Sec$on2.星の構造と性質

2.1星の構造

2.2星の明るさと色

•星の基本的な性質を理解する• 星の構造と星の進化

• 星の爆発で何が起きているのかを理解する• 超新星の爆発メカニズムと元素の合成

•宇宙の元素の起源を理解する•時間軸天文学を味わう

恒星物理学特論I

「宇宙における爆発天体の理論と観測」

•全体の概論

•星の構造と性質

•星の進化

•超新星爆発のメカニズム

•超新星爆発の観測

•元素の起源

•中性子星合体と重力波

•銀河の化学進化

•時間軸天文学

内容

成績 • 出席、質問

• レポート

講義資料と日程h.ps://www.astr.tohoku.ac.jp/~masaomi.tanaka/tohoku2018

*なるべく

一話完結にする予定

*半分板書、半分スライド

*研究上の用事で欠席する

場合は事前に連絡を

前回もらった質問

超新星の分類：分光学C: NASA/HST

3000 4000 5000 6000 7000 8000

Rel

ativ

e flu

x +

cons

t

Rest wavelength (Å)波長（オングストローム）

硫黄 ケイ素

水素カルシウム

ヘリウム

鉄

超新星：４つのタイプ水素

II型

I型 なし あり

Ia型Ib型 Ic型

ケイ素あり

なし

ヘリウムあり なし

II型超新星のバラエティThe Astrophysical Journal Letters, 756:L30 (6pp), 2012 September 10 Arcavi et al.

0 20 40 60 80 100 120 140

0

0.5

1

1.5

2

SN2005cs

SN2009krSN2011dhSN1993J

Days Since Explosion (estimated)

Shi

fted

R−B

and

Mag

nitu

de

SN1999em

SN Ib/c Template

0 20 40 60 80 100 120 140

−17.5

−17

−16.5

−16

−15.5

−15

−14.5

SN2005au

SN2005bw

SN2005aa SN2004et

SN2004er

SN2004du

Days Since Explosion (estimated)

Abs

olut

e R

−Ban

d M

agni

tude

SN1999em

SN2005cs

SN2005aySN2004fx

Figure 1. Top panel: R-band light curves of 15 Type II SNe from CCCP (excluding the four events presented in Figure 4), normalized in peak magnitude (SN2004fxdata taken from Hamuy et al. 2006; SN2005ay data taken from Gal-Yam et al. 2008a; SN2005cs data taken from Pastorello et al. 2009). A clear subdivision into threedistinct subtypes is apparent: plateau, slowly declining, and rapidly declining SNe (the latter consisting only of SNe IIb). Reference SNe are shown for comparison(SN1999em from Leonard et al. 2002; SN2009kr from Fraser et al. 2010, found to be a member of the IIL subclass as claimed by Elias-Rosa et al. 2010; SN1993Jfrom Richmond et al. 1994; SN2011dh from Arcavi et al. 2011). We also overplot the SN Ib/c template derived by Drout et al. (2011). The data have been interpolatedwith spline fits (except for SN2005by, where a polynomial fit provided a better trace to the data). The shaded regions denote the average light curve ±2σ of eachsubclass. The maximal 7 day uncertainty in determining the explosion times is illustrated by the interval in the top right corner. Bottom panel: R-band light curves of9 Type IIP SNe from CCCP with respect to their estimated explosion time (except for SN2005au and SN2005bw, marked by dashed lines, for which the explosion dateis not known to good accuracy). The light curve of SN2004fx is taken from Hamuy et al. (2006), that of SN2005ay from Gal-Yam et al. (2008a), and that of SN2005csfrom Pastorello et al. (2009). SN1999em (Leonard et al. 2002) is shown for comparison. A spread in plateau luminosities is apparent while plateau lengths seem toconverge around 100 days. Spline fits were applied to the data.(A color version of this figure is available in the online journal.)

continuum, we find that the light curves group into three distinctsubclasses: plateau, slowly declining (1–2 mag/100 days), andinitially rapidly declining (5–6 mag/100 days) events (see alsoTable 1). We note that the three rapidly declining events areall Type IIb and that they display similar light curve shapesto those of Type Ib/c SNe (Drout et al. 2011). We perform aKolmogorov–Smirnov test and find that the probability that themeasured ∆M15R values for the rapid- and slow-decline groupsare drawn from a single underlying distribution is 2%.

