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

SLIDE 1

Collective Neutrino Oscillations in SNe

Huaiyu Duan University of New Mexico

SLIDE 2

Outline

Introduction
Numerical models and results
Recent progress and challenges
Summary

SLIDE 3

Standard Model

u

up

2.4 MeV

! "

c

charm

1.27 GeV

! "

t

top

171.2 GeV

! "

d

down

4.8 MeV

#

"

s

strange

104 MeV

"

#

b

bottom

4.2 GeV

"

#

!e

electron neutrino

<2.2 eV

"

!µ

muon neutrino

<0.17 MeV

"

!"

tau neutrino

<15.5 MeV

"

e

electron

0.511 MeV

1

"

µ

muon

105.7 MeV

"

1

"

tau

1.777 GeV

"

1

#

photon 1

g

gluon 1

Z

91.2 GeV

1 weak force

W

±

80.4 GeV

1

±1

weak force mass$ spin$ charge$

Quarks Leptons Bosons (Forces) I II III

name$ Wikimedia: Standard Model of Elementary Particles

Neutrinos in Standard Model:

Three flavors
No mass
No electric charge,

interacting weakly

SLIDE 4

νe + n → p + e-

WFO T≈0.9MeV T≈0.75MeV T≈0.25MeV radius, wind speed temperature, density nucleosynthesis

2n + 2p → α

4He(αn,γ)9Be 4He(αα,γ)12C

… seeds (A = 50 ~100) n’s + seed → heavy (A=100 ~ 200)

r-process neutron star heating region

νe + p ⇌ n + e+ _ νe + n ⇌ p + e-

cooling region

Neutrinos in Supernovae

~1053 ergs, 1058

neutrinos in ~10 seconds

All neutrino species,

10~30 MeV

Dominate energetics
Influence

nucleosynthesis

Probe into SNe

SLIDE 5

Vacuum Oscillations

SLIDE 6

Matter Effect

vac. osc. freq. ω = δm2

2Eν electron number density i d dx

⇥νe|ψν⇤

⇥νµ|ψν⇤ ⇥ = 1 2

2

⇧ 2GFne ω cos 2θv ω sin 2θv ω sin 2θv ω cos2θv ⇥ ⇥νe|ψν⇤ ⇥νµ|ψν⇤ ⇥ |νH⇥ |νe⇥ |νL⇥ |νµ⇥ |νH = |ν2 |νL = |ν1

ne

MSW Res. Cond.: δm2 2Eν

⇥

2GFne

Mikheyev, Smirnov (1985)

SLIDE 7

Three Flavor Mixing

weak flavor states vacuum mass eigenstates   |νe⇥ |νµ⇥ |ντ⇥   =   c12c13 c13s12 s13 c23s12eiφ c12s13s23 c12c23eiφ s12s13s23 c13s23 s23s12eiφ c12c23s13 c12s23eiφ c23s12s13 c13c23  

∗ 

 |ν1⇥ |ν2⇥ |ν3⇥  

δm2

12 ⇥ δm2 ⇥ ⇥ 7–8 105eV2,

θ12 ⇥ θ⇥ ⇥ 0.6 |δm2

23| ⇥ δm2 atm ⇥ 2–3 10−3eV2,

θ23 ⇥ θatm ⇥ π 4

CP violation phase

φ is unknown |δm2

13| ' |δm2 23| ' 2–3 ⇥ 10−3eV2,

θ13 ' 0.15

SLIDE 8

Mass Hierarchy

νµντ νe νµ ντ νe νµ ντ

ν3 ν2 ν1

δm2

atm

δm2

m2

ν

normal mass hierarchy

νµντ νe νµ ντ νe νµ ντ

ν3 ν2 ν1

δm2

atm

δm2

inverted mass hierarchy

SLIDE 9

Density Matrix

ρ ∝  nνe nνx

Pure State:

Example: |νei = ) ρ =  1

Mixed State:

|ψi = ) ˆ ρ = |ψihψ|

SLIDE 10

In Dense Medium

H = M2 2E + √ 2GF diag[ne, 0, 0] + Hνν

mass matrix neutrino energy electron density ν-ν forward scattering (self-coupling)

(∂t + ˆ v · r)ρ = −i[H, ρ] Hνν = √ 2GF Z d3p0(1 − ˆ v · ˆ v0)(ρp0 − ¯ ρp0)

SLIDE 11

Oscillations in SN

H = M2 2E + √ 2GF diag[ne, 0, 0] + Hνν

neutrino sphere νk νq νp

SLIDE 12

Outline

Introduction
Numerical models and results
Recent progress and challenges
Summary

SLIDE 13

Numerical Models

Coherent forward scattering outside neutrino sphere

ρ(t; r, Θ, Φ; E, ϑ, ϕ)

SLIDE 14

Numerical Models

Stationary emission

ρ(r, Θ, Φ; E, ϑ, ϕ)

SLIDE 15

Numerical Models

Axial symmetry around the Z axis

ρ(r, Θ; E, ϑ, ϕ)

SLIDE 16

Numerical Models

Spherical symmetry about the center (inconsistent?)

