Collective Neutrino Oscillations in SNe Huaiyu Duan University of - PowerPoint PPT Presentation

Collective Neutrino Oscillations in SNe Huaiyu Duan University of New Mexico

Outline • Introduction • Numerical models and results • Recent progress and challenges • Summary

Standard Model I II III mass $ 0 # 2.4 MeV 1.27 GeV 171.2 GeV u c t ! ! charge $ ! 0 Neutrinos in Standard " " spin $ " 1 Model: name $ up charm top photon 0 g 4.8 MeV 104 MeV 4.2 GeV s d b • Three flavors - # - # - # 0 Quarks " " " 1 down strange bottom gluon • No mass <0.17 MeV <15.5 MeV 91.2 GeV 0 <2.2 eV ! e ! µ ! " Z 0 0 0 0 " " " 1 • No electric charge, electron weak muon tau neutrino force neutrino neutrino Bosons (Forces) interacting weakly 0.511 MeV 105.7 MeV 1.777 GeV 80.4 GeV e µ " ± W -1 -1 ± 1 -1 Leptons " " " 1 weak electron muon tau force Wikimedia: Standard Model of Elementary Particles

Neutrinos in Supernovae n’s + seed → heavy (A=100 ~ 200) r-process • ~10 53 ergs, 10 58 seeds (A = 50 ~100) T ≈ 0.25MeV … neutrinos in ~10 4 He( αα , γ ) 12 C 4 He( α n, γ ) 9 Be seconds temperature, density 2n + 2p → α radius, wind speed T ≈ 0.75MeV ν e + n → p + e - • All neutrino species, nucleosynthesis 10~30 MeV WFO • Dominate energetics T ≈ 0.9MeV ν e + n ⇌ p + e - _ ν e + p ⇌ n + e + • Influence heating nucleosynthesis region • Probe into SNe neutron cooling star region

Vacuum Oscillations neutrino mass eigenstates ≠ weak interaction states | ν 1 ⇥ = cos θ v | ν e ⇥ + sin θ v | ν µ ⇥ with mass m 1 | ν 2 ⇥ = � sin θ v | ν e ⇥ + cos θ v | ν µ ⇥ with mass m 2 vacuum mixing angle initially | ψ ( x = 0) i = | ν e i ✓ δ m 2 x ◆ P ν e ν e ( x ) ⌘ | h ν e | ψ ( x ) i | 2 = 1 � sin 2 2 θ v sin 2 4 E ν neutrino survival probability

Matter Effect electron number density ⇧ � ⇥ � ⇥ � ⇥ i d ⇥ ν e | ψ ν ⇤ = 1 ⇥ ν e | ψ ν ⇤ 2 G F n e � ω cos 2 θ v ω sin 2 θ v 2 ⇥ ν µ | ψ ν ⇤ ⇥ ν µ | ψ ν ⇤ ω sin 2 θ v ω cos2 θ v d x 2 vac. osc. freq. ω = δ m 2 2 E ν | ν H ⇥ � | ν e ⇥ | ν H � = | ν 2 � | ν L ⇥ � | ν µ ⇥ MSW Res. Cond.: δ m 2 ⇥ | ν L � = | ν 1 � 2 G F n e � 2 E ν n e Mikheyev, Smirnov (1985)

Three Flavor Mixing weak flavor states vacuum mass eigenstates ∗       | ν e ⇥ | ν 1 ⇥ c 12 c 13 c 13 s 12 s 13 � c 23 s 12 e i φ � c 12 s 13 s 23 c 12 c 23 e i φ � s 12 s 13 s 23 | ν µ ⇥ | ν 2 ⇥  = c 13 s 23      s 23 s 12 e i φ � c 12 c 23 s 13 � c 12 s 23 e i φ � c 23 s 12 s 13 | ν τ ⇥ | ν 3 ⇥ c 13 c 23 ⇥ ⇥ 7–8 � 10 � 5 eV 2 , δ m 2 12 ⇥ δ m 2 θ 12 ⇥ θ ⇥ ⇥ 0 . 6 θ 23 ⇥ θ atm ⇥ π atm ⇥ 2–3 � 10 − 3 eV 2 , | δ m 2 23 | ⇥ δ m 2 4 23 | ' 2–3 ⇥ 10 − 3 eV 2 , | δ m 2 13 | ' | δ m 2 θ 13 ' 0 . 15 φ is unknown CP violation phase

