自転、磁場超新星の爆発シナリオ(Current status of aspherical Type II supernovae models)固武慶（早大理工）

in collaboration with
山田章一(早大理工）佐藤勝彦（東大理）
第17回「宇宙ニュートリノ」研究会 2005年6/29

Plan of my talk and timetable

Section１

Introduction （〜3 min）

Section 2 Standard Supernova Physics（〜 7 min）
Section 3 Explosion Mechanism of Core-Collapse
Supernovae （〜25min）「Asymmetry & Explosion Mechanism 」
Section 4 Gravitational Waves
from anisotropic neutrino emissions
in the supernova core(~10 min)
Prospects

１.Introduction（〜5 min)
What are core-collapse supernovae？

Ancient Time
Meigetuki (明月記） by Sadaie Fujiwara（藤原定家）（at the end of Heian epoch）

Several historical supernovae
are known.

Modern time
１９３２ Zwicky & Baarde categorized supernovae into two types
Without H Line / withType Ⅰ

Type Ⅱ

Core-collapse supernovae(Collapse-driven supernovae)

Triggered by the gravitational
Collapse of massive stars(NASA HP)

Nowadays
Importance of Core-collapse SNe
Core-collapse supernovae

GW astronomy
Not yet

観測的示唆

Not yet

SN1987A

Neutrino Astronomy
Not yetGamma-Ray Bursts

LIGO

However one cannot tell the explosion mechanism clearly.
surface

Stellar radius(Wilson 1982)

Shock wave

No explosion!

Neutrino heating（hot）Protoneutron star

２０yearStellar center(Rampp et al. 2002)

Assuming spherical symmetry of the star,
only neutrino heating cannot produce the successful explosions !

Rotation and Magnetic field
It’s
It’s because
because rotation
rotation andand magnetic
magnetic field
fieldareare supported
supportedby
byObservations,： Massive stars in main sequence
rotate very fast ( ~ 200km/s) .
: Ring like circumstellar matterin SN 1987A (Plait et al. ‘95)
: Polarization observations show thatcore collapse supernovae are generally(HST Image)asymmetric. (Wang et al. ‘02)
: Neutron star, produced after explosion, are strongly magnetized.

We should investigate the effects of rotationand magnetic fields on the neutrino heating mechanism.

2.Standard Supernova
Physics
超新星爆発に至るまでの典型的な系の時間発展そこでの物理Standard scenario of core-collapse supernovae
cor e collapse

trapping

cor e bounce

C+O
He

H

Si
Fe

SN explosionNSshock in envelope

shock pr opagation in cor eHow massive stars end their life ?

Heger et al. 03

metalicity

Solar metalicity

Zero metalicity
１０Mｓ

２５Mｓ

Initial stellar mass

Stellar structure just before gravitational collapse

H
e

C
g
e
M
O N
a S
O
Ar C
Si
O Si

H

Fe

Standard scenario of core-collapse supernovae
cor e collapse

trapping

cor e bounce

C+O
He

H

Si
Fe

SN explosionNSshock in envelope

shock pr opagation in cor e

重力崩壊型超新星爆発のstandard scenario
cor e collapse

trapping

cor e bounce

C+O
He

H

Si
Fe

SN explosionNSshock in envelope

shock pr opagation in cor eStep 2 Neutrino Trapping（K.Sato,1975)
ニュートリノ参考：

Weak interacting particle＜＜

超新星コアに於ける最も断面積が大きな反応＝原子核によるcoherent scattering

Neutrino がコアにトラップされるかどうか調べるためには、二つのtimescale を比べればよい。
コアの落下時間

Coherent 散乱によるdiffusion timescale=Free escaping region

Neutrino Sphere
鉄コア

Neutrino sphereの出現

Diffusion region

Standard scenario of core-collapse SNecor e collapse

trapping

cor e bounce

C+O
He

H

Si
Fe

SN explosionNSshock in envelope

shock pr opagation in cor eCore bounce の続き（Cooperstein et al ‘89)

Bounce(跳ね返り）の後、Shock が生まれる

核密度を越えると、状態方程式が硬くなる。
１０＾９
ｃｍ
ｓ＾−１

Adiabatic index:

Infall phase

数 １０ ｋｍStandard scenario of core-collapse SNecor e collapse

trapping

cor e bounce

C+O
He

H

Si
Fe

SN explosionNSshock in envelope

shock pr opagation in cor eSupernova Explosion： Prompt explosion

Prompt explosion fails!
mainly due to photodissociation of Fe nuclei.