ρ(r; E, ϑ, ϕ)

SLIDE 17

Numerical Models

Azimuthal symmetry around any radial direction

ρ(r; E, ϑ)

Bulb model

SLIDE 18

δm2 = 3 10−3 eV2 ⇥ δm2

atm, θv = 0.1, Lν = 0

SLIDE 19

δm2 = 3 ⇥ 10−3 eV2 ' δm2

atm, θv = 0.1, Lν = 1051 erg/s

SLIDE 20

20 40 60 80 0.2 0.4 0.6 0.8 1 20 40 60 80 0.2 0.4 0.6 0.8 1 20 40 60 80 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 20 40 60 80 0.2 0.4 0.6 0.8 1

Pνν Eν (MeV)

neutrino antineutrino normal mass hierarchy inverted mass hierarchy

cos ϑR

HD, Fuller, Qian & Carlson (2006)

SLIDE 21

Numerical Models

Trajectory independent neutrino flavor evolution

ρ(r; E)

Equivalent to the expansion

f a homogeneous, isotropic gas

Single-angle model

SLIDE 22

neutrino antineutrino normal mass hierarchy inverted mass hierarchy

10 20 30 40

0.4
0.2

0.2 0.4 (a)

νez

Eνe (MeV)

10 20 30 40

0.4
0.2

0.2 0.4 (b)

¯ νez

E ¯

νe (MeV)

10 20 30 40

0.4
0.2

0.2 0.4 (c)

νez

Eνe (MeV)

10 20 30 40

0.4
0.2

0.2 0.4 (d)

¯ νez

E ¯

νe (MeV)

ς ς ς ς

single-angle multi-angle

Duan+ (2006)

SLIDE 23

Neutronization Burst

E [MeV]

Avg. Spectra

ν1 ν2 ν3

solar split

atm. split

Lνe = 1053 erg/s hEνei = 11 MeV

Normal Mass Hierarchy

O-Ne-Mg Core-Collapse Neutronization Pulse

r = 5000 km

10 20 30 40

νe initial

Single Angle: Duan+ (2007) Multi-Angle: Cherry+ (2010)

SLIDE 24

Dasgupta et al (2009)

Multiple Spectral Splits

Antineutrinos IH Neutrinos IH 10 20 30 40 Energy [MeV] NH 10 20 30 40 50 Energy [MeV] NH

SLIDE 25

Outline

Introduction
Numerical models and results
Recent progress and challenges
Summary

SLIDE 26

Dimension matters

50 100 150 200 250

r [ k m ]

10

5

10

4

10

3

10

2

10

1

1

S p e c t r a l D i s t

r

t i

n

s i n g l e

a

n g l e

Duan & Friedland (2010)

Flavor instability

Bulb

SLIDE 27

Nucleosynthesis

Duan, Friedland, McLaughlin & Surman (2011)

solar no osc. multiangle single-angle

SLIDE 28

Trajectory Dependence

ρ(r; E, ϑ) ρ(r; E)

SLIDE 29

Directional Symmetry

Monopole (l=0) and dipole (l=1) modes are

unstable in opposite neutrino mass hierarchies.

Unstable dipole (l=1) modes break the

directional symmetry.

Hνν = √ 2GF Z d3p0(1 − ˆ v · ˆ v0)(ρp0 − ¯ ρp0) (1 − ˆ v · ˆ v0) = 4π " Y0,0(ˆ v)Y ⇤

0,0(ˆ

v0) − 1 3 X

m=0,±1

Y1,m(ˆ v)Y ⇤

1,m(ˆ

v0) #

Duan (2013)

SLIDE 30

Inverted Hierarchy

1 2 3 4

τ

10

7

10

6

10

5

10

4

10

3

10

2

|~ q| |~ q00| |~ q10| |~ q1c| |~ q1s|

Duan (2013)

SLIDE 31

Normal Hierarchy

1 2 3 4

τ

10

7

10

6

10

5

10

4

|~ q| |~ q00| |~ q10| |~ q1c| |~ q1s|

Duan (2013)

SLIDE 32

Chakraborty, Mirizzi (2013)

Breaking Axial Symmetry

SLIDE 33

NH IH ne mN = Ye r = 1 09 g c m-3 1011 1010 108 107 106 105 100 1000 50 300 500 0.1 1 10 102 103 104 103 102 10 1 0.1

r HkmL

l Hkm-1L m Hkm-1L ∝ L/r4

∝ ρ/r2

Raffelt+ (2013)

Matter Suppression Self Suppression

SLIDE 34

ρ(r; E, ϑ, ϕ)

Directional Symmetry

ρ(r; E, ϑ)

SLIDE 35

x translation symmetry
left-right symmetry

R

Line Model

x z R L

Duan & Shalgar (2015)

ρm(z) = 1 L Z L ρ(x, z)−2mπix/L dx

SLIDE 36

Spatial Symmetry

µ ∝ GFnν α = n¯

ν/nν

Duan & Shalgar (2015)

SLIDE 37

50 100 200 500 1000 100 101 102 103 104 105 106 10-1 100 101 102 103 104 Radius HkmL l Hkm-1L m Hkm-1L SN Density

k = 0

102

103

∝ L/r4 ∝ ρ/r2

Chakraborty+ (2015)

Matter Suppression No Self Suppression

SLIDE 38

ρ(r, Θ, Φ; E, ϑ, ϕ) ρ(r; E, ϑ, ϕ)

Spatial Symmetry

SLIDE 39

Temporal Symmetry

Abbar & Duan (2015) Dasgupta & Mirizzi (2015)

Matter suppression is relieved for high-frequency modes

SLIDE 40

Fast Neutrino Oscillations

Usually flavor instabilities grow

at rates comparable to vacuum oscillation frequency.

Fast oscillations grow at rates

comparable to (GF nν).

Fast oscillations can occur

because of different angular distributions of νe and anti-νe.

Can fast oscillations occur

within the proto-neutron star?

νe sphere νe sphere _

Sawyer (2015) Chakraborty+ (2016)

SLIDE 41

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.

SLIDE 42

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.

SLIDE 43

Summary

Recent progress (Lecture 2):
Axial symmetry (in momentum space) -> oscillations in

both neutrino mass hierarchies.

Spherical symmetry (in real space) -> relief in self-

suppression.

Stationary assumption (time translation symmetry) ->

relief in matter suppression.

Same neutrino sphere (or angular distribution) for all

flavors -> fast oscillations.