1. Core-Collapse Supernovae and Supernova Relic Neutrinos
Cosmic History of
Core-Collapse Supernovae and
Supernova Relic Neutrinos
J. Suzuki13, T. Kajino123, G.J. Mathews4, T. Yoshida2
1 National Astronomical Observatory Japan, Tokyo, JPN
2 Tokyo University, Tokyo, JPN
3 The Graduate University for Advanced Studies, JPN
4 University of Notre Dame, Indiana, USA 1 1 1 1 1 1 1 1 1 1 1 1 1

2. １ Introduction Motivation of this work Time evolution of CCSN rate ↓
Measurement and prediction of core collapse supernova rate(CCSN rate) are different by a factor of 2
→　What causes the difference？ ↓
Existance of “dark SNe” is
suggested.
SN rate predicted from SFR
SN　measured rate
CCSN：
Neutrinos carry away the gravitational binding energy.
→Detecting “SRN”
clarify the question?
Supernova rate
Horiuchi et al.,2011,arXiv,

3. Aims of this work
[１] 　To clarify the physics about “dark SNe” suggested by the difference between massive star formation rate and CCSN measured rate by detecting SRN energy spectrum and to add more strict constraint to massive star formation history.　
[２] To establish the method of deriving SRN detection rate on 10^6 ton class water Cherenkov detector in high precision.
　 a. Employing reliable data of SFR observation
　 b. Considering 4 types of CCSNe removing
　 c. Assuming SN neutrino temperatures from reliable simulation uncertainties
and observation.
[３]To discuss the possibility to constrain neutrino oscillation parameters and SN equation of state (EOS) by SRN detection.

4. ２ Method of calculating differential Number Flux of SRNs
CCSN types: O-Ne-Mg SN, NS-SN, fSN(black hole SN), GRB
（A）: Cosmic expansion（z:redshift）　（ΛCDM model,Ωm=0.3,ΩΛ=0.7）
（B）： Star formation rate (event number of SRN)
（C）： Supernova rate (event number and energy spectrum of SRN)
（D）：Neutrino oscillation (energy spectrum of SRN)
（E）：Energy spectrum（E´ν） of single CCSN
（F) ：EOS of fSN (incompressibility of EOS change energy spectrum)
（※)：Detection rate & condition of detection
E´ν = (1+z)Eν 4 4 4 4 4 4 4 4 4 4 4 4 4

5. ※：Detection SK（22.5Kｔ, efficiency：0.8）
　reaction：p + νe → e+ + n
※νe：not concerned in this work
Neutrino Flux：
Event rate：
Fig: Sketch of Hyper Kamiokande
（Shiozawa et al.,Data for 2008 Users’ conference）
∵ε：efficiency, σ：cross section、Eν＝Ee (MeV)
SK（22.5Kｔ, efficiency：0.8）
→ HK（1.0Mt, efficiency：1.0）: assumed in this work
Water Cerenkov type, GdCl3 - laden(0.2%)　
　cross section：Strumia&Vissani, 2003, PhLB, 564, 42）による
　SRN detection lower limit：10.0MeV 5 5 5 5 5 5 5 5 5 5 5

6. B: Star formation rate as functions of z
red：infrared
blue：optical
magenta：ultra violet
Light blue：X-ray,γ-ray
green：radio
　 S F R
χ^2 test
Concerning Dust correction
　(UV, Ir, sub-mm)
red thick line：approximate
red thin line：maximum and minimum
Black dotted line：Yuksel et al., 2008,
　　　　　　　ApJ., 683, L5
Fitting formula:
(Yuksel et al., 2008, ApJ., 683, L5)
Coefficients:: 6 6 6 6 6 6 6 6 6 6 6
Log SFR(M◎/Mpc^3/Yr)‏