Neutrino Heating Mechanism (Wilson ’85)で爆発させる！

Neutrino Sphere
原始中性子星１秒

Delayed Explosion

Order Estimation
Heating rate

e n

e n

e

e

p

p

Binding energy

Shedding of neutrinos about
0.25 s is sufficiently to expel aneutron.

Summary of Standard Supernova Scenarios.
Explosion Mechanism of Collapse-Driven Supernovae

Prompt Explosion

Delayed Explosion

Fe coreShock wave
Stalled shock

PNS
DIFFICULTLIKELYWilson から ２０年！
(Wilson 1982)

ニュートリノ加熱

1D models,Comparison of different groups,
AGILE-BOLTZMANN (Oak –Ridge)
Hydro: implicit GR
Neutrino transport; 1D, Sn method(Mezzacappa & Bruenn 1993)
VERTEX

Shock Radius

Status of Spherical Models
VERTEX

Shock stalls.
AGILE

(MPA)

Hydro; explicit Newtonian
Neutrino transport: VEF method(Rampp & Janka 2002)

Time(Liebendoefer et al. 2003)

cannot produce explosions.

Step beyond Spherical Models
For realistic supernovae simulations, many physical ingredients
had better be taken into account.
More realistic
Macro Physics:
・Convection
・Rotation
・Magnetic fields
・General Relativity
MultiD simulations are urgent.

Micro Physics:
・Equation of state
・Neutrino transport

Section 3：
Asymmetry<->
Explosion mechanism
What causes “Asymmetry” ?
How “Asymmetry” affects
the neutrino heating ?

超新星の何処で対流が起こるか？
Heating domintated
Stalled shock
Cooing domintated~200km

PNS~ 100 km (Gain Radius)
Heating rateとcooling rate

Cooling rate ~ R^{-6}
Heating rate ~ R^{-2}

10 km

Stellar radius

Scheck
et al. 2004

The convective unstable region ?
（Answer） above gain radius below stalled shockShock radius

Convections rise the efficient of neutrino heating

Shedding time of neutrinos（ｓ）（Janka et al. 96）

As a result of convections, neutrino
Heating is enhanced.

Effect of SASI = Standing Accretion-Shock Instability
Standing shock and non-radial perturbation

Pressure-wave and fluid element

Blondin et al. 2002

Growth of the non-radial perturbation

L = 1 mode prevails!

Short summary：Effect of convection
・ Convection enhances the neutrino heating・ SASI may be able to produce the large
asymmetry(Incoherent scattering and SASI,
Ohnishi, Kotake, Yamada in prep)

Another possible cause of“Asymmetry”:Rotation

KK et al. 2003

Observed Asymmetry in Supernovae
Polarization Observations:・ All core collapse supernovae show significant polarization,~ 1 %, requires distortion axis rations of ~ 2 to 1. (Wang et al. ‘96)
・ Bipolar nature,(Wang et al. 01,
Wang et al. 03)

Bipolar explosion

SN 1999em

Is rotation good for the prompt explosions ?

Faster rotation

Explosion energy

Yamada and Sato. 94、 simplified EOS＋2D hydro+ adiabatic calculations

Faster rotation
Explosion monotonically decreases with theangular momentum.
Rotation is found to do no good to prompt explosions.
It is because rotation reduces thereleased gravitational energy at bounceUnknown and Known things about rotation
Rotation

Is rotation good for prompt
Explosion ? No!
(Yamada & Sato, ‘94)

Next to be investigated is whether
rotation does good or not to theneutrino heating mechanism.

Ｒｅｆ.
LeBlanc & Wilson ‘70, Mueller & Hillebrandt ‘81, Bodenheimer & Woosley ‘83 ,Symbalisty ‘84, Moenchemeyer & Mueller ‘89, Janka & Moenchmeyer ‘89
Yamada & Sato ‘94, Fryer & Heger 2000, Bueas et al. 03, Fryer & Warren 2003,
etc…

2D rotational core-collapse simulations

Shell +strong diff rot Cyl+ weak diff rot Cyl +strong diff rot

rapid

moderate

slow

Shell + weak diff rot

KK et al. 03

No prompt explosions occur.

Comparison of the neutrino sphere between
spherical and rotating models.
The shapes

Temperatures on neutrino spheres

・The shape of the neutrino sphere is deformed to be oblateby rotation.
・ As a result, the temperature near the rotational axis
becomes higher than that near the equatorial plane.
(These features are common to the other models)Heating Rates outside the neutrino sphere.
Reaction:
Heating Rate

(Janka. ‘01)

Assuming neutrino radiation is isotropic locally,
Therefore,z
Ray from neutrino
spherey
Neutrino SpherexHeating rates outside the neutrinosphere
M oderate, w eak diff rot (Heger’s).