Three events (SN2004ek, SN2005ci, and SN2005dp;Figure 4) display prolonged rising periods in their light curves.They do not show signs of interaction in their spectra andmay be explosions of compact blue supergiant progenitors(Kleiser et al. 2011; Pastorello et al. 2012), as demonstrated

directly in the case of SN 1987A (see Arnett et al. 1989 fora review).

Finally, one event (SN2004em; Figure 4) displays a verypeculiar photometric behavior. For the first few weeks it issimilar to a Type IIP SN, while around day 25 it suddenlychanges behavior to resemble an SN 1987A-like event.

The full photometric data set is available online throughWISeREP15 (Yaron & Gal-Yam 2012).

3.1. Declining SNe

Aside from establishing a different rate of decline for SNeIIb compared to SNe IIL, Figure 1 (top panel) suggests that the

15 http://www.weizmann.ac.il/astrophysics/wiserep

3

プラトー

単調に暗くなるIb,Ic型

IIP型(plateau):平坦な部分がある

IIL型(linear):単調に暗くなる

Arcavi+11

水素の吸収線拡大図

水素Hアルファ

0

1

2

6000 6200 6400 6600 6800 7000

Flux

Wavelength (A)

吸収“P-Cygni”プロファイル

λλ0

観測者

光のドップラー効果=3

� =�

c� v

c

��0

=3

v

c=

(�0 � �)�0

古典新星(Classicalnova)

ListofGalac,cNovaeh1ps://projectpluto.com/galnovae/galnovae.htm

M31(アンドロメダ銀河)「発見数」~30-60個/yrSha=er&Irby2001

真のイベントレート~60個/yrぐらいcompletenessの補正,Darnleyetal.2006

超新星(~0.01個/yr)よりも1,000倍以上高い頻度

銀河系内「発見数」~10個(~5-15)/yr*全てを見ているわけではないことに注意(銀河中心の向こう側)

(Credit:K.Ulaczyk)

Sec$on2.星の構造と性質

2.1星の構造

2.2星の明るさと色

太陽

水素

ヘリウムJAXA/ISAS

「核融合」

明るさ4x1033erg/s=4x1026ジュール/秒(W)

日本の1年間の消費電力：1.5x1019ジュール

==>日本の消費電力の2500万年分が1秒で放出

エネルギー源：E=mc2水素

水素原子核 4つ　＞　ヘリウム原子核0.7％重い

1.007 kg の水素　➡　1kg のヘリウム

E ＝ mc2 ＝ 0.007 kg × （3×108 m/s）2

＝ 6×1014 ジュール

ヘリウム0.7%重い

1.007g 1.000g

1.007kgの水素核融合から取り出せるエネルギー

E=Δmc2 光速c=3x1010cm/s

(1秒間に30万km)

問題１：太陽が生み出すことができる全エネルギーは？

（使える水素は太陽の質量の約10%とする）太陽の質量：3x1033g

問題２：太陽は何年輝ける？

102年 104年 106年 108年 1010年 1012年

100 1万 100万 1億 100億 1兆

1年~3x107秒

明るさ4x1033erg/s

(C)Ma1hewSpinelli

リゲル

ベテルギウス

h.p://astronomy.nmsu.edu/geas/lectures/lecture23/slide04.html

Hertzsprung-Russeldiagram(HR図)

温度(K)

光度

赤色巨星

赤色超巨星

白色矮星

主系列星の性質：質量と半径の関係

R~M0.7

なぜ？？

−1 0 1

−2

0

2

4

6

log (M / Msun)

log

(L /

L sun

)

−1 0 1−1.0

−0.5

0.0

0.5

1.0

log (M / Msun)

log

(R /

Rsu

n)

Figure 1.3. Mass-luminosity (left) and mass-radius (right) relations for components of double-lined eclipsingbinaries with accurately measured M, R and L.

