Neutrino oscillation�in Failed Supernovae"

Masamichi Zaizen1 (master’s 1st in Umeda lab.)"

Takashi Yoshida1, Kohsuke Sumiyoshi2," Hideyuki Umeda1"

1"

新学術「地下素核研究」第４回超新星ニュートリノ研究会"" "2018/1/8 @四季の湯強羅静雲荘 "

1:University of Tokyo, 2:Numazu College of Tech."

•  Failed supernova"•  Neutrino oscillation"

–  (Vacuum oscillation)"– MSW effect"– Collective oscillation"

•  Methods"•  Results"•  Summary"•  Future work"

2"

Outline"

Massive star undergoes core-collapse."Shock wave stalls due to accretion matter.""In failed SNe, the shock wave can not revive due to heavy infall of outer layer."The proto-neutron star evolves into a black hole."

PNS Failed

Success

Shock stallsBH"

formation"

explosion"

3"

What is Failed Supernova？"

4"

Example for a failed SN ?"

N6946-BH1"25M¤, Red super giant, 6Mpc, Cygnus & Cepheus"

(c) NASA"

Gerke et al. 2015, Adams et al. 2017"

•  Failed SN is faint in EM, but bright in neutrino."•  Surrounding matter continues to accrete onto the PNS."•  Neutrino emission stops when covering neutrino sphere

with BH event horizon formed in the center. "

•  Neutrino spectra depend on EoS of high temperature and high density, so the observation enables us to understand it."

•  Neutrinos are the important tool to get information on failed SNe."

•  How many neutrinos do we observe on the Earth?"

5"

Failed SNe and Neutrinos"

6"

Mass hierarchy is not yet known. "(We’re looking forward to this solution.)"We assume two hierarchy cases in this work."

m12

m32

m22

inverted�hierarchy

m32

�m?+

-�m?

normal�hierarchy

2. Neutrino oscillation"

And we choose the modified flavor basis:"

Dighe et al. 2000, Dasgupta et al. 2008"

⌫x

= cos ✓23⌫µ � sin ✓23⌫⌧

⌫y

= sin ✓23⌫µ + cos ✓23⌫⌧

Then νx doesn’t include ν3 and θ13."Thereby νx isn’t affected by the oscillation associated with θ13, ∆m13." ex.) H resonance, 2 flavor collective…"

⌫e

$ ⌫y

⌫e

$ ⌫x

1-to-1 oscillation sets"

•  MSW effect (the matter oscillation)"

7"

2. Neutrino oscillation"

P PNH sin2 ✓13 sin

2 ✓12 cos2 ✓13 cos2 ✓12IH cos2 ✓13 sin

2 ✓12 sin2 ✓13 cos2 ✓12

Survival probability of electron neutrino after undergoing adiabatic MSW H and L resonances."Shock wave effects don’t exist in failed SNe, unlike success SNe."

cos

2 ✓13 ⇠ 1

cos

2 ✓12 ⇠ 0.7

�2

�1

�3

�3

�2

�1

ne

m2

L

H

(SN core)(SN surface)

← inverted case"" normal case →"

�2

�1

�3�3

�2

�1

ne

m2

L

H

(SN core)(SN surface)

•  Collective oscillation（Self-interaction effect）"

8"

2. Neutrino oscillation"

The collective oscillation is due to ν-ν inteaction and causes the spectral splits."This effect is important near the supernova core."

r

Neutrino�sphere

R� �interaction" ν"

ν"PNS"

Bulb model"

0 1 2 3 4 5 6 7 8 9

10

0 20 40 60 80 100

Num

ber [×

1055

]

Energy: E [MeV]

ix init.iy init.ie init.

ixiyie

r~O(100, 1000 km)"

�e ,p

vx ,q vx ,p

�e ,q

We obtain the flavor evolutions by solving the following equation of motion for the density matrix;"

9"

In this work, we assume the single-angle approximation. This approximation is that wave functions don’t depend on the angle of incidence. "

VO" MSW" Collective (non-linear term)"

i@t⇢p =

+U

M2

2pU†

+

p2GFL+

p2GF

Zd

3q

(2⇡)3(1� cos ✓pq)

�n⌫(q)⇢q � n⌫(q)⇢q

, ⇢p

�

3. Method"

The multi-angle simulation is … under construction."I face several difficulties and the results are incomplete."

•  Calculation by Sumiyoshi"•  40M¤、EoS:LS220、1D model"

–  Sumiyoshi et al. 2007, 2008"•  Top left figure shows neutrino

luminosity."•  Bottom left figure shows

neutrino averaged energy."•  These values continue to

increase after core bounce."

•  At several time steps, we carry post-process calculation in the normal and inverted hierarchy."

