Stellar Structure Gas Mass Radiatio n Energ y • Generation • Transport Radiative Convective • Temperatur e • Density • Compositio n Hydrostatic Equilibrium:
Dec 24, 2015
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