TAUP2007Sep. 11-15, 2007 Sendai, Japan

Shiou KAWAGOEThe Graduate University for Advanced Studies (SOKENDAI) / NAOJ

JSPS Research Fellow

T. Kajino, The Graduate University for Advanced Studies (SOKENDAI) / NAOJ

H. Suzuki,Tokyo University of Science/NAOJ

K. Sumiyoshi,Numazu College of Technology

S. YamadaWaseda University

Outline

1 ． Introduction

2. Purpose

3 ． Result and Discussions ・ The adiabatic prompt explosion model ・ The observation of supernova neutrinos 4 ． Summary

Gravitational Collapse

Shock wave

Supernova

Neutrino trapping

Neutrino

Introduction (1)Collapse-driven Supernova

,,,,, ee

・ All of kinds of neutrinos are generated.

・ The energy spectrum is different.

・ T < O(100) MeV → nnne

, ,,,x

xeeEEE

Introduction (2)Supernova Neutrinos

enp

epn

e

e

νe

νe

νx

Energy (MeV) F

lux

(co

un

t /

MeV

) Wilson’s model

・ The gravitational energy:

The mass squared difference The mixing angle

Inverted Normal

23

Introduction (3)Neutrino Oscillations

?

Introduction (4)The Matter (MSW) Effect

Inverted

L

H

Normal

L

H

● 　 H-resonance ：

● 　 L-resonance ：

adiabatic

non adiabatic

adiabatic

.

.

ne

m2

shock13

2 2sin

dr

dn

dr

dn

e

eIs large. 　　and

Is small. 　　 or132 2sin Is large.

Is small.

ne

The shock wave is influenced on neutrino oscillation.

--MSW effect---

We estimate the supernova neutrino events which observed with Super-Kamiokande and SNO.

★We study how the influence of the shock wave appears in neutrino oscillations.

★Can we constrain θ １３ and the mass hierarchy?

Purpose

We succeeded in calculating propagation of shock waves

from iron core through the envelopes in single step.

D

ensi

ty

[g/c

m3]

R [cm] 1010

103

105・ Implicit lagrangian code for general relativistic spherical hydrodynamics Yamada et al. 1997•One-dimensional simulation•Adiabatic prompt 　　　　　　　　 explosion model•15Msolar star Woosley and Weaver,1995

The Adiabatic Prompt Explosion Model

Target number

Efficiency

Distance of supernova → 10kpc

Spectrum ( 5 < E < 60MeV)

Cross section

☆Survival Probability of neutrino

☆Neutrino spectra

　

☆Event number

spectra Original spectra

The Calculation of Event Number

eeFee rnG

U

E

EUdt

di

000

000

00)(2

00

00

0001

31

21

Normal hierarchy Inverted hierarchy 　

☆target : pure water (32,000 ｔ )☆ 　　 enpe

☆inverted mass hierarchy 　 → The event rates are depending on the parameters.

Event rate of Super-Kamiokande

Time [s]

213

2 102sin

413

2 102sin 5

132 102sin

313

2 102sin

Eve

nt

Rat

e [/

s]

Eve

nt

Rat

e [/

s][s

ho

ck

/ n

o s

ho

ck]

[sh

oc

k /

no

sh

ock

]

Time [s]

213

2 102sin

413

2 102sin 5

132 102sin

313

2 102sin

Normal hierarchy Inverted hierarchy

213

2 102sin

413

2 102sin 5

132 102sin

313

2 102sin

Event rate of SNO ・・・ has stopped （≧ ω≦ ） .

☆heavy water (1,000 t) 　 ☆ eppde

213

2 102sin

413

2 102sin 5

132 102sin

313

2 102sin

☆normal mass hierarchy 　 → The event rates are depending on the parameters.

Eve

nt

Rat

e [/

s][s

ho

ck

/ n

o s

ho

ck]

Result

☆The event rates of SK change greatly.　　→ θ13 is large and the hierarchy is inverted.

☆The event rate of SNO change greatly. 　　→ θ13 is large and the hierarchy is normal.

☆The event rates of SK and SNO decrease simply.　　→ θ13 is small.

Summary

☆The event rates are different depending on the value of θ13. →There is possibility that we can constrain the parameters whether θ13 is large or small.

☆θ13 is large. →The influence of the shock wave appears to the event 　　　 rates.　 → We can suggest the mass hierarchy by the observation.

☆We will calculate other detector .

☆Improvement underway Detailed studies of the cooling effect of the proto-neutron star are underway.