1.2 Stellar populations

Stars in the Galaxy are divided into different populations:

• Population I: stars in the galactic disk, in spiral arms and in (relatively young) open clusters.These stars have ages ∼< 109 yr and are relatively metal-rich (Z ∼ 0.5 − 1Z⊙)

• Population II: stars in the galactic halo and in globular clusters, with ages ∼ 1010 yr. These starsare observed to be metal-poor (Z ∼ 0.01 − 0.1Z⊙).

An intermediate population (with intermediate ages and metallicities) is also seen in the disk of theGalaxy. Together they provide evidence for the chemical evolution of the Galaxy: the abundanceof heavy elements (Z) apparently increases with time. This is the result of chemical enrichment bysubsequent stellar generations.

The study of chemical evolution has led to the hypothesis of a ‘Population III’ consisting of thefirst generation of stars formed after the Big Bang, containing only hydrogen and helium and noheavier elements (‘metal-free’, Z = 0). No metal-free stars have ever been observed, probably due tothe fact that they were massive and had short lifetimes and quickly enriched the Universe with metals.However, a quest for finding their remnants has turned up many very metal-poor stars in the halo,with the current record-holder having an iron abundance XFe = 4 × 10−6XFe,⊙.

1.3 Basic assumptions

We wish to build a theory of stellar evolution to explain the observational constraints highlightedabove. In order to do so we must make some basic assumptions:

• stars are considered to be isolated in space, so that their structure and evolution depend only onintrinsic properties (mass and composition). For most single stars in the Galaxy this conditionis satisfied to a high degree (compare for instance the radius of the Sun with the distance to its

5

LectureNotebyPols

−1 0 1

−2

0

2

4

6

log (M / Msun)

log

(L /

L sun

)

−1 0 1−1.0

−0.5

0.0

0.5

1.0

log (M / Msun)lo

g (R

/ R

sun)

Figure 1.3. Mass-luminosity (left) and mass-radius (right) relations for components of double-lined eclipsingbinaries with accurately measured M, R and L.

1.2 Stellar populations

Stars in the Galaxy are divided into different populations:

• Population I: stars in the galactic disk, in spiral arms and in (relatively young) open clusters.These stars have ages ∼< 109 yr and are relatively metal-rich (Z ∼ 0.5 − 1Z⊙)

• Population II: stars in the galactic halo and in globular clusters, with ages ∼ 1010 yr. These starsare observed to be metal-poor (Z ∼ 0.01 − 0.1Z⊙).

An intermediate population (with intermediate ages and metallicities) is also seen in the disk of theGalaxy. Together they provide evidence for the chemical evolution of the Galaxy: the abundanceof heavy elements (Z) apparently increases with time. This is the result of chemical enrichment bysubsequent stellar generations.

The study of chemical evolution has led to the hypothesis of a ‘Population III’ consisting of thefirst generation of stars formed after the Big Bang, containing only hydrogen and helium and noheavier elements (‘metal-free’, Z = 0). No metal-free stars have ever been observed, probably due tothe fact that they were massive and had short lifetimes and quickly enriched the Universe with metals.However, a quest for finding their remnants has turned up many very metal-poor stars in the halo,with the current record-holder having an iron abundance XFe = 4 × 10−6XFe,⊙.

1.3 Basic assumptions

We wish to build a theory of stellar evolution to explain the observational constraints highlightedabove. In order to do so we must make some basic assumptions:

• stars are considered to be isolated in space, so that their structure and evolution depend only onintrinsic properties (mass and composition). For most single stars in the Galaxy this conditionis satisfied to a high degree (compare for instance the radius of the Sun with the distance to its

5

主系列星の性質：質量と光度の関係

L~M4

質量が太陽の10倍

=>明るさは104倍

=>寿命は1/103

100億年/103

~1000万年

なぜ？？

LectureNotebyPols

核融合

クーロン障壁E~(Z1Z2e2)/r~106eV(MeV)

ガスの典型的なエネルギーE~kT~103eV(keV)<=107K

TextbookbyPols

=>トンネル効果

温度が高いほど核融合が

起こりやすい

Nuclear structure effects on the cross-section

A typical thermonuclear reaction proceeds as follows. After penetrating the Coulomb barrier, thetwo nuclei can from an unstable, excited compound nucleus which after a short time decays into theproduct particles, e.g.

