Download Stellar Structure

Stellar Structure
Hydrostatic Equilibrium:
Radiation
Mass
Energy
• Generation
• Transport
Radiative
Convective
Gas
• Density
• Temperature
• Composition
Hydrostatic Equilibrium
A
Dm
Fp
DFg
F’p
Dr
The Pressure Integral
A
q
m = cosq
DA
p
v
Dx
Overcoming the Coulomb Barrier
Ucl = (3/2) kTcl
Ut = (3/2) kTt
→ kTcl ~ 107 K
rt ~ ldeBrogle = h/p
→ kTcl ~ 1010 K
The PP Chain
The CNO Cycle
4
p
2He
12
g
ne
6C
13
p
15
ne
7N
7N
e+
13
15
8O
e+
14
g
6C
p
g
7N
p
Binding energy per nucleon
Convection
Adiabatic
expansion:
P = K*rg
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|
R/R*
1
Stellar energy transport structure
as a function of stellar mass
0.08
0.25
1.2 1.3
90 M/M0
Low-mass stars
(M < 0.25 M0):
Sun-like stars
High-Mass stars
(0.25 M0 < M < 1.2 M0):
(M > 1.3 M0):
Completely
convective
Radiative core;
convective envelope
Convective core;
radiative envelope
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
HertzsprungRussell Diagram
The higher a star’s mass,
the more luminous
(brighter) it is:
L ~ M3.5
High-mass stars have
much shorter lives than
low-mass stars:
tlife ~ M-2.5
Sun: ~ 10 billion yr.
10 Msun: ~ 30 million yr.
0.1 Msun: ~ 3 trillion yr.
Masses in units
of solar masses
40
18
6
3
1.7
1.0
0.8
0.5
Summary:
Stellar Structure
Convective Core,
radiative envelope;
Energy generation
through CNO Cycle
Radiative Core,
convective envelope;
Energy generation
through PP Cycle
Sun
Energy Transport Structure
Inner convective,
outer radiative
zone
Inner radiative,
outer convective
zone
CNO cycle dominant
PP chain dominant