Stellar Structure

Gas

MassRadiation

Energy

• Generation

• Transport

Radiative

Convective

• Temperature• Density

• Composition

Hydrostatic Equilibrium:

Hydrostatic Equilibrium

A Fp

m rFg

F’p

The Pressure Integral

A

A

x

vp

cos

Overcoming the Coulomb Barrier

Ucl = (3/2) kTcl → kTcl ~ 1010 K

Ut = (3/2) kTt

→ kTcl ~ 107 K

rt ~ deBrogle = h/p

The PP Chain

The CNO Cycle

126C

p

137N

e

e+

136C p

14

7N

p

158O

e

e+

157Np

42He

Binding energy per nucleon

Exo

ther

mic

EndothermicE

nerg

y ca

n be

libe

rate

d vi

a nu

clea

r fu

sion

Energy can be liberated via nuclear fission

Convection

Adiabatic expansion:

P = K*

Favorable Conditions for Convection

• Large Opacities → Large |dT/dr|rad

• Partial Ionization Zones → Brings 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|

Stellar energy transport structure as a function of stellar mass

Low-mass stars (M < 0.25 M0):

Completely convective

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

M/M0

R/R*

1

0.25 1.31.20.08 90

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)

Masses of Stars in the

Hertzsprung-Russell Diagram

0.5

18

6

3

1.7

1.0

0.8

40

Masses in units of solar masses

Low m

asses

High masses

Mass

The higher a star’s mass, the more luminous

(brighter) it is:

High-mass stars have much shorter lives than

low-mass stars:

Sun: ~ 10 billion yr.

10 Msun: ~ 30 million yr.

0.1 Msun: ~ 3 trillion yr.

L ~ M3.5

tlife ~ M-2.5

MassSun

Radiative Core, convective envelope;

Energy generation through PP Cycle

Convective Core, radiative envelope;

Energy generation through CNO Cycle

Summary:

Stellar Structure

Energy Transport Structure

Inner radiative, outer convective

zone

Inner convective, outer radiative

zone

CNO cycle dominant PP chain dominant