self-induced flavor evolution of supernova neutrinos without axial...
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SELF-INDUCED FLAVOR EVOLUTION OF SUPERNOVA NEUTRINOS
WITHOUT AXIAL SYMMETRY (Based on 1308.1402; 1308.5255)
(Alessandro MIRIZZI, Hamburg U.)
Bari Xmas Theory Workshop 2013 Bari, 23 December 2013
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normal hierarchy
inverted hierarchy
dm2/2
-dm2/2
Dm2
-Dm2
dm2/2
-dm2/2
n1 n1
n2 n2
n3
n3
Mixing parameters: U = U (q12, q13, q23, d) as for CKM matrix
Mass-gap parameters: M2 = - , + , ± Dm2 dm2 2
dm2 2
“solar” “atmospheric”
3n FRAMEWORK
13 13 12 12 1
23 23 12 12 2
23 23 13 13 3
1
1
1
i
e
i
c e s c s
c s s c
s c e s c
d
d
n n
n n
n n
-
-
- - -
c12= cos q12, etc., d CP phase
2n subsector: (Dm2, q13)
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SNAP-SHOTS OF SN DENSITY PROFILES
• Matter bkg potential
• n-n interaction
n nGF2
~ R-3
~ R-2
eF NG2
E
m
2
2D
• Vacuum oscillation frequencies
When >>, SN n oscillations dominated by n-n interactions
Equivalent n
density ~R2
astro-ph/0407132
Collective flavor transitions at low-radii [O (102 – 103 km)]
[see Duan et al, arXiv:1001.2799 for a review]
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*
*
e
e
eeee
DENSITY MATRIX FOR THE NEUTRINO ENSEMBLE
Diagonal elements related to flavor content
Off-diagonal elements responsible for flavor conversions
),(
),(
rEF
rEFn
],[ ppp Hi t
The EOMs for the time evolution in a homogeneous medium are the Liouville equations (e.g. Early Universe)
In 2n scenario. Decompose density matrix over Pauli matrices to get the “polarization” (Bloch) vector P. Survival probability Pee =1/2(1+Pz) . Pz = -1 -> Pee =0 ; Pz = 0 -> Pee =1/2 (flavor decoherence)
Alessandro Mirizzi Xmas Theory Workshop 23 December 2013
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MULTI-ANGLE (M.A.) EOMs FOR SN NEUTRINOS
xpxpxpx Hi ,,',p ),,,(v
Evolution in space for n’s streaming from a SN core in quasi-stationary situation
Liouville operator for free streaming n
) ) -- xqxqqF qdGH ,,p vv1 2 nn
MULTI-ANGLE n-n HAMILTONIAN
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BULB MODEL
[see, e.g., Duan et al., astro-ph/0606616]
Neutrinos are emitted uniformly and (half)-isotropically from the surface of a sphere (n-sphere), like in a blackbody. Physical conditions depend only on the the distance r from the center of the star (azimuthal symmetry) Only multi-zenith-angle (MZA) effects in terms of u = sin2 qR
RqRq
Rq
First large-scale multi-angle simulations
rxp drvv
Project evolution along radial direction (ODE problem)
Azimuthal angle
zenith angle
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SINGLE-ZENITH-ANGLE (SZA) APPROXIMATION
Introduce an average of the MZA factor (1-cosqpq) .
SZA n-n Hamiltonian
( ) 2 1 cosFr G nn q -
[Hannestad et al., astro-ph/0608695]
No effect in NH
Complete self-induced conversions in IH. Bimodal instability
Toy model: Monochromatic n beam. Only ne and ne , with an excess of ne
Alessandro Mirizzi Xmas Theory Workshop 23 December 2013
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MULTI-ZENITH-ANGLE DECOHERENCE
) ), ,2 1 cos F pq q x q xH G dqnn q - -
Flux term
Is the MZA decoherence relevant for SN neutrinos?
Alessandro Mirizzi Xmas Theory Workshop 23 December 2013
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MZA EFFECTS FOR SN NEUTRINOS
( ) ( )
( ) ( )
e e
e x
F F
F F
n n
n n
-
-Flavor asymmetry
Quasi single-angle behaviour
Nothing occurs in NH (stable configuration)
Complete conversions in IH (bimodal instability)
Flavor equilibration in both NH & IH
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MULTI-AZIMUTHAL-ANGLE (MAA) INSTABILITY
Self-induced flavor conversions are associated to an instability in the flavor space
Instability required to get started (exponential growth of the off-diagonal density matrix part)
[Sawyer,0803.4319; Banerjee, Dighe & Raffelt, 1107.2308]
The onset of the conversions can be found through a stability analysis of the linearized EOMs.
In [Raffelt, Sarikas, Seixas, 1305.7140] a stability analysis of the EOMs has been performed including the azimuthal angle f of the n propagation and without enforcing axial symmetry also starting with an intial axial symmetric n emission.
A new multi-azimuthal-angle (MAA) instability has been found!!
In the unstable case, numerical simulations are mandatory.
Alessandro Mirizzi Xmas Theory Workshop 23 December 2013
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MAA EFFECTS FOR SN NEUTRINOS
Monochromatic n beam
MZA & MAA
SZA & MAA
NH becomes unstable under MAA effects! SZA vs MZA marginal impact New effects in IH only for small
[A.M., 1308.1402]
System of only ne and ne with an excess of ne
Alessandro Mirizzi Xmas Theory Workshop 23 December 2013
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TOY MODEL NEUTRINO SPECTRA
System of only ne and ne with an excess of ne
Fermi-Dirac energy distributions with <E>=15 MeV
ne
ne
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SPECTRAL SPLITS =1.5)
ne
ne
Oscillated spectra
Initial
Final SZA & MAA
Final MZA & MAA
Swap function
SZA & MAA
MZA & MAA
split swap split
swap
Spectral swaps and splits in both NH (MAA) & IH (Bimodal)
Antinu split smeared by MZA effects
[A.M., 1308.1402]
Alessandro Mirizzi Xmas Theory Workshop 23 December 2013
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SPECTRAL SPLITS FOR SN NEUTRINO FLUXES
ne -nx
nx -ne
(accretion phase)
: : 2.4 :1.6 :1.0e e xF F Fn n n
split swap split
swap
Spectral swaps and splits in both NH & IH !!
In the axial symmetric case, only IH instable
[A.M., 1308.5255]
Alessandro Mirizzi Xmas Theory Workshop 23 December 2013
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SPECTRAL SPLITS FOR SN NEUTRINO FLUXES
Nu fluxes present a spectral split at E= 12 MeV (fixed by lepton number conservation) Antinu fluxes are swapped
ne
nx
[A.M., 1308.5255]
Alessandro Mirizzi Xmas Theory Workshop 23 December 2013
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CONCLUSIONS
A new multi-azimuthal-angle (MAA) instability emerges in the dense SN neutrino gas, removing the axial symmetry in the nu-nu interaction term
For simple systems of only ne and ne , with an excess of ne , MAA effects can lead to spectral splits (for large flavor asymmetry) or flavor decoherence (for small flavor asymmetry) in NH.
For SN n spectra as in the accretion phase, MAA effects would induce swaps and splits in NH.
A change of paradigm in the SN neutrino self-induced effects?
Still many open points (e.g. role of dense ordinary matter, initial nu angular distributions...)
LOT OF WORK TO BE DONE ...WAITING THE NEXT SN EXPLOSION !