•  t = 30, 100, 200, 300" , 400, 500, 600, 750 ms"

10"

Using model"

0 2 4 6 8

10 12 14 16 18 20

0 0.2 0.4 0.6 0.8 1

Lum

inos

ity [1

052 e

rg/s

]

time after bounce [sec]

iei-eixpurple: e"

green: e"blue: x"

_"

0

5

10

15

20

25

30

35

0 0.2 0.4 0.6 0.8 1

Aver

age

ener

gy <

Ei>

[MeV

]

time after bounce [sec]

iei-eix

time after core bounce [sec]"

11"

Result ex.: 600ms, Neutrino, IH & NH"

0 1 2 3 4 5 6 7 8 9

10

0 20 40 60 80 100

Num

ber [× 1

055]

Energy: E [MeV]

ix init.iy init.ie init.

ixiyie

red : e"green: x"blue : y"

Energy [MeV]"

0 1 2 3 4 5 6 7 8 9

10

0 20 40 60 80 100

Num

ber [× 1

055]

Energy: E [MeV]

ix init.iy init.ie init.

ixiyie

red : e"green: x"blue : y"

Energy [MeV]"

0 1 2 3 4 5 6 7 8 9

10

0 20 40 60 80 100

Num

ber [×

1055

]

Energy: E [MeV]

ix init.iy init.ie init.

ixiyie

red : e"green: x"blue : y"

Inverted hierarchy"

0 1 2 3 4 5 6 7 8 9

10

0 20 40 60 80 100

Num

ber [×

1055

]

Energy: E [MeV]

ix init.iy init.ie init.

ixiyie

red : e"green: x"blue : y"

Normal hiearchy"

0 1 2 3 4 5 6 7 8 9

10

0 20 40 60 80 100

Num

ber [×

1055

]

Energy: E [MeV]

Initial neutrino spectra

ie init.ix init.iy init.

Initial spectra"

red : e"green: x"blue : y"

Collective"

MSW resonance"

12"

Result ex.: 600ms, Antineutrino, IH & NH"

0

1

2

3

4

5

6

7

8

9

0 20 40 60 80 100

Num

ber [× 1

055]

Energy: E [MeV]

ix init.iy init.ie init.

ixiyie

red : e"green: x"blue : y"

Energy [MeV]"

0

1

2

3

4

5

6

7

8

9

0 20 40 60 80 100

Num

ber [×

1055

]

Energy: E [MeV]

Initial anti-neutrino spectra

ie init.ix init.iy init.

Initial spectra"

red : e"green: x"blue : y"

0

1

2

3

4

5

6

7

8

9

0 20 40 60 80 100

Num

ber [× 1

055]

Energy: E [MeV]

i-x init.i-y init.i-e init.

i-xi-yi-e

red : e"green: x"blue : y"

Energy [MeV]"

0

1

2

3

4

5

6

7

8

9

0 20 40 60 80 100

Num

ber [×

1055

]

Energy: E [MeV]

i-x init.i-y init.i-e init.

i-xi-yi-e

Normal hiearchy"

red : e"green: x"blue : y"

0

1

2

3

4

5

6

7

8

9

0 20 40 60 80 100

Num

ber [×

1055

]

Energy: E [MeV]

i-x init.i-y init.i-e init.

i-xi-yi-e

red : e"green: x"blue : y"

Inverted hierarchy"

Collective"

MSW resonance"

•  Oscillation effects are qualitatively same at the time except for the neutronization burst at t = 30 ms."

"•  At the neutronization burst, collective effects are

suppressed."–  Due to the excess of electron neutrinos."–  Therefore the differences occur between two

hierarchies by MSW."

13"

Results at other time steps."

0 10 20 30 40 50 60 70 80 90

100

0 10 20 30 40 50

Num

ber [×

1055

]

Energy: E [MeV]

Initial neutrino spectra

ix init.i-e init.ie init.red : e"

blue : e"green: x"

-"

⌫e

⌫e

$ ⌫x

⌫x

Pair conversion -> no collective"

•  Neutrinos arrive at the Earth."•  How many electron antineutrinos are detected by

Super-Kamiokande?"•  Super-Kamiokande have a high sensitivity to

inverse beta decay with water Cherenkov detector."

⌫̄e + p ! n+ e+

14"

Detectionability at Super-Kamiokande"

�

�

� �e_

50 kpc"

Abe et al. 2011"

•  Event rate of antineutrinos by Super-Kamiokande"–  Np : proton number" = fiducial volume 22.5 kton"–  d : distance to Failed SN (LMC, assume 50 kpc)"–  Eth : threshold energy" = 4.79 MeV (3.5 MeV for recoil electrons)"–  φ(E) : spectrum at the detector"–  σ(E) : cross section of IBD (Strumia et al. 2003)"

15"

Detectionability at Super-Kamiokande"

dN⌫

dt=

Np

4⇡d2

Z 1

Eth

�(E)�(E)dE

0

50

100

150

200

250

300

350

0 100 200 300 400 500 600 700 800

accu

mul

ated

neu

trino

eve

nt [n

umbe

r]

times after bounce: t [ms]

inverted hierarchynormal hierarchy

no oscillation 0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700 800

even

t rat

e [n

umbe

r /se

c]

times after bounce: t [ms]

inverted hierarchynormal hierarchy

no oscillation

Hundreds of neutrinos are detected without EM counterpart.""Event number rate is same in normal and inverted hierarchy."

