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Stellar Structure
• Read Your Textbook: Foundations of Astronomy
– Chapter 12
• Homework Problems Chapter 12
– Review Questions: 2, 3, 8, 9
– Review Problems: 3, 7-9
– Web Inquiries: 1
Theoretical “Hyashi” Tracks
Proto-stellar
evolution
on the H-R
diagram.
Hydrostatic Equilibrium
Gravity versus Pressure
Force due to Gravity
FG = mGM/R2
Force due to Radiation and Gas Pressures
Pgas = rkT
Pg ~ sT4
gas pressure
radiation pressure
Equilibrium
FG = Pgas + Pg
Stellar Structure Laws
Stellar Zoo
Luminosity
L = 4pR2 sT4
Mass
Chemical
Composition
H-R Diagram
Fusion of Hydrogen
• Fusion of Hydrogen into Helium
• Efficient Storage, Inefficient Consumption
• At the temperature in the core of the sun…
Energy Required to overcome
proton-proton repulsive barrier
• Tsurface = 5800 K
• Tcore = 15,000,000 K
Number
Number
ofofHH
Nuclei
Nuclei
99.999% of H Is not tapped
Energy
Energy
Proton-Proton Chain
Proton-Proton Chain
+ e+ + n (positron + neutrino)
• 1H + 1H
2H
• 1H + 2H
3He
• 3He + 3He
+g
4He
(photon)
+ 1H + 1H + g
• Net effect:
– 4 H nuclei (protons) form 1 He nuclei (alpha) + photons
Energy Generation
DE = Dm c2
mHe = 3.97 mH
Dm = 0.03 mH
Four protons weigh more than one alpha.
Conservation of Mass??!
Einstein says Mass is converted into energy.
DE = Dmc2 = 6x1018 ergs/gram
1 gram of H
Power
DE = Dm c2 = 6x1018 ergs/gram
1 gram of H
The human body requires 109 ergs/sec to live.
1 gram of hydrogen nuclei fused into helium nuclei
will release enough energy to power a human for
200 years.
Energy Generation
• Each second the sun converts 600 million tons of
Hydrogen
– 7000 Aircraft carriers
• And makes 596 million tons of Helium
• Yielding 4 million tons of Radiation
– 50 Aircraft carriers
• This takes place in the inner 15-25 % of the star.
Energy Consumption
Stellar Lifetimes
depend on mass.
High mass stars are
bright and short lived,
use their fuel up rapidly.
Low mass stars are
faint and have longevity,
use fuel slowly and efficiently.
Stellar Masses
P = Pg + Pgas
radiation pressure and gas pressure
M/Msolar
0.1
1 (sun)
10
100
Pg/P
Pgas/P
0.0016
0.9984
0.1160.894
0.570
0.430
0.850
0.150
Stellar Mass Range
Upper Limit for Stability
The most massive stars would have enough
radiation pressure to counteract gravity and
literally blow themselves apart. M < 100 Msolar
Lower Limit for Stability
Need to have T = 1.5 x 106 K for Hydrogen fusion
M > 0.05 Msolar In order to have nuclear fusion.
Stellar Lifetimes
Stellar Masses
0.05 Msolar < M < 100 Msolar
Core Mass 0.01 Msolar < M < 10 Msolar
LUMINOSITY 10-4 Lsolar < L < 104 Lsolar
Lifetimes: t ~ Mass/Luminosity
Stellar Lifetimes
Stellar Masses
0.05 Msolar < M < 100 Msolar
Core Mass 0.01 Msolar < M < 10 Msolar
LUMINOSITY 10-4 Lsolar < L < 104 Lsolar
Lifetimes: t ~ Mass/Luminosity
tstar = 10 tsolar/104 = 10-3 tsolar
Burn out quick
tstar = 0.01 tsolar/10-4 = 100 tsolar Longevity
Stellar Life Times
3.05
1.10
1.00
1.04
Main Sequence Lifetime
Main Sequence Histogram