M oderate, strong diff rot.

[MeV/nuc/sec]

Surfaceof neutrino
sphere[MeV/nuc/sec]

R apid, w eak diff rot

Neutrino heats matter near the rotational axis
preferentially.

[MeV/nuc/sec]

Stalled
Shock
wave[MeV/nuc/sec]

Spherical m odel

Convective stability analysis
Solberg & Hoiland instability condition,

Hoiland condition

Ledoux condition(j ; specific ang. momentum, X:distance from the rotational axis, a is effective gravity)

Convection are likely to occur near the rotational axis (~10 ms).

Detailed estimation of neutrino emissivity
Multigroup Flux Limited Diffusion Scheme (MGFLD) KK et al in prep
Input neutrino physics

Radiation equations with LP flux limitter
Bruenn (1985)

Neutrino Emissivity in rotating core(~30msec after bounce of Heger’s
rotating evolution model : Omega_0 ~ 4 rad/s)

Anisiotropic Neutrino radiations do exist

Test Calculations of our MGFLD code
Kotake, Ohnishi, Yamada, Sato, 2005 in prep.
Distribution function of electron-neutrino/muon-neutrino per neutrinoenergy-bin (16 energy mesh-points from 0.9MeV ~ 110 MeV logarithmically)

Compared with the Monte Carlo simulations by Janka et al,our code is able to successfully reproduce their result.

Short Summary of
Effect of rotation on neutrino heating（1) Neutrino spheres are deformed to be oblate due torotation, and the temperatures on the spheres arehigher near the rotational axis.
（２） Neutrino radiation from the deformed neutrino
sphere heats matter near the rotational axis more
preferentially.
（3) Regions near the rotational axis are convective
unstable.
These results suggest that the jet like explosion
might be induced. (Shimizu et al. ‘01)

Is anisotropic neutrino radiation good for explosion ?
Shimizu et al. 01, Madokoro et al. 03,04--- 2D hydro--- light bulb approx from the fixed neutrino
sphere--- outside neutrino sphere onlyt = 18 ms

t = 15 ms

t = 53 ms

If the anisotropic neutrino heating
survives in the later phases, it will
be good!
t = 30 ms

Is anisotropic neutrino rad. good for explosion？
Evidence ２、 critical luminosity for shick revival is lowered（Yamada,KK,Yamasaki,2004、Yamasaki& Yamada05)

M
Standing shock

Spherical modelLν
PNS
Rotating model

Accretion rate

Rotational Core-collapse with Detailed neutrino transport

Hydro:2dim Newtonian
Neutrino transfer: VEF(must be one dimension)
Input physics: state-of-art
Weak interactions

Rotating model

Lateral heating of
Neutrino should be
Important!

Spherical modelDecember
2004

Anisotropy ratio is
about 1 ~ 2.5

Consistent with ours

Not mentioned yet that explosion isreally obtained.

Another possible cause of“Asymmetry”:Magnetic field

超新星コア

ニュートリノ

KK et al. 04,05

(SGR, AXP)

Kouveliotou et al. 2003

・12 magnetars are known
・concentrated on the galactic planeWhy strong magnetic fields ?
Rotational energy= dipole radiation

O(~10^{11})Bdipole ~ 10^{14}~10^{15} Gauss

How massive stars end their life ?

Heger et al. 03

metalicity

Solar metalicity

Zero metalicity
１０Mｓ

２５Mｓ

星の質量

How massive stars end their life ?

metalicity

Heger et al. 03

n
o
i
t
rota

星の質量

Magnetic field

Magnetohydrodynamic Effects on Core-Collapse Supernovae
Yamada & Sawai, ApJ, (2004)
Takiwaki,KK,Nagataki,Sato ApJ (2004)
Sawai, KK, Yamda (2005) ApJ in press

一番問題なのは、初期磁場の強さ
・初めから強いと仮定。
・初めは弱くてもダイナモ等で増幅させる。
角速度や初期磁場をいろいろ変えてこれらの影響を調べた
初期条件
一様 Poloidal な
磁場
Z
X
親星は、
２０太陽質量モデル

角速度

200km 密度2000kmMagnetohydrodynamics
高速回転（realistic モデルの３倍）
強磁場モデル（中心集中型）

爆発エネルギー ~10^{50} ergs,
弱いながらも爆発（Delayed explosion が必要。）

何故ジェット状の爆発になるか？
Field wrapping

KK et al. 05

何故ジェット状の爆発になるか？

Contour of entropy per baryon

Contour of plasma β:Pmag/ Pmatter

Shock wave is shown to be magneto-driven.

