Sec on 5.
Stellar evolu on (II)5.1 Equa on of statetitititi

5.2 Evolu onary track

Let’s understand these ques ons
with the words of physics• Why are stars so luminous?
• Why do stars show L ~ M ?
• Why do stars evolve?
• Why does the des ny of stars depend on the mass?
• Why do some stars explode?
• Why don’t normal star explode?
• Why does stellar core collapses?
• Why is the energy of supernova so huge?
•…
titi

4

Sec on 5.
Stellar evolu on (II)5.1 Equa on of state

titi

titi

5.2 Evolu onary track

Stellar life

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

titi

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

titititititititititititi

become dominant in the rho-T diagram.

レポート課題 22a. 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

M惑星状星雲> 10 Msun

1. Massive stars
軽い星

赤色巨星

~ 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

HHeC+OElectrons do not become degenerate
FeSiNe + Mg

Images are not to scale1-10 Gyr
赤色超巨星
重い星
2.
Low-mass stars

図の大きさは天体の大きさと一致していません(C: Essay Web)

超新星爆発
中性子星
M < 10 Msun

ブラックホール

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 statetitititi

5.2 Evolu onary trackEOSEvolu on of T_c and ρ_c10108log Tclog Tc

radiation
MCh8100

66ideal gasdegenerate
NRER

10
1.0
0.1

4−505log ρc

10g/cm3

4−505log ρc

10g/cm3ti

Figure 8.2. The equation of state in the log T c – log ρc plane (left panel), with approximate boundaries between
regions where radiation pressure, ideal gas pressure, non-relativistic electron degeneracy and extremely relatextbook by Pols
tivistic electron degeneracy dominate, for a composition of X = 0.7 and Z = 0.02. In the right panel, schematic
evolution tracks for contracting stars of 0.1 – 100 M! have been added.

Contrac on of the core
= Expansion of the envelope

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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 starsti

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
luminosity,
the EV
maintainsimilarmassinevolution
maintainsimilarmass evolutio
theparameter
ηBlenvelopein the mass-loss
formu
the parameter
mass-loss
MESAstar andηBl
0.1ininthe
EVOL.
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effMESA thestar
andstar
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EVOL.
etailorMESA
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tailorthe evolution
MESA starmodel
to the toEV
theAGBis very
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the AGBevolution
very sensitivetowhich
depends
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which depends onthe mixing
assumptio
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duringthe preceding
H
Consequently,
smalldifferenceson the TPConsequently,
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the TP
when
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Ascontrac
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Figure23,
the EVOLwell ininofthetheH-R
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Tabla=>compare
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properties
differinbythelessthan5%. MESA
compare well
H-R
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Ta=>toproperties
Redgiant
imposeadifferminimumsizethanon convectio
by less
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overshootis ignored.
EVOL
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the coreovershootmixingis ignored.
EVOL
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TP-AGBcharacterized
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sequence byat theinstabilitiesof theisHe-shell,leading
The TP-AGB
characterized
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Theseprocesses
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MESA
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in pF
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These processes
ofMESAstarstar
to calculateastherevealed
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MESA
calculations,ininsmoothandtocontinuous
evenof aMESA
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calculate manner
the evolutio
thermalpulseandphasesand beyond
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mannereve
The
top panel
evolution
thermalpulseshowsphasestheandbeyond inis thedemH
thepanelshowsevolutionofThebottom
top panelshowsthe theevolution
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shows coolingthe evolution
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etal.to2011
C/O core.
Theadiabaticcoolingin theof the C/O core) is evident in the down

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

titiFigure 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
1/3
as 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 envelopetititi

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

Summary: stellar evolu on (II)es of gas (microscopic)• Proper==> 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 di erent areas in the rho-T diagram• Stellar evolu onstop contrac on when supported by degeneracy• Starspressure=> No temperature rise => End of nuclear burningti

fftitititititi• The core of low mass stars become generate

Let’s understand these ques ons
with the words of physics• Why are stars so luminous?
• Why do stars show L ~ M ?
• Why do stars evolve?
• Why does the des ny of stars depend on the mass?
• Why do some stars explode?
• Why don’t normal star explode?
• Why does stellar core collapses?
• Why is the energy of supernova so huge?
•…
titi4

Thermodynamics

Electromagne sm

Classical
mechanics

Sta s calmechanics

Astrophysics
Hydrodynamics

titititi

Rela vity

Quantummechanics
Nuclear physics