7. C:Progenitor mass and explosion model
Salpeter mass function and boundary progenitor mass determine the ratio of each explosion.
Neutron Star
Black　Hole
（20％）
（80％）
（Tνe, Tνx） ＝ （5.6, 6.5）
（Eνe, Eνx）＝ （4.7, 2.3）
EOS in Shen et al. (1998)
（Tνe, Tνx） ＝ （8.0, 11.3）
（Eνe, Eνx）＝ （7.5, 11,1）
EOS in Lattimer&Swesty (1991)
（47％）
（33％）
（Tνe, Tνx） ＝ （5.0, 6.0）
（Eνe, Eνx）＝ （5.0, 5.0）
（Tνe, Tνx） ＝ （5.3, 4.4）
（Eνe, Eνx）＝ （32,0, 1,9）
（M◎）
（Tνe, Tνx） ＝ （3.6, 3.6）[MeV]
（Eνe, Eνx）＝ （2.7,11,1）[×1052erg]

8. D: Neutrino Oscillation
・Neutrino：3 flavors and their anti particles
(νe, νe, νx=νμ,τ, νμ,τ）
・SRN energy spectrum on the earth is
different from that at production due to the
effect of neutrino oscillation.
case A
Normal mass hierarchy
Adiabatic & non adiabatic
Inverted mass hierarchy
Non adiabatic
case B
Adiabatic　
case C：No oscillation
　subscript ”０” represents particles
at production.
(Dighe,Smirnov,2000, Phys, Rev. D, 62, 3007)‏ 8 8 8 8 8 8 8 8 8

9. E: Constraining Tν in NS-SNe （１）
We cannot observate Tν iin CCSN in a direct way.
So we must constrain Tν in other ways.
x=Eν/Tν
・Assuming Fermi-Dirac Dist.
・Concerning neutrino oscillation
　・Tν（newly constrained）
・ην: 0 in this work
（Tν with±10% error、
　Yoshida et al.,2005)
・Statistically reliable area that
the pairs of (Tνe,Tνx） are
allowed to exist.
(Yoshida et al., 2005, Phys. Rev. Let., 94, )‏
・○ & ●：pairs of Tν shown in
previous works
（●：original, published） ‏ 9 9 9 9 9 9 9 9 9 9
Tνe(MeV)‏
Tνe(MeV)‏
Tνe(MeV)‏
Tνx(MeV)‏

10. Constraining Tν in NS-SN（２）： using 11B
Yoshida et al., 2008.,ApJ., 686, 448‏
Constraining Tν in NS-SN（２）：
using 11B
・Contour: 11B yield per single SN
（unit：10-7　solar mass）
・Upper & lower limit of
gravitational binding energy
of SN (1987A model）
・Upper & lower limit of 11B yield
based on galactic chemical evolution
and isotope ratio of B in meteorites
・Upper & lowe limit of Tνμ,Tντ
　4.3MeV ＜　Tνx ＜ 6.5MeV
(Yoshida et al., 2008,ApJ, 686, 448)
・Statistical constraint（light blue circle）
・Tνe ＜ Tνe ＜ Tνx
Hierarchy of neutrino temperature）
⇒ 3.9MeV ＜　Tνe ＜ 6.0MeV
＋：pairs of Tν shown in
previous works
（Thick＋：original, published） ‏

11. 3 Results -Influence of “dark SN” rate
SN rate predicted from SFR
Existance of “dark SNe” is suggested.
SN　measured rate
Supernova rate
Horiuchi et al.,2011,arXiv,

12. ４．　　　　　　　　　　＝ Summary ＝
　Motivation：　To clarify the physics about “dark SNe” suggested by the difference between massive star formation rate and CCSN rate measurements by detecting SRN energy spectrum and to add more strict constraint to massive star formation history.　
　Methods： To establish the method of deriving SRN detection rate on 10^6 ton class water Cerenkov detector in high presicion.
Results
Detecting SRN for 10 yrs of runtime on HK,
（Ａ）The case that dark SNe are failed SNe （Black hole SNe)：
　● The difference between SN rate and Salpeter function will be clarified.　
　　　　　　⇒It will be contributed to massive star formation history.
　● Neutrino oscillation parameters and SN EOS will be constrained.　
　　　　　　⇒It will be contributed to neutrino physics, high-temperature physics.
（Ｂ）The case that dark Sne are O-Ne-Mg SNe：
　● The difference between SN rate and Salpeter function will not be clarified.
　● Neutrino oscillation parameters and SN EOS will not be constrained.