Mass Hierarchy normal mass hierarchy inverted mass hierarchy ν µ ν τ ν 3 ν e ν µ ν τ ν 2 δ m 2 � δ m 2 ν 1 ν e ν µ ν τ atm m 2 ν δ m 2 ν e ν µ ν τ ν 2 atm δ m 2 � ν e ν µ ν τ ν 1 ν µ ν τ ν 3

Density Matrix Pure State: | ψ i = ) ˆ ρ = | ψ ih ψ |  � 1 0 Example: | ν e i = ) ρ = 0 0 Mixed State:  � 0 n ν e ρ ∝ 0 n ν x

In Dense Medium ( ∂ t + ˆ v · r ) ρ = − i[ H , ρ ] mass matrix electron density M 2 √ = + 2 G F diag[ n e , 0 , 0] + H H νν 2 E neutrino energy ν - ν forward scattering (self-coupling) Z √ d 3 p 0 (1 − ˆ v 0 )( ρ p 0 − ¯ v · ˆ H νν = 2 G F ρ p 0 )

Oscillations in SN M 2 √ = + 2 G F diag[ n e , 0 , 0] + H H νν 2 E neutrino sphere ν k ν q ν p

Outline • Introduction • Numerical models and results • Recent progress and challenges • Summary

Numerical Models Coherent forward scattering outside neutrino sphere ρ ( t ; r, Θ , Φ ; E, ϑ , ϕ )

Numerical Models Stationary emission ρ ( r, Θ , Φ ; E, ϑ , ϕ )

Numerical Models Axial symmetry around the Z axis ρ ( r, Θ ; E, ϑ , ϕ )

Numerical Models Spherical symmetry about the center (inconsistent?) ρ ( r ; E, ϑ , ϕ )

Numerical Models Azimuthal symmetry around any radial direction ρ ( r ; E, ϑ ) Bulb model

δ m 2 = 3 � 10 − 3 eV 2 ⇥ δ m 2 atm , θ v = 0 . 1 , L ν = 0

δ m 2 = � 3 ⇥ 10 − 3 eV 2 ' δ m 2 atm , θ v = 0 . 1 , L ν = 10 51 erg / s

neutrino antineutrino P νν 1 1 1 normal mass hierarchy 0.9 0.8 0.8 0.8 0.7 0.6 0.6 0.6 0.5 0.4 0.4 0.4 0.3 0.2 0.2 0.2 cos ϑ R 0.1 0 0 0 20 40 60 80 0 20 40 60 80 1 1 inverted mass hierarchy 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0 20 40 60 80 0 20 40 60 80 HD, Fuller, Qian & Carlson (2006) E ν (MeV)

Numerical Models Trajectory independent neutrino flavor evolution ρ ( r ; E ) Single-angle model Equivalent to the expansion of a homogeneous, isotropic gas

neutrino antineutrino normal mass hierarchy 0.4 0.4 0.2 0.2 ν e z ν e z 0 0 ¯ ς ς -0.2 -0.2 (a) (b) -0.4 -0.4 0 10 20 30 40 0 10 20 30 40 E ν e (MeV) E ¯ ν e (MeV) inverted mass hierarchy single-angle 0.4 0.4 multi-angle 0.2 0.2 ν e z ν e z 0 0 ¯ ς ς -0.2 -0.2 (c) (d) -0.4 -0.4 0 10 20 30 40 0 10 20 30 40 E ν e (MeV) ν e (MeV) E ¯ Duan+ (2006)

Neutronization Burst Normal Mass Hierarchy solar split atm. split O-Ne-Mg Core-Collapse ν e initial Neutronization Pulse L ν e = 10 53 erg / s ν 3 h E ν e i = 11 MeV Avg. Spectra r = 5000 km ν 2 ν 1 0 10 20 30 40 E [MeV] Single Angle: Duan+ (2007) Multi-Angle: Cherry+ (2010)

Multiple Spectral Splits Antineutrinos Neutrinos IH IH NH NH 0 10 20 30 40 0 10 20 30 40 50 Energy [MeV] Energy [MeV] Dasgupta et al (2009)