–  collective effect and H resonance cancel each other in inverted hierarchy."

16"

Event rate at Super-Kamiokande"

•  Deep Underground Neutrino Experiment"•  A next generation detector in the United States."•  Finish all construction by 2028."•  DUNE have a high sensitivity to Charged-Current reaction

with liquid argon."

17"

Detectionability at DUNE"

40Ar + ⌫e !40 K⇤ + e�

•  How many electron neutrinos are detected by DUNE ?"

•  Event rate of neutrinos by DUNE"–  NAr : Argon number" = fiducial volume 4×10 kton"–  d : distance to Failed SN (LMC, assume 50 kpc)"–  Eth : threshold energy" = 8.28 MeV (5 MeV electron cut-off)"–  φ(E) : spectrum at the detector"–  σ(E) : cross section of CC (Suzuki et al. 2013)"

18"

Detectionability at DUNE"

dN⌫

dt=

NAr

4⇡d2

Z 1

Eth

�(E)�(E)dE

0

200

400

600

800

1000

1200

1400

0 100 200 300 400 500 600 700 800

even

t rat

e [n

umbe

r /se

c]

times after bounce: t [ms]

inverted hierarchynormal hierarchy

no oscillation 0

100

200

300

400

500

600

0 100 200 300 400 500 600 700 800

accu

mul

ated

neu

trino

eve

nt [n

umbe

r]

times after bounce: t [ms]

inverted hierarchynormal hierarchy

no oscillation

"•  Event number is same in normal and inverted hierarchy."

–  Spectra are different between two hierarchies."–  Why?"

19"

Event rate at DUNE"

20"

Cross section of CC reaction"

Suzuki et al. 2013"

Cross section in DUNE case"(CC reaction)"

Cross section increases in the order with energy."

0 1 2 3 4 5 6 7 8 9

10

0 20 40 60 80 100

Num

ber [×

1055

]

Energy: E [MeV]

ix init.iy init.ie init.

ixiyie

red : e"green: x"blue : y"

Energy [MeV]"

Inverted mass hierarchy"

0 1 2 3 4 5 6 7 8 9

10

0 20 40 60 80 100

Num

ber [×

1055

]

Energy: E [MeV]

ix init.iy init.ie init.

ixiyie

Normal mass hiearchy"

red : e"green: x"blue : y"

Energy [MeV]"

21"

Future work"

The multi-angle approximation?"

22"

Future work"

VO" MSW" Collective (non-linear term)"

i@t⇢p =

+U

M2

2pU†

+

p2GFL+

p2GF

Zd

3q

(2⇡)3(1� cos ✓pq)

�n⌫(q)⇢q � n⌫(q)⇢q

, ⇢p

�

d

dtP =

"+!B + �D

vr,u+

p2GF

2⇡R2⌫

R2⌫

2r2

ZdE0du0

✓1

vr,uvr,u0� 1

◆�n⌫P � n⌫P

�#⇥ P

multi-angle approximation"polarization vector"

•  verify the multi-angle matter suppression"

longer path to the same radius r1"

experience larger matter effect."

vr,u = cos ✓ =

r1� sin

2 ✓RR2

⌫

r2

Neutrino sphere

radius r1

�

•  How large do we use the angle bin?"–  a lack of angle samplings causes the artificial

collective oscillations."–  good resolution :Nθ ~ O(103). 1000 ?, 2000 ?, …5000 ?"

23"

Future work"

0.4

0.42

0.44

0.46

0.48

0.5

0.52

0.54

0.56

0.58

100 150 200 250 300 350 400

l ee

r [km]

Nu = 500Nu = 1000Nu = 1500Nu = 2000

multi-angle"

8⇥NE ⇥N✓ ⇥ 2 . 1, 000, 0001D × 2D calculation.

single-angle"

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0 200 400 600 800 1000 1200 1400

l ee

Radius [km]

10 MeV

•  We calculate 3-flavor neutrino oscillation for 1-D failed supernova model."

•  Hundreds of neutrinos and antineutrinos are detected from a failed SN located in LMC (50 kpc)."

•  The event numbers of neutrino and antineutrino are identical in both hierarchy cases."–  High energy components are dominant at DUNE."

•  We tackle the multi-angle approximation."

24"

Summary"