第21回理論懇シンポジウム＠国立天文台
2008年12月16日（火）

非熱的ニュートリノで探る
星の強磁場
堀内 俊作
（宇宙理論・東京大学 Ｄ３）
SH, Yudai Suwa, Hajime Takami, Shin’ichiro Ando, Katsuhiko SatoMNRAS, 391, 1893 (2008)

Magnetic Fields
In Early-type stars:– Recently, B ~ 103 G[Donati et al. 2006, etc]

Origin scenarios:– Fossil field ?

In Neutron stars:– Typically B ~ 1011 – 1014 G– SGRs, AXPs,… B ~ 1015 G
Origin scenarios:– Dynamo ?

stellar magnetic
field inputs[Thompson&Duncan1993]– Fossil field ?
[Ruderman1972,Ferario2006]

SourceO stars

Surface B-field [G]? – 103Radius [cm]1012

B-flux [G cm2]
< 1028

Neutron stars

1011 – 1015

106

< 1028

第21回理論天文学宇宙物理学懇談会シンポジウム

堀内俊作 2Use neutrinos to see inside
Supernova shock

Adopt the fossil scenario andinvestigate neutrino emission
First-order Fermi acceleration
at supernova shockp[Blandford&Eichler 1987][Drury 1983

High-energy proton +target proton/photon

pp → pn p →  → n Secondary  decay

 →    →  ee
第21回理論天文学宇宙物理学懇談会シンポジウム

堀内俊作 3

Supernova of a Magnetic star
Surface B-field: observed

Eventually becomes magnetar B-field
Assuming fossil field hypothesis, the Fe
core B-field is given by conservation of Br2 :Feshock

Assume a power-law :BRFe
第21回理論天文学宇宙物理学懇談会シンポジウム

Rn;n2surfaceR
堀内俊作 4

Acceleration (timescale)
9. 5v
10cm/sVelocity Use: se.g. [Kitaura et al. 2006]

shock

Acceleration time (Bohm limit   1 ) :
Fe
rc
10g
5p t  10 secacc
2vs 3R
Shock crossing time : minutes – hoursvs

第21回理論天文学宇宙物理学懇談会シンポジウム

堀内俊作 5

Maximum Proton energy[Horiuchi et al. 2008]

Proton cooling includes
1. pair-production
2. synchrotron
3. inverse-Compton(include effects of electron
synchrotron photons)
4. proton-proton collision

FastestpAcceleration
NOT possibleR vst acc  tcool yields the maximum proton energy
第21回理論天文学宇宙物理学懇談会シンポジウム

堀内俊作 6

Total neutrino event
are fractions of
the total energy:

Fluence: p ~ 0 .1

 event number, for 10 ergs Supernova at 10 kpc :
51

Soure

Neutrino E-max@ Super-K@ IceCube

Type II

20 GeV130200Type Ib

400 GeV1606000

Type Ic

600 GeV

70600

Background ~ 10/day

Background ~ 100 /day

Detectable above background.
第21回理論天文学宇宙物理学懇談会シンポジウム

堀内俊作 7

Discussion of event numbers
Source@ Super-K@ IceCube

Type II

130200Type Ib

160

6000

Type Ic

70600

due to weakacceleration
due to energy
loss of pions

IbdN νE
dE ν
2Ic

Ib

Type II

第21回理論天文学宇宙物理学懇談会シンポジウム

Ic

堀内俊作 8

Summary• Magnetic fields inside stars provides information
for field origins [e.g., fossil scenario]• Non-thermal neutrinos from supernovae ofstrongly magnetic stars:– Energy: ~ GeV– Time: ~ hours after thermal neutrinos• Neutrinos observable above background from
Galactic supernovae.
• Future work
– Stellar magnetic field configuration– Acceleration efficiency with geometry
第21回理論天文学宇宙物理学懇談会シンポジウム

堀内俊作 9Future• Future work
– Stellar magnetic field configuration– Acceleration efficiency with geometry

第21回理論天文学宇宙物理学懇談会シンポジウム

堀内俊作 10

Particle Acceleration
Shock front

First order Fermi acceleration
is a favourite. Shocks areefficient proton accelerators.
Drury, PhyRep (1983)
Blandford, Eichler ,PhyRep (1987)

pParticles are deflected by plasma wave-particle interactions.
Does photons prohibit this?
Photon-electron collision frequency :  e  c T ne  3108 s 1
q 2 ne 2 1013 s 1
Plasma frequency :  p me 0qB
g 
 5  10 5 s 1
Gyrofrequency :2 pNo.
第21回理論天文学宇宙物理学懇談会シンポジウム

堀内俊作 11

Acceleration time
Solve the diffusion-convection equation
f: dist. func. foraccelerated particles
d/dt

diffusion

convection

Test-particle approx (reaction is ignored). The residence time t are
downstream
upstreamu2
u1
In each cycle:4 2
t2 u2v

1n  nv 141t1   u1  4 u1v

4Up p3v

Acceleration timept3   1  2  3 1   ~tacc 
p U  u1 u2  u1 u1
第21回理論天文学宇宙物理学懇談会シンポジウム

Limit of u1 >> u2
and dropping T2
堀内俊作 12