1. 19. Main-Sequence Stars & Later
The end of core hydrogen fusion creates a red giant
Core helium fusion in red giants
Star clusters & red giant evolution
Star evolution produces two distinct star populations
Many mature stars pulsate
Mass transfer can affect close binary stars

2. Termination of Core Hydrogen Fusion
Critical concepts
Zero-age main-sequence stars ZAMS
On-going hydrogen fusion begins within the core
Hydrostatic & thermal equilibrium are established
Main-sequence lifetime
The total time hydrogen fusion continues within the core
Chemical changes in a star’s core
Initial mass ~ 74% H ~ 25% He ~ 1% “metals”
Atoms ~ 91 H ~ 8 He ~ 1 “metals”
Final mass ~ 0% H ~ 99% He ~ 1% “metals”
Atoms ~ 0 H ~ 25 He ~ 1 “metals”
Physical changes in a star’s core
Progressively fewer atoms as He replaces H
Core diameter decreases & temperature increases
Rate of hydrogen fusion gradually increases

3. Changes In the Sun Physical Chemical Position on an H-R diagram
The Sun is ~ 40% more luminous than at ZAMS
The Sun is ~ 6% larger in diameter than at ZAMS
The Sun is ~ 300 K hotter than at ZAMS
Chemical
The Sun’s core is already > 50% He
Position on an H-R diagram
Increased temperature moves it slightly to the left
Increased luminosity moves it slightly upward

4. H & He In the Sun’s Interior

5. The Maturing Sun

6. Main-Sequence Lifetimes
Basic physical relationships
Einstein’s famous equation…
E = f . M . c2
…where f is the fraction of mass lost in fusion
Definition of luminosity…
L = E / t
E = L . t
Combining the two…
L . t = f . M . c2
t µ M / L
Considering the mass-luminosity relationship…
L µ M+3.5
t µ M–2.5

7. Lifetimes of Main-Sequence Stars

8. Red Giant: The Sun In 5 Billion Years

9. Changes As Core H Is Exhausted
Basic physical processes
Core temperature drops as H fusion ends
Core pressure decreases
Gravity again dominates
Core diameter decreases
H just outside the old core compresses & heats
H-shell fusion begins
No core-He fusion as yet
He core eventually reaches ~ 100,000,000 K
He fusion into C & O begins while H-shell fusion continues
Differences due to mass
High- mass stars
He fusion begins gradually
Low- mass stars
He fusion begins in a flash

10. Three Evolutionary Stages for Stars

11. The Pauli Exclusion Principle
Two different kinds of pressure
Temperature- dependent
Ordinary gas pressure Ideal gas law
Force resisting gravity is directly proportional to temperature
Temperature- independent
Degenerate electron pressure Pauli exclusion principle
Force resisting gravity is independent of temperature
The Pauli exclusion principle
One expression of quantum mechanics
Only effective when core gases become ionized
Some electrons roam freely
Such electrons may not get extremely close to each other
Quantum exclusion keeps these electrons apart
This exclusion is completely independent of temperature

12. Degenerate Electrons in Ordinary Metal

13. Star Clusters & Red Giant Evolution
The transition to core-He fusion
This marks the move into the Red Giant phase
The details are determined entirely by mass
Analysis of star clusters
All the cluster’s stars formed at about the same time
Many different masses are represented among those stars
High- mass stars evolve very quickly
Some leave the main sequence before low-mass stars can form
Low- mass stars evolve very slowly
The cluster’s H-R diagram depends on the cluster’s age
The lower right band slowly approaches the main sequence
The upper left band moves away from the main sequence
The turn-off gives the cluster’s age

14. Mass Determines Every Star’s Evolution
The main sequence is a band

15. Main Sequence Turn-Off Points

16. Two Distinct Star Populations
Remnants of the Big Bang
Very few atoms heavier than H & He formed
Noticeable deficiency of “metals”
The oldest stars contain little metal
These are Population II stars
Remnants of supernovae explosions
Relative abundance of “metals”
Some even as heavy as Uranium
The newest stars contain abundant metal
These are Population I stars

17. Metal-Poor & Metal-Rich Stars
Metal-poor Population II stars
Metal-rich Population I stars
A “metal” in this context is any element heavier than helium

18. Many Mature Stars Pulsate
Critical differences
Main sequence stars
Characterized by hydrostatic & thermal equilibrium
No significant change in diameter
Pulsating stars
Distinct lack of hydrostatic & thermal equilibrium
Cyclical change in diameter
Some examples of pulsating stars
Long-period variables
Cool red giants that vary in luminosity by a factor of ~ 100
Cepheid variables
Vary over periods of ~ 1 to ~ 100 days
RR Lyrae variables
Vary over periods of < 1 day

19. Cepheid Variables As Standard Candles
Two types of Cepheid variables
Type I Metal-rich Population I stars
More luminous than Type II Cepheids
Type II Metal-poor Population II stars
Less luminous than Type I Cepheids
Standard candles
Basic properties
Very bright objects of known luminosity
Relatively abundant throughout galaxies
Cepheids
Luminosity is sufficient to be visible at millions of parsecs
Luminosity is directly proportional to period

20. Variable Stars On An H-R Diagram

21. d Cephei: A Pulsating Star

22. Mass Transfer Can Affect Close Binaries
Critical concepts
Binary star systems
> 50% of all stars are in binary systems
Roche lobes
Three-dimensional surfaces marking gravitational domains
Inner Lagrangian point
The gravitational balance point between binary stars
Types of binary star systems
Detached Neither star fills its Roche lobe
Semi-detached One star fills its Roche lobe
Contact Both stars fill their Roche lobes
Over-contact Both stars over-fill their Roche lobes

23. Roche Lobes of Close Binary Stars

24. Three Kinds of Eclipsing Binary Stars
…Semi-detached
without
mass transfer
…with
mass
transfer
Over-contact…

25. Important Concepts Termination of core hydrogen fusion
Zero-age main-sequence stars
Main-sequence lifetime of stars
Proportional to M2.5
Progressive increase in luminosity
Number of atoms in core decreases
4 H atoms become 1 He atom
Core contracts & heats
Three evolutionary stages of stars
Start of core-H fusion into He
Birth of a ZAMS star
End of core-H fusion into He
Start of shell-H fusion
Start of core-He fusion into C & O
~ 30% as long as core-H fusion
Two kinds of pressure
Ordinary gas pressure
Degenerate e– pressure
Does not depend on temperature
Star cluster analysis
Same birthday but different masses
H-R turn-off gives cluster age
Two distinct star populations
Metal-poor Population II stars
Formed soon after the Big Bang
Metal-rich Population I stars
Formed long after the Big Bang
Variable stars
Long-period variables
Cepheid variables
Used as standard candles
RR Lyrae variables
Binary star systems
Detached
Semi-detached
Contact
Over-contact Mass transfer