrino signals
We have ~ 20 SN neutrinos detected from SN1987a- Confirms the basic picture of core-collapse SN model- Set limit on the absolute neutrino mass from the time-of-flightNeutrino mixing among active flavors

Energy hierarchy of supernova neutrinos
There exists an energy hierarchy between the emitted neutrinos :because of (a) muon and tau abundances are suppressed(b) more neutrons than protons(Fischer et. al., A&A 517A, 80F, 2010)

Neutrino flavor oscillations
might affect supernova
physics!

The next galactic supernova?
(Kate Scholberg., Ann.Rev.Nucl.Part.Sci, 62, 2012)(d=10 kpc)

- Supernova explosion : Explosion mechanism, shock propagation, progenitor
structure, NS or BH?...
- Properties of proto-neutron star : Nuclear equation of state, hadron-quark phasetransition....
- Properties of neutrinos : Neutrino mass hierarchy, absolute neutrino mass,
non-standard interaction? sterile neutrinos?...

Diffusive supernova neutrino background(Bays et. al., [SuperK Coll.] PRD 2012)

Better understanding of neutrino oscillations in supernovae
allows us to extract more information!

Active-active Neutrino Oscillations in Supernovae

Separation of two regimes :Inside the neutrinospheres → neutrinos are trapped, no flavor oscillations,described by Boltzmann transport
Outside the neutrinospheres → free-streaming, flavor oscillations
described by one-particle Schrödinger-like equation in flavor spaceNeutrino flavor evolution :vacuum term :MSW term : H m =±√ 2 G F ne diag (1,0,0) (Wolfenstein 1978; Mikheyev & Smirnov, 1985)
Δ m 2ijcos 2 θ ji=> MSW resonance : ±√ 2 G F ne =2 EνMostly adiabatic, but may be disturbed by the passing of supernova shockNeutrino flavor evolution :neutrino-neutrino term :(Fuller, et. al., 1987; Pantaleone, 1992;
Sigl & Raffelt, 1992; Pehlivan & Balantekin 2006)=> coupled non-linear equation=> collective neutrino oscillations
would occur closer to the PNS

Why “collective”?
Two flavor, pure isotropic neutrino gas :Neutrino “spin” :d s⃗i⃗ V −μ ∑ s⃗j= s⃗i × ωi Hdtj(when μ≫ ωi , 2 ℜa *e a x 1s ≡ 〈  ∣  / 2∣  〉 = 2 ℑ a *e a x 2∣a 2e∣−∣a 2x∣)

ωi ≡∣δ m2∣
2 Eiμ≡2 √ 2G F n νd⃗si≈ −μ ⃗si × ⃗Sdt

S→ every neutrino “spin” essentially aligns with VH≈ 〈  〉

SdS
V⇒
≈ 〈〉 S ×H
dt
All neutrino “spins” precess (oscillate) V with a collective frequency 〈  〉.
around Hs iω≈μ∣⃗S∣collective
oscillations

H-resonance
L-resonanceShockRevival~O(102 km)

v-driven
Wind~O(103 km)

v-induced
nucleosynthesis
in He shell~O(105 km)

NeutrinosignalsCollectiveOscillations

No(?)

Maybe

Yes

Yes

MSW
H-resonance

NoNo

Yes

Yes

MSW
L-resonance

NoNoNoYesNeutrino signals and mass hierarchy
In the accretion phase of Fe-core SN, collective oscillations are expected to be
suppressed by the large matter potential.

Neutrino signals and mass hierarchy
In the accretion phase of Fe-core SN, collective oscillations are expected to be
suppressed by the large matter potential.
→ possibility of using SN signal to distinguish the neutrino mass hierarchy bycomparing the event rates and spectra using multiple detection channels.

34k-ton LAr detector

Super-K(MRW, Qian, Martinez-Pinedo, Fischer, in preparation)

Neutrino-bulb model for collective oscillations(Duan et. al., PRD 74, 105014, 2006)- Supernova environment is spherically symmetric.
- All neutrinos are emitted from a sharp neutrinosphere.
- All neutrinos are in pure flavor states at the neutrino sphere.
→ ray-tracing neutrinos with different energy Ev and emission angle θ.

Spectral splits (swaps) :The collective frequency

gives rise to the “spectral splits”(“spectral swaps”)(Raffelt 2007, 2011. Duan et. al. 2007. Dasupta et. al.,2009. MRW & Qian 2011, Volpe et. al., 2011)Spectral splits (swaps) :The collective frequency

gives rise to the “spectral splits”(“spectral swaps”)(Raffelt 2007, 2011. Duan et. al. 2007. Dasupta et. al.,2009. MRW & Qian 2011, Volpe et. al., 2011)

Warning :The results sensitively depend on :(a) relative spectra of electron (anti)neutrinos and mu/tau (anti)neutrinos.
(b) competition of matter potential and neutrino-neutrino potential.
(MRW, Qian, Martinez-Pinedo, Fischer, in preparation)→ possibility to explore
the micro-physics that
determines the neutrino
spectra.

Problems of the neutrino-bulb model :- Numerically, requires a large numbers of angular bins/modes (~102-104) toprevent spurious flavor instability.

