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Chapter 12 Stellar Evolution

Guidepost This chapter is the heart of any discussion of astronomy. Previous chapters showed how astronomers make observations with telescopes and how they analyze their observations to find the luminosity, diameter, and mass of stars. All of that aims at understanding what stars are. This is the middle of three chapters that tell the story of stars. The preceding chapter told us how stars form, and the next chapter tells us how stars die. This chapter is the heart of the story—how stars live. As always, we accept nothing at face value. We expect theory to be supported by evidence. We expect carefully constructed models to help us understand the structure inside stars. In short, we exercise our critical faculties

Guidepost (continued) and analyze the story of stellar evolution rather than merely accepting it. After this chapter, we will know how stars work, and we will be ready to study the rest of the universe, from galaxies that contain billions of stars to the planets that form around individual stars.

Outline I. Main-Sequence Stars A. Stellar Models B. Why There Is a Main Sequence C. The Ends of the Main Sequence D. The Life of a Main-Sequence Star E. The Life Expectancies of Stars II. Post-Main-Sequence Evolution A. Expansion into a Giant B. Degenerate Matter C. Helium Fusion D. Fusing Elements Heavier than Helium

Outline (continued) 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

The structure and evolution of a star is determined by the laws of Main Sequence Stars The structure and evolution of a star is determined by the laws of 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.

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

Minimum Mass of Main-Sequence Stars Mmin = 0.08 Msun At masses below 0.08 Msun, stellar progenitors do not get hot enough to ignite thermonuclear fusion. Gliese 229B  Brown Dwarfs

Many have been detected in star forming regions like the Orion Nebula. 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.

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

Future of the Sun (SLIDESHOW MODE ONLY)

Evolution on the Main Sequence (2) A star’s life time T ~ energy reservoir / luminosity Energy reservoir ~ M Luminosity L ~ M3.5 T ~ M/L ~ 1/M2.5 Massive stars have short lives!

Evolution off the Main Sequence: Expansion into a Red Giant Hydrogen in the core completely converted into He: “Hydrogen burning” (i.e. fusion of H into He) ceases in the core. 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

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!

Degenerate Matter 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.

“Triple-Alpha Process” Red Giant Evolution 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: 4 H → He He He fusion through the “Triple-Alpha Process” 4He + 4He  8Be + g 8Be + 4He  12C + g

Helium Fusion He nuclei can fuse to build heavier elements: When pressure and temperature in the He core become high enough,

Red Giant Evolution (5 solar-mass star) C, O Inactive He

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).

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

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

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

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

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!

HR Diagram of a Star Cluster

Cluster Turnoff (SLIDESHOW MODE ONLY)

Example: HR diagram of the star cluster M 55 High-mass stars evolved onto the giant branch Turn-off point Low-mass stars still on the main sequence

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

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

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

Cepheid Distance Measurements Comparing absolute and apparent magnitudes of Cepheids, we can measure their distances (using the 1/d2 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.

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 %.

Pulsating Variables: The Valve Mechanism Partial He ionization zone is opaque and absorbs more energy than necessary to balance the weight from higher layers. => Expansion Upon expansion, partial He ionization zone becomes more transparent, absorbs less energy => weight from higher layers pushes it back inward. => Contraction. Upon compression, partial He ionization zone becomes more opaque again, absorbs more energy than needed for equilibrium => Expansion

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.

New Terms conservation of mass law conservation of energy law stellar model brown dwarf zero-age main sequence (ZAMS) degenerate matter triple alpha process helium flash open cluster globular cluster turnoff point horizontal branch variable star intrinsic variable Cepheid variable star RR Lyrae variable star period–luminosity relation instability strip  

Discussion Questions 1. How do we know that the helium flash occurs if it cannot be observed? Can we accept an event as real if we can never observe it? 2. Can you think of ways that chemical differences could arise in stars in a single star cluster? Consider the mechanism that triggered their formation.

Quiz Questions 1. Which of the following is NOT considered in making a simple stellar model? a. Hydrostatic equilibrium. b. Energy transport. c. Magnetic field. d. Conservation of mass. e. Conservation of energy.