何故ジェット状の爆発になるか？
Contour of entropy per baryon

Contour of Fhoop/Fmag

磁場で絞る効果
Fhoop =
磁場で膨らむ効果
Fmag =

磁場の効果で絞られている。
これがjet-like explosionの原因

爆発の強さの比較のまとめ
Takiwaki,KK,Nagataki,Sato(2005)

T/|W| 弱磁場でも爆発に寄与
磁場 ガ(ウス )0109
3×1010
1012

最大

1%
2%
0
0
0.05 0.00077
4.7
0.73
44.0
5.6

4%
0
0
0.03
1.8

爆発のエネルギー(10^50 erg)

回転↑
細い衝撃波
爆発のエネルギー↓

磁場↑
細い衝撃波
爆発のエネルギー↑

爆発のエネルギーはShock Frontが1500kmに達したときにエネルギーが正の部分の和

爆発は回転が弱く磁場が強いほうが強い。

North-South heating asymmetry in strongly
magnetized core and pulsar kicks(KK et al. 2005)
Weinberg & Salam theory
Mag. field line Ｂ->

parity violation: left-handed neutrinosｎCross section：
Horowitz 1999, Duan and Qian 03, Ando 03

磁場の効果マイナス σ（B）

Neutrino sphere＝ σ（B=0）（1＋ｎ・Ｂ α）

Neutrino heating becomes northSouth asymmetric
磁場の効果> Cause for the pulsar kickプラス

Neutrino heating rate in the strongly magnetized coreStandard model

Configuration Of B-field

Heating rate（with B）/（without B）

Along the rotational axis, B-field is in the same direction.
Strength of B-field is strongest there.
ー＞ B-field plays an important role for producing the asymmetry

Neutrino heating
rate in the strongly magnetized core
Heating rate（with B）/（without B）
Standard model

Configuration Of B-field

Heating rate（with B）/（without B）

At the north pole, B-field reduces
the heating (~ 0.5 %),In the convective regions, magnetic fields are bent.
while enhances it at the south pole.
Inner product of neutrino direction and B-field becomes negativeMeaning of 〜０．5 ％ of the neutrino heating asymmetry
Scheck et al. (2004) added 0.1 % random density perturbation

In their models, the directions ofpulsar kicks are totally random
600ｋｍ/stime

Our results suggest that themagnetar is kicked toward thenorth pole of the star.

Short summary of Section 3：
Asymmetric Supernovae & Explosion mechanism

Why“Asymmetric” supernovae ??

Although all the known microphysical process are included,
spherical models cannot produce explosion.

“Asymmetric” supernovae
Convection
・Good for enhancing neutrino heating, however,
only with it, successful explosions are notobtained.（Buras et al. 2003)
・Importance of SASI (Blondin 2002, Fogglizo 2002)(Without rotation or B-field, large anisotropy islikely to be produced.)
Rotation・Rotation induced anisotopic neutrino radiation
does really exist. (KK et al. 2003, Walder et al. 05)
・ Meanwhile, it is not yet know whether it really
produces the explosion (KK et al. in preparation)
Magnetic Field
・Likely to be a seed for the natal kick (KK et al. 2005)
・There remain many issues to be addressed, suchas MRI(Sawai et al. 2005, Takiwaki et al,05)

Since 2003, multi-D studies has begun to blossom
Sawai et al. (3)Kotake et al. (1)Burrows et al. (9)Kotake et al. (9)Takiwaki et al. (7)Number of paper

Liebendoerfer et al. (8)Fryer et al. (3)Kotake et al. (1)Livne et al. (12)Fryer (12)Fryer (9)1D fails

ze
ro
！
！
（２０
０２）

Scheck et al. (7)Yamada et al.(1)Kotake et al. (5) （D2)time

Buras et al. (3)

2003

2004
Epoch-making?

2005

Supernova group (explosionist) in the world
Germany

dimension

neutrinoidea

２D

Boltzmann

SASI

２D

MGFLD

Anisotropic
neu. Rad.

３D

SEFLD

?

U.S.

２D（B-field） MGFLD

Anisotropic
neu. Rad.

