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Exam #3 Study Guide
• The Hertzsprung-Russell (H-R) Diagram
– Plot of Luminosity vs. Temperature for stars.
• Features:
– Main Sequence (most stars)
– Giant & Supergiant Branches
– White Dwarfs
• Luminosity Classification
H-R Diagram
Supergiants
Luminosity (Lsun)
106
104
102
Giants
1
10 -2
10 -4
40,000
White Dwarfs
20,000
10,000
Temperature (K)
5,000
2,500
Main Sequence
• Most nearby stars (85%), including the Sun, lie
along a diagonal band called the
• Main Sequence
• Ranges of properties:
– L=10-2 to 106 Lsun
– T=3000 to >50,0000 K
– R=0.1 to 10 Rsun
Giants & Supergiants
• Two bands of stars brighter than Main
Sequence stars of the same Temperature.
– Means they must be larger in radius.
• Giants
R=10 -100 Rsun L=103 - 105 Lsun T<5000 K
• Supergiants
R>103 Rsun L=105 - 106 Lsun T=3000 - 50,000 K
White Dwarfs
• Stars on the lower left of the H-R Diagram
fainter than Main Sequence stars of the same
Temperature.
– Means they must be smaller in radius.
– L-R-T Relation predicts:
R ~ 0.01 Rsun (~ size of Earth!)
• Main Sequence:
– Strong correlation between Luminosity and
Temperature.
– Holds for 85% of nearby stars including the sun
• All other stars differ in size:
– Giants & Supergiants:
Very large radius, but same masses as M-S stars
– White Dwarfs:
Very compact stars: ~Rearth but with ~Msun!
Mass-Luminosity Relationship
• For Main-Sequence stars:
 L   M 

  

 Lsun   M sun 
3.5
In words:
“More massive M-S stars are more luminous.”
Not true of Giants, Supergiants, or White Dwarfs.
• Observational Clues to Stellar Structure:
– H-R Diagram
– Mass-Luminosity Relationship
– The Main Sequence is a sequence of Mass
• Equation of State for Stellar Interiors
– Perfect Gas Law
– Pressure = density  temperature
• Stars are held together by their self-gravity
• Hydrostatic Equilibrium
– Balance between Gravity & Pressure
• Core-Envelope Structure of Stars
– Hot, dense, compact core
– cooler, low-density, extended envelope
• Stars shine because they are hot.
– need an energy source to stay hot.
• Kelvin-Helmholtz Mechanism
– Energy from slow Gravitational Contraction
– Cannot work to power the present-day Sun
• Nuclear Fusion Energy
– Energy from Fusion of 4 1H into 1 4He
– Dominant process in the present-day Sun
• Energy generation in stars:
– Nuclear Fusion in the core.
– Controlled by a Hydrostatic “thermostat”.
• Energy is transported to the surface by:
– Radiation & Convection in normal stars
– Conduction in white dwarf stars
• With Hydrostatic Equilibrium, these determine
the detailed structure of a star.
• Main Sequence stars burn H into He in their
cores.
• The Main Sequence is a Mass Sequence.
– Lower M-S: p-p chain, radiative cores &
convective envelopes
– Upper M-S: CNO cycle, convective cores &
radiative envelopes
• Larger Mass = Shorter Lifetime
Putting Stars Together
• Physics needed to describe how stars work:
•
•
•
•
•
Law of Gravity
Equation of State (“gas law”)
Principle of Hydrostatic Equilibrium
Source of Energy (e.g., Nuclear Fusion)
Movement of Energy through star
Proton-Proton Chain:

p  p H  e  e (twice)
2
H  p He   (twice)
3
3
4
He He He  p  p
2
3
3-step Fusion Chain
CNO Cycle:
C + p N  
12
13
13
13
14
N  C  e  e
C  p N  
14
N  p O  
15
15
15

13

O N  e   e
15
N  p C He
12
4
Main Sequence Membership
• For a star to be located on the Main Sequence
in the H-R diagram:
– must fuse Hydrogen into Helium in its core.
– must be in a state of Hydrostatic Equilibrium.
• Relax either of these and the star can no
longer remain on the Main Sequence.
The Main Sequence is a Mass Sequence.
• The location of a star along the M-S is
determined by its Mass.
– Low-Mass Stars: Cooler & Fainter
– High-Mass Stars: Hotter & Brighter
• Follows from the Mass-Luminosity Relation:
• Luminosity ~ Mass3.5
Main Sequence Lifetime
• How long a star can burn H to He depends on:
– Amount of H available = MASS
– How Fast it burns H to He = LUMINOSITY
• Lifetime = Mass  Luminosity
• Recall:
Mass-Luminosity Relationship:
• Luminosity ~ Mass3.5
Main Sequence Lifetime
• Therefore:
• Lifetime ~ 1 / M2.5
• The higher the mass, the shorter its life.
• Examples:
Sun: ~ 10 Billion Years
30 Msun O-star: ~ 2 Million years
0.1 Msun M-star: ~ 3 Trillion years
Summary of Post-Main Sequence
Evolution
•Stage:
•Energy Source:
•Main Sequence
•Red Giant
•Horizontal Branch
•Asymptotic Giant
•White Dwarf
•H Burning Core
•H Burning Shell
•He Core + H Shell
•He Shell + H Shell
•None!
Post-Main Sequence Evolution of a
High Mass Star
• End of the Life of a Massive Star:
– Burn H through Si in successive cores
– Finally build a massive Iron core
• Iron core collapse & core bounce
• Supernova explosion:
– Explosive envelope ejection
– Main sources of heavy elements
Stellar Remnants
• White Dwarf:
– Remnant of a star <8 Msun
– Held up by Electron Degeneracy Pressure
– Maximum Mass ~1.4 Msun
• Neutron Star:
– Remnant of a star < 18 Msun
– Held up by Neutron Degeneracy Pressure
– Pulsar = rapidly spinning neutron star
The Milky Way:
• The Milky Way is our Galaxy
– Diffuse band of light crossing the sky
– Galileo: Milky Way consists of many faint stars
• The Nature of the Milky Way
– Philosophical Speculations: Wright & Kant
– Star Counts: Herschels & Kapteyn
– Globular Cluster Distribution: Shapley
The Milky Way and Other Galaxies:
• Disk & Spheroid Structure of the Galaxy
• Pop I Stars:
– Young, metal-rich, disk stars
– Ordered, nearly circular orbits in the disk
• Pop II Stars:
– Old, metal-poor, spheroid stars
– Disordered, elliptical orbits in all directions
• Gives clues to the formation of the Galaxy.