Problems of the neutrino-bulb model :- Numerically, requires a large numbers of angular bins/modes (~102-104) toprevent spurious flavor instability.
- Break down of spherical symmetry from the azimuthal-angle induced
instability → ultimate need of reduced 6-D problem? (Raffelt et. al, PRL, 2013)

Problems of the neutrino-bulb model :- Numerically, requires a large numbers of angular bins/modes (~102-104) toprevent spurious flavor instability.
- Break down of spherical symmetry from the azimuthal-angle induced
instability → ultimate need of reduced 6-D problem?
- Are the two regimes (Boltzmann & Schrodinger-like) really separable?
(Cherry et. al, PRL, 2012)

Problems of the neutrino-bulb model :- Numerically, requires a large numbers of angular bins/modes (~102-104) toprevent spurious flavor instability.
- Break down of spherical symmetry from the azimuthal-angle induced
instability → ultimate need of reduced 6-D problem?
- Are the two regimes (Boltzmann & Schrodinger-like) really separable?
- Is there any neutrino-antineutrino coherent flavor transformation near the(Volpe et. al, PRD, 2013, Vlasenko et. al., 2013)
neutrinosphere?

More works to be done both analytically andnumerically!

Summary (I)- Neutrinos play essential roles in core-collapse supernovae. To reallyunderstand their effects in supernovae and to extract more informationfrom SN neutrino signals, it is important to understand their flavor
transformation.
- If collective neutrino oscillations are suppressed during the accretion
phase of Fe-CCSNe. There is a possibility of using the neutrino signals
to identify the neutrino mass hierarchy.
- Collective neutrino oscillations among active flavors typically produce
spectral splits/swaps. However, many more challenges are still aheadof us.

Active-sterile Neutrino Oscillations in Supernovae

eV sterile neutrinos?

(Kopp, Machado, Maltoni, Schwertz, JHEP05 (2013) 050)

The anomaly of electron antineutrino disappearance experiments from short-baseline
reactors & Gallium solar neutrino experiments may be accounted for by introducing eVscale sterile neutrinos.
In 3+1 scheme :Hints from different experiments/observations- LSND, MiniBooNE- Long-base line accelerator experiments- Cosmology/BBN- Solar Neutrinos

Role of eV sterile neutrinos in supernovae?
First pointed out in [Nunokawa, Peltoniemi, Rossi & Valle, PRD 56, 1704(1997)]
that eV sterile neutrinos might have effects on shock-revival and electron fraction
In the ejecta.
However, the feedback on the electron-to-baryon ratio (Ye) was not treatedin a consistent manner.

Neutrino oscillations in medium
With two-flavor approximation and in the free-streaming regime, the neutrino flavor
evolution is governed by the vacuum Hamiltonian + matter-induced Hamiltonian :different from the MSW
potential that for active
flavors because of theneutral-current=> MSW resonance :Supernova profiles- Because of the deleptoniztion that occurs during the collapse and the shock
break-out, the electron-to-baryon ratio Ye ~ 0.1 around the neutrinospheresuch that active-sterile MSW resonance could occur between theneutrinosphere and the shock.
- Collective neutrino oscillations are suppressed because at IR in bulb model,andMSW flavor transformation at the inner resonance
For neutrinos :For antineutrinos :Electron (anti)neutrinos may be transformed to sterile (anti)neutrinos
when they cross Ye~1/3.

MSW flavor transformation at the inner resonanceLandau-Zener survival probability :The oscillation length at resonance :The resonant width :Time evolution of RIR and E0.5 with Ye from an 8.8 SN Model- The inner resonance happens at radius that increases with shock
expansion initially, and then retreats with PNS cooling later.
- E0.5 follows the change of RIR, exceeding the average neutrinoenergy ~ 10 MeV for substantial amount of time.

(MRW, Fischer, Martinez-Pinedo, Qian, arXiv:1305.2382)

Feedback on Ye profile?
Since (1) Ye is determined by the competition of rates of electron/positronand electron (anti)neutrino captures :(2) electron (anti)neutrino capture rates are affected by the flavor oscillations
which depends on Ye profiles→ Need to evolve the Ye along with the active-sterile flavor transformation!

Feedback on Ye profile:
We follow the evolution of Ye for relevant mass shells, assuming thehydrodynamics are not affected.

Ye plateau!

Effect on the oscillations
The formation of the Ye plateau breaks the degeneracy between
neutrinos and antineutrinos and induces more flavor transformationin the shock expansion phase.

- Reduce the capture rates of electron neutrinos more than that ofelectron antineutrinos.
- Greatly reduce the v-heating rates around the phase of shock
break-out.

Effect on nucleosynthesis- Ye at alpha freeze-out in the ejecta is reduced from ~0.5 to ~0.4.
- For the 8.8Mʘ SN model, the main products of nucleosynthesis shift
from the iron peak to Sr-Ru.

Effect on v-heating rates
The reduction of heating rate around the shock break-out :Possibility of using SN models to constrain the parameter
space of sterile neutrinos?

Summary (II)- If light eV sterile neutrinos exist, active-sterile MSW flavor conversion
in supernovae might happen between the neutrinosphere and theshock.
- The flavor conversion reduces the neutrino heating rates (dynamics)
substantially and change the ratio of electron neutrino capture andelectron antineutrino capture rates (nucleosynthesis).
- Including the feedback on Ye creates a plateau around Ye~1/3 andfurthers enhance the effects.
- It would be interesting to include it in a supernova simulation to see if
it could provide firm constraints on the parameter space of sterile
neutrinos and study the signature in neutrino signals.

Thanks for your attention!