TAMA300
Section 4
Gravitational Waves
from core-collapse supernovae

LIGO

Introduction

重力波の放
出源

重力波の強度

重力崩壊型
超新星爆発

SN @ 10 kpc

周波数

現在稼動中の重力波検出範囲内
更に、次世代検出器、LCGT(日本）、LIGO II（アメリカ）などが計画予定。

Introduction
cor e collapse

trapping

コアバウンス時
cor e bounce

C+O
He

H

Si
Fe

SN explosionNSshock in envelope

shock pr opagation in cor eRotational Axis

Equatorial plane

Contour ofentropy
K.K et al.
(2003)

コアバウンス時の重力波
2D or 3D, realistic or polytropic EOS, detailed neutrino reaction
一様回転、標準自転速度
NR:Moenchmeyer et al. ’91,Yamada et al. ’95Zwerger etal. ’97,Rampp et al. ’98,Dimmelmeier et al. ’02
Fryer et al. 02,Ott et al. ’03,(2D, LS EOS),Mueller et al. ’03,Fryer
et al. ’04 (3D), KK et al. (03,04)
GR:Shibata(03),Shibata&Sekiguchi (04).

Type I

SN @ 10 kpc

微分回転、高速自転Type II

銀河中心の超新星バウンス
時の重力波は、現在稼動中の検出器の限界内にある。

GWs discussed until now are emitted at core bounce!

Today’s cook recipe

C 今日の料理

Other cites for the GW sources,
namely,Convective motions in the core
Anisotropic neutrino radiation

What is GW from anisotropic neutrino radiation ?

Neutrino radiation field,(exact form)
Epstein ‘78, Turner ‘78

TT gauge taken.
Standard formula,Typical amplitude and frequency of GWs fromneutrinos
Neutrino origin：

Typical amplitude：~ as large as the one at bounce

Typical frequency：とわかる。

Frequencies of GWs from neutrinos arerather low!

我々の研究自転の様子（微分回転の程度）によって、
ニュートリノ起源の重力波がどのように変化するか調べたい。
(K.K et al. PRD 2005)
初期モデル
Strength:
自転： T/|W| = 0.５ % <- Heger et al. (200１)

Configurations
Cylindrical：

Ro, Xo を1000km
から100 kmづつ
減らして行く。

Shell-type rotation

20 model 計算した。

Results： Waveforms from anisotropic neutrino radiation
Comparison between differential or uniformally rotating model
Aspect ratio of shocks （pole/equator）

waveform

Dif. rotation
Differential rotation

Uniform rotation

Differential rotation is found to
dominantly determine the waveforms
from the anisotropic neutrino radiation.

Uniform rotation

Plus

Minus

SN @ 10 kpc

Stronger differential rotation

Relation between the degree of differential rotationand the waveforms.

Gravitational radiation from anisotropic neutrino radiation
Spectrum Analysis
Uniform rotation model

Differential rotation model

TAMA
1st LIGO
MatterNeutrino

LCGT

LIGO II

GWs from neutrinos dominate over the ones frommatter at the lower frequency of ~ 100 Hz.

Detectability of GWs from neutrinos

SN @ 10 kpc
This is the window for GWs from neutrinos

LCGT

Advanced LIGO

They are within the detection limits of LIGO II or LCGT.

ニュートリノ起源の重力波：爆発メカニズムへの示唆（その１）Given 鉄コアの自転

非対称なニュートリノ放射

爆発メカニズムに良いセンス。

重力波

爆発メカニズムの理解の一助になるかもしれない。

ニュートリノ起源の重力波：背景重力波（その２）
Buonnanno et al. 2004

自転モデル (s15r model)
におけるニュートリノ重力波

Mueller et al. （０３） の数値計算

Neutrino emission Convective
motionBBOなどの次世代検出器で背景重力波として観測される可能性をもつ

展望と議論
重力崩壊型超新星

重力波天文学

まだ

観測的示唆

理論的予言
バウンス時○○
ニュートリノ△（面白い）
背景重力波△

理論的予言
球対称モデルに限られる。

SN1987A

ニュートリノ天文学
非球対称超新星ニュートリノは？？
まだ
まだ

理論的予言
衝突＋ニュートリノ ○背景重力波 ×（観測難）

理論的予言
TeV neutrino（背景ニュートリノ△
単体△）

もうすこし、お待ちください。。
ガンマ線バースト
現在、進行中です。

Thanksupernovae
you veryhasmuch!
Study of asymmtricjust begun to blossom.