Sec$on 2.
Stellar structure and proper$es (I)2.1 Hydrosta$c equilibrium
2.2 Nuclear burning

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

Our sunL = 4 x 1033 erg/s = 4 x 1026 J/s (W)Electronic power consump$on in Japan
1.5 x 1019 J / year==> Japanese power consump$on for 2 x 107 yr= solar radia$on in 1 second

HNuclearburning

HeJAXA/ISASEnergy source: E = mc2

ヘリウム

0.7% heavier
水素4 x mp

水素原子核 4 つ＞

ヘリウム原子核

0.7％重いmα

Q1: How much energy is released for one nucleon? (核子あたり)
1.007 kg の水素➡

1kg のヘリウム2
E ＝ mc2 ＝ 0.007 kg ×（3×10 8 m/s）

E = Δmc2＝ 6×1014 ジュール

Solar mass：2 x 1033 g

Q2: How much energy does the Sun can produce?
(assume 10% of solar mass can be used for nuclear burning)
Q3: How many years the sun can keep shining?
L = 4 x 1033 erg/s

1 yr ~ 3 x 107 sec

Binding energy of nuclei
Eb = [NmN + Zmp - mi] c2
P+nNuclei

Higher binding energy= strongly “bound”= more stable= “lighter”

Fe is the most stable nucleus

What is going on at the center of the star?
How does nuclear burning occurs?

The energy levels of the compound nucleus play a crucial rolesection, see Fig. 6.2. Let Emin be the minimum energy required to r
state of C to infinity, analogous to the ionization energy of an atom
spond to bound states in an atom; these can only decay by γ-emissi
These ‘stationary’ energy levels have long lifetimes τ and corre
6according to Heisenberg’s uncertainty relation

Nuclear burning
Coulomb barrier E ~ (Z1Z2e2)/r ~ 10 eV (MeV)
Typical energy of the gas E ~ kT ~Γ10!3 eV (keV) <= 107 K= .
τ=> Tunnel eﬀects

ECMeV
V(r)
E’keVenergy

E0rcrnE min−V0rFigure 6.2. Schematic depiction of thetential, shown as a thick line. The potension at distances r > rn , and by nuclea
particle with kinetic energy E at infinity
rc . The horizontal lines for 0 < r < rn innucleus formed during the reaction. Th
quasi-stationary levels with E > 0 are btimes. If the incoming particles have en
they can find a resonance in the compou~10-13 cm (1 fm)
Textbook by Pols

Condi$on of H-burning

Fusionreactor

Si−b
O−b
C−b(K)
log Tc~108 K

10He−b8
H−b100610
1.00.1-104−505log ρc10Figure 8.3. The samin Fig. 8.2, together w
the log T c – log ρc plaoccur.

(g cm-3)
Lecture Note by Pols

Hertzsprung-Russel diagram
Luminosity
Red giants

Mainsequence

White dwarfs

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

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

1.0

Contamina$on ofevolved stars

0.5

R ~ M0.70.0

Outcome of
the 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

Summary: Stellar structure and proper$es (I)• Energy source of the stars• Nuclear burning• E = mc
• Stellar structure• Hydrosta$c Equilibrium• Central temperature of the stars T ~ 10 K
• Require tunnel eﬀects for nuclear burning• Stellar proper$es• Almost constant central T => R ~ M• Observed mass-radius rela$on (R ~ M )27

0.7