1. Stellar Structure Hydrostatic Equilibrium: Radiation Mass Gas Energy
Hydrostatic Equilibrium:
Radiation
Mass
Gas
Energy
Generation
Density
Transport
Temperature
Radiative
Composition
Convective

2. Hydrostatic EquilibriumA Fp Dm
DFg Dr
F’p

3. The Pressure Integral A
m = cosq q DA p v Dx

4. Overcoming the Coulomb Barrier
Ucl = (3/2) kTcl
→ kTcl ~ 1010 K
Ut = (3/2) kTt
→ kTcl ~ 107 K
rt ~ ldeBrogle = h/p

8. The PP Chain

9. The CNO Cycle p 42He g 126C ne 137N p 157N e+ ne 136C p 158O g e+ 147Np
42He g
126C ne
137N p
157N e+ ne
136C p
158O g e+
147N g p

10. Binding energy per nucleon
Endothermic
Energy can be liberated via nuclear fission
Exothermic
Energy can be liberated via nuclear fusion

11. Convection
Adiabatic expansion:
P = K*rg

12. Favorable Conditions for Convection
Large Opacities → Large |dT/dr|rad
Partial Ionization Zones → Brings g close to 1 → small |dT/dr|ad
Low g → small |dT/dr|ad = g/Cp
Strongly T-dependent energy generation (CNO cycle!) → large |dT/dr|

13. Stellar energy transport structure as a function of stellar mass
R/R* 1
M/M0 90
0.08
0.25
1.2
1.3
Sun-like stars
(0.25 M0 < M < 1.2 M0):
Radiative core; convective envelope
High-Mass stars
(M > 1.3 M0):
Convective core; radiative envelope
Low-mass stars (M < 0.25 M0):
Completely convective

14. => Almost 1-dimensional Zero-Age Main Sequence (ZAMS)
Vogt-Russell Theorem
The mass and composition of a star uniquely determine its radius and luminosity, internal structure, and subsequent evolution.
=> Almost 1-dimensional Zero-Age Main Sequence (ZAMS)

15. Masses of Stars in the Hertzsprung-Russell Diagram
Masses in units of solar masses 40 18
The higher a star’s mass, the more luminous (brighter) it is:
High masses 6 3
L ~ M3.5
1.7
1.0
High-mass stars have much shorter lives than low-mass stars:
Mass
0.8
0.5
tlife ~ M-2.5
Sun: ~ 10 billion yr.
Low masses
10 Msun: ~ 30 million yr.
0.1 Msun: ~ 3 trillion yr.

16. Convective Core, radiative envelope;
Summary:
Stellar Structure
Convective Core, radiative envelope;
Energy generation through CNO Cycle
Sun
Mass
Radiative Core, convective envelope;
Energy generation through PP Cycle

17. Energy Transport Structure
Inner convective, outer radiative zone
Inner radiative, outer convective zone
CNO cycle dominant
PP chain dominant