1. Stellar Evolution Chapter 12

2. Stars form from the interstellar medium and reach stability fusing hydrogen in their cores. This chapter is about the long, stable middle age of stars on the main sequence and their old age as they swell to become giant stars. Here you will answer three essential questions: What happens as a star uses up its hydrogen? What happens when a star exhausts its hydrogen? What evidence do astronomers have that stars really do evolve? Guidepost

3. Stars evolve over billions of years because of changes deep inside. That raises an interesting question about how scientists can understand such processes: How can astronomers study the inside of stars? This chapter is about how stars live. The next two chapters are about how stars die and the strange objects they leave behind. Guidepost (continued)

4. I. Main-Sequence Stars A. Stellar Models B. Why is there a Main Sequence? C. The Upper End of the Main Sequence D. The Lower End of the Main Sequence E. The Life of a Main-Sequence Star F. The Life Expectancies of Stars II. Post-Main-Sequence Evolution A. Expansion into a Giant B. Degenerate Matter ( 簡併物質 ) C. Helium Fusion D. Fusing Elements Heavier than Helium Outline

5. III. Evidence of Evolution: Star Clusters A. Observing Star Clusters B. The Evolution of Star Clusters IV. Evidence of Evolution: Variable Stars A. Cepheid and RR Lyrae Variable Stars B. Pulsating Stars C. Period Changes in Variable Stars Outline (continued)

6. The structure and evolution of a star is determined by the laws of Stellar Models Hydrostatic equilibrium Energy transport Conservation of mass Conservation of energy A star’s mass (and chemical composition) completely determines its properties. That’s why stars initially all line up along the main sequence.

7. Maximum Masses of Main-Sequence Stars a) More massive clouds fragment into smaller pieces during star formation. b) Very massive stars lose mass in strong stellar winds Example: Eta Carinae: Binary system of a 60 M sun and 70 M sun star Dramatic mass loss; major eruption in 1843 created double lobes M max ~ 100 solar masses

8. Minimum Mass of Main-Sequence Stars M min = 0.08 M sun At masses below 0.08 M sun, stellar progenitors do not get hot enough to ignite thermonuclear fusion.  Brown Dwarfs

9. Brown Dwarfs Hard to find because they are very faint and cool; emit mostly in the infrared. Many have been detected in star forming regions like the Orion Nebula.

10. Evolution on the Main Sequence (1) Zero-Age Main Sequence (ZAMS) Main-Sequence stars live by fusing H to He. Finite supply of H => finite life time

11. Evolution on the Main Sequence (2) Luminosity L ~ M 3.5 A star’s life time T ~ energy reservoir / luminosity T ~ M/L ~ 1/M 2.5 Energy reservoir ~ M Massive stars have short lives!

12. Evolution off the Main Sequence: Expansion into a Red Giant When the hydrogen in the core is completely converted into He: H burning continues in a shell around the core. He Core + H-burning shell produce more energy than needed for pressure support Expansion and cooling of the outer layers of the star  Red Giant  “Hydrogen burning” (i.e. fusion of H into He) ceases in the core.

13. Expansion onto the Giant Branch Expansion and surface cooling during the phase of an inactive He core and a H- burning shell Sun will expand beyond Earth’s orbit!

14. Degenerate Matter Matter in the He core has no energy source left.  Not enough thermal pressure to resist and balance gravity  Matter assumes a new state, called degenerate matter: Pressure in degenerate core is due to the fact that electrons can not be packed arbitrarily close together and have small energies.

15. Red Giant Evolution 4 H → He He H-burning shell keeps dumping He onto the core. He-core gets denser and hotter until the next stage of nuclear burning can begin in the core: He fusion through the “Triple-Alpha Process” 4 He + 4 He  8 Be +  8 Be + 4 He  12 C + 

16. Red Giant Evolution (5 solar-mass star) Main Sequence Expansion to red giant Red giant Helium ignition in the core Development of Carbon-Oxygen Core Helium in the core exhausted; development of He-burning shell

17. Fusion Into Heavier Elements Fusion into heavier elements than C, O requires very high temperatures; occurs only in very massive stars (more than 8 solar masses).

18. The Life “Clock” of a Massive Star (> 8 M sun ) Let’s compress a massive star’s life into one day… 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 Life on the Main Sequence + Expansion to Red Giant: 22 h, 24 min. H burning H  He He  C, O He burning: (Red Giant Phase) 1 h, 35 min, 53 s

19. The Life “Clock” of a Massive Star (2) H  He He  C, O C  Ne, Na, Mg, O Ne  O, Mg H  He He  C, O C  Ne, Na, Mg, O 12 1 2 3 4 5 6 7 8 9 10 11 C burning: 6.99 s Ne burning: 6 ms 23:59:59.996

20. The Life “Clock” of a Massive Star (3) H  He He  C, O C  Ne, Na, Mg, O Ne  O, Mg O burning: 3.97 ms 23:59:59.99997 O  Si, S, P H  He He  C, O C  Ne, Na, Mg, O Ne  O, Mg Si burning: 0.03 ms The final 0.03 msec!! O  Si, S, P Si  Fe, Co, Ni

21. Summary of Post Main-Sequence Evolution of Stars M > 8 M sun M < 4 M sun Evolution of 4 - 8 M sun stars is still uncertain. Fusion stops at formation of C,O core. Mass loss in stellar winds may reduce them all to < 4 M sun stars. Red dwarfs: He burning never ignites M < 0.4 M sun Supernova Fusion proceeds; formation of Fe core.

22. Evidence for Stellar Evolution: Star Clusters Stars in a star cluster all have approximately the same age! More massive stars evolve more quickly than less massive ones. If you put all the stars of a star cluster on a HR diagram, the most massive stars (upper left) will be missing!

23. HR Diagram of a Star Cluster

24. Example: HR diagram of the star cluster M3

25. Estimating the Age of a Cluster The lower on the MS the turn-off point, the older the cluster.

26. Evidence for Stellar Evolution: Variable Stars Some stars show intrinsic brightness variations not caused by eclipsing in binary systems. Most important example:  Cephei Light curve of  Cephei

27. Cepheid Variables: The Period-Luminosity Relation The variability period of a Cepheid variable is correlated with its luminosity. => Measuring a Cepheid’s period, we can determine its absolute magnitude! The more luminous it is, the more slowly it pulsates.

28. Cepheid Distance Measurements Comparing absolute and apparent magnitudes of Cepheids, we can measure their distances (using the 1/d 2 law)! The Cepheid distance measurements were the first distance determinations that worked out to distances beyond our Milky Way! Cepheids are up to ~ 40,000 times more luminous than our sun => can be identified in other galaxies

29. Pulsating Variables: The Instability Strip For specific combinations of radius and temperature, stars can maintain periodic oscillations. Those combinations correspond to locations in the Instability Strip Cepheids pulsate with radius changes of ~ 5 – 10 %.

30. Period Changes in Variable Stars Periods of some Variables are not constant over time because of stellar evolution.  Another piece of evidence for stellar evolution