Sec$on 5.
Stellar evolu$on (II)5.1 Equa$on of state
5.2 Evolu$onary track

Goals of this lecture• Standard proper$es of stars• Stellar structure and proper$es• Stellar evolu$on• Origin of the elements in the Universe• Nucleosynthesis in stars and supernovae• Explosion mechanism of supernovae• Topics in $me-domain astronomy• Radia$on from explosive phenomena• Mul$-messenger astronomy

Sec$on 5.
Stellar evolu$on (II)5.1 Equa$on of state
5.2 Evolu$onary track

Stellar life

(C: Essay Web)Why does the des$ny of the stars depend on the mass?

Microscopic proper$es of the gas play important roles

Assignment 2
2a. Derive pressure of ideal gas from the Maxwell distribu$on
2b. Derive pressure of degenerate electrons(both for non-rela$vis$c case and rela$vis$c case)
2c. Derive radia$on pressure from Planck func$on
2d. Draw the regions where- ideal gas pressure- degenerate pressure of non-rela$vis$c electrons- degenerate pressure of rela$vis$c electrons- radia$on pressure
become dominant in the rho-T diagram.

レポート課題 2
2a. マクスウェル分布から理想気体の圧力の式を導け
2b. 電子が非相対論的、超相対論的なときの縮退圧の式を導き、実際に数字を入れて計算せよ
2c. プランク関数から輻射圧の式を導け
2d. 密度 - 温度平面で- 理想気体のガス圧- 電子の縮退圧（非相対論的）- 電子の縮退圧（超相対論的）- 輻射圧がそれぞれ支配的になる境界を求め、図示せよ

1. Massive stars
軽い星

赤色巨星

惑星状星雲
M > 10 Msun

~ 10 Myr

図の大きさは天体の大きさと一致していません(C: Essay Web)

白色矮星

H

He

C+OElectrons do not become degenerate
Fe

Si
Ne + Mg

Images are not to scale1-10 Gyr
赤色超巨星

超新星爆発

重い星
2. Low-mass stars

中性子星
M < 10 Msun

(C: Essay Web)

ブラックホール

図の大きさは天体の大きさと一致していませんHHe

C+O

Stars can be supported byelectron degeneracy pressure
White dwarf

Images are not to scale

C+OWhite dwarf: supported degeneracy pressure
普通の気体の圧力
普通の気体の圧力

Ideal gas
温度を下げる
温度を下げるT decreases
圧力が下がる

圧力が下がる

縮退圧

縮退圧

Degeneracy pressure
座れない ＝ 反発

座れない ＝ 反発

P is non-zeroeven at T=0
温度がゼロでも圧力が生まれる

温度がゼロでも圧力が生まれる

星が「死ぬ」とはどういうことか（ベレ出版）

Sec$on 5.
Stellar evolu$on (II)5.1 Equa$on of state
5.2 Evolu$onary track

Contrac$on of the core= Expansion of the envelope

Shell burning => energy genera$on(more than required to support the envelope )(A color version of this figure is available in the online journal.)(A color version of this figure is available in the online journal.)

Figureblack23. line)
2 M⊙and, Z MESA= 0.01
tracksupgrayto thefirsi(solidstar(thickline)(solid black line) and MESA star (thick gray line

Low/intermediate
mass stars

Figure 22. Top: MESA star H-R diagram for 2–10 M⊙ models from the PMS
to the end of the first thermal pulse (2–7 M⊙ ) or into C-burning (8 and 10 M⊙ ).

mass, and hence luminosity, in the EVO
mass, andhenceenvelope
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TheAstrophysicalAstrophysical Journal
Journal Supplement(35pp),
2011
January
The
SupplementSeries,Series,192:3
192:3(35pp),
2011
January

Massive stars(un$l He-burning)

Core contrac$on=> Expansion of the envelope=> Red super giant

Figure 29. Top: H-R diagram for 10–100 M⊙ models from the PMS to the end ofcore Helium burning for Z = 0.02 but with zero mass loss. Bottom: trajectories

Figure 30. Evolution of the central temperature andmetallicity Mi = 25 M⊙ models from different stella
Figure30. Evolutionof thecentral
temperatur
locationsof corehelium, carbon,
neon,
oxygen,and sili
1/3as ismetallicity
the relationM
Tci ∝=ρc25 .M⊙ models from differen
locations of core helium, carbon, neon, oxygen, a(A color version of this figure1/3
is available in the online

ρc al.
. 2011
as is the relation
Tc ∝ etPaxton(A color version of this figure is available in theContrac$on of the core
= Expansion of the envelope

Evolu&on in the rho-T plane is determinedby the proper&es of the core
T ~ M2/3 ρ1/3
M decreases => Lower part of the ρ-T plane

Massive stars（un$l Si burning）

Finally degeneracy pressure
becomes importantdege
nerat
ee

lectrons

relativistic electrons

textbook by PolsMESA code
h_p://mesa.sourceforge.net/index.html

1 Msun (ρ-T)

1 Msun (HR diagram)20 Msun (ρ-T)

20 Msun (HR diagram)

Summary: stellar evolu$on (II)of gas (microscopic)• Proper$es==> proper$es of stars (macroscopic)• Equa$on of states• Ideal gas P ~ ρT
• Degeneracy pressure P ~ ρ (non-rel)、P ~ ρ (rel)• Radia&on pressure P ~ T
5/3

4/3

4=> Important in diﬀerent areas in the rho-T diagram• Stellar evolu$on
stop contrac&on when supported by degeneracy• Starspressure=> No temperature rise => End of nuclear burning• The core of low mass stars become generate

Let’s understand these ques$ons
Knowing = Understanding
with the word of physics• Why do some stars explode?
• Why don’t normal star explode?
• Why do stars show L ~ M ?
• Why do stars evolve?
• Why does the des$ny of stars depend on the mass?
• Why does stellar core collapses?
• Why is the energy of supernova so huge?
•…
4Thermodynamics

Electromagne$sm

Classical
mechanics

Sta$s$cal
mechanics

Astrophysics
Hydrodynamics

Rela$vity

Quantummechanics
Nuclear physics