Outline • Introduction • Numerical models and results • Recent progress and challenges • Summary

Dimension matters s i n g l e - a n g l e 1 - 1 10 n o i t r o t - 2 s 10 i D l a r t - 3 c 10 e Flavor instability p S - 4 Bulb 10 - 5 10 50 100 150 200 250 r [ k m ] Duan & Friedland (2010)

Nucleosynthesis solar no osc. multiangle single-angle Duan, Friedland, McLaughlin & Surman (2011)

Trajectory Dependence ρ ( r ; E ) ρ ( r ; E, ϑ )

Directional Symmetry Z √ d 3 p 0 (1 − ˆ v 0 )( ρ p 0 − ¯ v · ˆ H νν = 2 G F ρ p 0 ) " # v 0 ) − 1 X v 0 ) = 4 π v ) Y ⇤ v ) Y ⇤ v 0 ) (1 − ˆ v · ˆ Y 0 , 0 (ˆ 0 , 0 (ˆ Y 1 ,m (ˆ 1 ,m (ˆ 3 m =0 , ± 1 • Monopole ( l =0) and dipole ( l =1) modes are unstable in opposite neutrino mass hierarchies. • Unstable dipole ( l =1) modes break the directional symmetry. Duan (2013)

Inverted Hierarchy -2 10 |~ q 00 | |~ q 10 | -3 10 |~ q 1c | |~ q 1s | -4 10 q | |~ -5 10 -6 10 -7 10 0 1 2 3 4 τ Duan (2013)

Normal Hierarchy -4 |~ 10 q 00 | |~ q 10 | |~ q 1c | |~ q 1s | -5 10 q | |~ -6 10 -7 10 0 1 2 3 4 τ Duan (2013)

Breaking Axial Symmetry Chakraborty, Mirizzi (2013)

m H km - 1 L ∝ L/r 4 10 3 10 2 10 1 0.1 10 4 Matter Suppression 10 11 NH ∝ ρ /r 2 10 3 n e 10 10 m N IH = Y e l H km - 1 L r 10 2 = 1 0 9 g c m - 3 10 7 10 10 8 10 6 1 10 5 0.1 50 100 300 500 1000 Self Suppression r H km L Raffelt+ (2013)

Directional Symmetry ρ ( r ; E, ϑ ) ρ ( r ; E, ϑ , ϕ )

Line Model • x translation symmetry • left-right symmetry Z L ρ m ( z ) = 1 ρ ( x, z ) − 2 m π i x/L d x L 0 z L R R x Duan & Shalgar (2015)

Spatial Symmetry α = n ¯ ν /n ν µ ∝ G F n ν Duan & Shalgar (2015)

m H km - 1 L ∝ L/r 4 10 4 10 3 10 2 10 1 10 0 10 - 1 10 6 SN Density 10 5 ∝ ρ /r 2 10 4 Matter Suppression l H km - 1 L 10 3 10 2 10 1 10 2 10 3 k = 0 10 0 50 100 200 500 1000 Radius H km L No Self Suppression Chakraborty+ (2015)

Spatial Symmetry ρ ( r ; E, ϑ , ϕ ) ρ ( r, Θ , Φ ; E, ϑ , ϕ )

Temporal Symmetry Matter suppression is relieved for high-frequency modes Abbar & Duan (2015) Dasgupta & Mirizzi (2015)

Fast Neutrino Oscillations • Usually flavor instabilities grow _ at rates comparable to ν e sphere vacuum oscillation frequency. • Fast oscillations grow at rates comparable to ( G F n ν ). • Fast oscillations can occur because of different angular distributions of ν e and anti- ν e . ν e sphere • Can fast oscillations occur within the proto-neutron star? Sawyer (2015) Chakraborty+ (2016)

Summary • Neutrinos are important in SNe (dynamics, nucleosynthesis, new probe). • Neutrino oscillations are also important because they change fluxes in different flavors. • The dense neutrino medium surrounding the nascent neutron star can oscillate collectively ( Lecture 1 ). • Neutrino oscillations can be qualitatively different in different models.

Summary • Assumptions of the bulb model: • Axial symmetry (in momentum space). • Spherical symmetry (in real space). • Stationary assumption (time translation symmetry). • Same neutrino sphere (or angular distribution) for all flavors.