Sec$on 3.
Stellar structure and proper$es (II)

3.1 Luminosity of the stars
3.2 Opaci$es in the stars

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

Hertzsprung-Russel diagram
Luminosity
Red giants

Mainsequence

White dwarfs

Temperature (K)hJp://astronomy.nmsu.edu/geas/lectures/lecture23/slide04.html

Mass - radius rela$on for the main sequencelog (R / Rsun)

1.00.5R ~ M0.70.0

Outcome ofthe central propertyof the star

−0.5

−1.0

−101

log (M / Msun)

ius (right) relations for components of double-lined eclipsing

Lecture Note by Pols

Mass - luminosity rela$on of the main sequence stars
6Star with M = 10 Msun=>1.0L ~ 104 Lsun=> Life$me~ 1/103 of the Sun
0.5~ 1010 yr (100億年)/103

L ~ M4log (R / Rsun)log (L / Lsun)420~ 107 yr (1000万年)

0.0−0.5

More massive stars
have shorter life$me−2−10log (M / Msun)

1−1.0−10log (M / Msun)

Lectureby Pols of doubleFigure 1.3. Mass-luminosity (left) and mass-radius (right) relations
forNotecomponents

Why do stars show L~M4?
Why do more massive stars have higher temperature?

one of the processes discussed above dominates. At low density and high tempera
value given by electron scattering. Opacity increases towards higher ρ and low
4 K opacity decreases drastically dueandbound-freeabsorptions.
ForT<10Opacity inside the starshydrogen, the main opacity source here is the H− ion. At lower temperature

27log ρ (g cm-3)−10−8log κ
X = 0.70, Z = 0.02log Tlog κb-ff-f

T-3.5

48−6 −4 −2 0065e-scat−24OPAL opacities
X = 0.70, Z = 0.02−433456log T

78−10−5Lecture Note by Pols log

Figure 5.2. Rosseland mean opacities as a function of T and ρ, for a mixture of elements

where g is the bound-free Gaunt factor. If M is the ionization potential forthe initial level, Ubf is zero for w <on where

Bound-free opacity(10.55)rises abruptly to Eq. (10.54) at threshold w =onand then decreases roughly
as oP3.Near threshold, the Gaunt factor g is unity, to within 20%.

Ioniza$on edgehν ~ E ~ kTlog a

ν-3 or -3.5

Frequency
II1vi

v2v3+ log v

Figure 10.2 Schematic illustmtion of the frequency depndence of the absotption coefficient. The sharp rises, absorption edges, occur at the fmquency ofionization of a particular lewL

Rybicki & Lightman

Assignment 1Derive that the dependence of free-free opacity in stellar interior canbe approximated as κ ~ ρT-3.5
Hint: In equilibrium, the rate for free-free absorp$on matches withthat of free-free emission (thermal bremsstrahlung), i.e. jν = αν Bν(T)* Kirchhoﬀ’s law

レポート課題 1
恒星内部における自由-自由吸収の密度・温度依存性が近似的に次のように表せられることを示せ κ ~ ρT-3.5
ヒント：平衡状態では自由-自由吸収のrateと自由-自由放射 (熱的制動放射)のrateはつり合う jν = αν Bν(T)* キルヒホッフの法則

Hertzsprung-Russel diagramL
L = 4πR2 σT4T (K)Introduc$on to Astronomy (F. Shu)

Blackbody radia$on

Stellar spectrum

TypeM (Msun)

O

20-60

B3-18

A2-3

F

1.1-1.6G

0.9-1.05

K

0.6-0.8

M

0.08-0.5h"p://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit1/SpTypes/index.html

Applica$ons to galaxy studies
Spiral galaxy

Ellip$cal galaxy

M101

ESO 325-G004(C) NASA, ESA- Star forming- More “young" stars- More massive stars- Blue (high T radia$on)- No star forma$on- Old stars- Less massive stars- Red (low T radia$on)

Spectral models for galaxies

Bruzual & Charlot 2003
Ages of the galaxy
in 109 yr (10億年)

107 yr108 yrSummary: Stellar structure and proper$es (I)• Opaci$es in the stars• Thomson scaJering• free-free and bound-free absorp$on• Luminosity of the stars• L ~ E/t where t ~ (R/c) τ (<== τ = κρR)
• L~M
• Stellar proper$es
massive stars have
• More- Higher luminosity L ~ M (shorter life$me t ~ M )esc,esc

3-5

4- Higher temperature T ~ M0.5

• Founda$on to determine the galaxy spectra-3

Let’s understand these quesXons
with the word of physics

Knowing = Understanding• 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