X + a→ C∗ → Y + b .

Although the lifetime of the compound nucleus C∗ is very short, it is much longer than the crossingtime of the nucleus at the speed of light (∼ 10−21 s). Therefore by the time it decays, the compoundnucleus has no ‘memory’ of how it was formed, and the decay depends only on the energy.

The decay can proceed via different channels, e.g. C∗ → X + a, → Y1 + b1, → Y2 + b2, . . . , →C + γ. In the first case the original particles are reproduced, the last case is a decay to a stable energylevel of C with γ-emission. In the other cases the particles b1, b2, etc. may be protons, neutronsor α-particles. (Reactions involving electron and neutrino emission do not proceed via a compoundintermediate state, since the necessary β-decays would be prohibitively slow.) In order for a certainenergy level of C∗ to decay via a certain channel, the conservations laws of energy, momentum,angular momentum and nuclear symmetries must be fulfilled. The outgoing particles obtain a certainkinetic energy, which – with the exception of neutrinos that escape without interaction – is quicklythermalised, i.e. shared among the other gas particles owing to the short photon and particle meanfree paths in the stellar gas.

The energy levels of the compound nucleus play a crucial role in determining the reaction cross-section, see Fig. 6.2. Let Emin be the minimum energy required to remove a nucleon from the groundstate of C to infinity, analogous to the ionization energy of an atom. Energy levels below Emin corre-spond to bound states in an atom; these can only decay by γ-emission which is relatively improbable.These ‘stationary’ energy levels have long lifetimes τ and correspondingly small widths Γ, sinceaccording to Heisenberg’s uncertainty relation

Γ =!

τ. (6.16)

energy

r rn c

−V

CE

0

V(r)

min

r

E

E’

E

0

Figure 6.2. Schematic depiction of the combined nuclear and Coulomb po-tential, shown as a thick line. The potential is dominated by Coulomb repul-sion at distances r > rn, and by nuclear attraction for r < rn. An incomingparticle with kinetic energy E at infinity can classically approach to a distancerc. The horizontal lines for 0 < r < rn indicate energy levels in the compoundnucleus formed during the reaction. The ground state is at energy −Emin; thequasi-stationary levels with E > 0 are broadened due to their very short life-times. If the incoming particles have energy E′ corresponding to such a levelthey can find a resonance in the compound nucleus (see text).

80

~10-13cm(1fm)

MeV

keV

Introduc$ontoAstronomy(F.Shu)

Hertzsprung-Russeldiagram(HR図)

温度(K)

光度L=4πR2σT4

黒体輻射

星のスペクトル

h1p://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit1/SpTypes/index.html

Type M (Msun)

O 20-60

B 3-18

A 2-3

F 1.1-1.6

G 0.9-1.05

K 0.6-0.8

M 0.08-0.5

銀河への応用渦巻銀河 楕円銀河

-星を作っている

-若い星が多い

-重い星が多い

-青い

M101

-星を作っていない

-古い星が多い(若い星は爆発した)

-軽い星が多い

-赤い

ESO325-G004

(C)NASA,ESA

銀河のスペクトル(モデル)

銀河の年齢(Gyr=10億年)

1000万年

Bruzual&Charlot2003

星の構造と性質：まとめ• 星の構造

• 静水圧平衡

• 太陽の中心温度はT~107K

• トンネル効果で核融合反応

• 星の明るさと色

• 光度は質量に対して急激に増加(L~M4)=>重い星ほど寿命が短い

• 半径は質量に対して緩やかに増加(R~M0.7)=>重い星ほど温度が高い(L=4πR2σT4)

• 銀河の年齢と色を決める基礎