19. Main-Sequence Stars & Later

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

2. Core Hydrogen Fusion Termination • 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 changes • 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 changes • 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 µM+3.5 t µ M–2.5

7. Lifetimes of Main-Sequence Stars

8. Red Giant: 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 & 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 pressure • Ordinary gas pressure Ideal gas law • Force resisting gravity is proportional to temperature • Temperature-independent pressure • Degenerate electron pressure Pauli exclusion principle • Force resisting gravity is independent of temperature • 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 independent of temperature

12. Degenerate Electrons in Ordinary Metal

13. Star Clusters & Red Giant Evolution • The transition to core He fusion • Marks the move into the Red Giant phase • Details are determined entirely by mass • Analysis of star clusters • All a cluster’s stars formed at about the same time • All a cluster’s stars have different masses • High- mass stars evolve very quickly • Some leave the main sequence before low-mass stars can form • Low- mass stars evolve very slowly • A cluster’s H-R diagram depends on cluster age • Lower right band slowly approaches the main sequence • Upper left band movesaway fromthe main sequence • The turn-off gives the cluster’s age

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

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 “Metal” means 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. dCephei: A Pulsating Star

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

23. Roche Lobes of Close Binary Stars

24. 3 Kinds of Eclipsing Binary Stars …Semi-detached without mass transfer …with mass transfer Over-contact…

25. 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 Important Concepts