Quiz Questions 2. According to Figure 12-1, what is the approximate radius of the Sun's nuclear fusion zone? a. 0.10 solar radii b. 0.30 solar radii c. 0.50 solar radii d. 0.70 solar radii e. 0.90 solar radii

Quiz Questions 3. Why is there a lower mass limit of 0.08 solar masses for main sequence stars? a. This is an unsolved astronomical mystery. b. Objects below this mass can only form in HI clouds. c. Objects below this mass are not hot enough to fuse normal hydrogen. d. They form too slowly and hot stars nearby clear the gas and dust quickly. e. Our telescopes do not have enough light gathering power to detect dim objects.

Quiz Questions 4. Why is there an upper mass limit for main sequence stars of about 100 solar masses? a. Giant molecular clouds do not contain enough material. b. General relativity does not allow such massive objects to exist. c. The rotation rate is so high that such an object splits into a pair of stars. d. Objects above this mass fuse hydrogen too rapidly and cannot stay together. e. Objects above this mass do form in molecular clouds; however, they emit no light and are not considered stars.

Quiz Questions 5. Why are lower main sequence stars more abundant than upper main sequence stars? a. More low-mass main sequence stars are formed in molecular clouds. b. Lower main sequence stars have much longer lifetimes than upper main sequence stars. c. High-mass main sequence stars lose mass and become lower main sequence stars. d. Both a and b above. e. All of the above.

Quiz Questions 6. Why does a star's life expectancy depend on mass? a. Mass determines the amount of fuel a star has for fusion. b. More massive stars can fuse hydrogen for a longer time. c. Mass determines the rate of fuel consumption for a star. d. Both a and b above. e. Both a and c above.

Quiz Questions 7. Which of the following observable properties of a main sequence star is a direct indication of the rate at which energy is produced inside that star? a. Surface temperature. b. Luminosity. c. Diameter. d. Distance. e. Age.

Quiz Questions 8. Why does an expanding giant star become cooler? a. Less energy is produced in the star's interior. b. More energy is produced in the star's interior. c. Thermal energy is converted into gravitational energy. d. Both a and b above. e. Both a and c above.

Quiz Questions 9. Of the following, which main sequence star has a longer life expectancy than the Sun? a. Spectral type B9. b. Spectral type K2. c. Spectral type A7. d. Spectral type O5. e. Spectral type F4.

Quiz Questions 10. How does the main sequence lifetime of a star compare to its entire fusion lifetime? a. Stars spend about 10% of their fusion lifetimes on the main sequence. b. Stars spend about 30% of their fusion lifetimes on the main sequence. c. Stars spend about 50% of their fusion lifetimes on the main sequence. d. Stars spend about 70% of their fusion lifetimes on the main sequence. e. Stars spend about 90% of their fusion lifetimes on the main sequence.

Quiz Questions 11. Why does an expanding giant star become more luminous? a. Less energy is produced in the interior. b. More energy is produced in the interior. c. Thermal energy is converted into gravitational energy. d. Both a and b above. e. Both a and c above.

Quiz Questions 12. What increases the temperature of an inert helium core inside a giant star? a. Hydrogen shell fusion. b. Helium shell fusion. c. Gravitational contraction. d. The triple-alpha process. e. Both a and b above.

Quiz Questions 13. Twice during the late stages of the Sun's life it will move upward and ascend the giant branch on the H-R diagram. What will be going on in the Sun's core while it is climbing the giant branch? a. The Sun's core will fuse hydrogen to make helium during both ascents of the giant branch. b. The Sun's core will fuse helium to make carbon and oxygen during both ascents of the giant branch. c. The Sun's core will fuse hydrogen to make helium during the first ascent, and fuse helium to make carbon and oxygen during the second ascent of the giant branch. d. The Sun's core will fuse helium to make carbon and oxygen during the first ascent, and is inert during the second ascent of the giant branch. e. The Sun's core will be inert during both ascents of the giant branch.

Quiz Questions 14. Why will a helium flash never occur in some stars? a. Some stars will never leave the main sequence. b. Some stars do not develop degenerate helium cores. c. Some stars have a hydrogen flash in place of a helium flash. d. Some stars contain no helium. e. All of the above.

Quiz Questions 15. Why are lower-mass stars unable to ignite more massive nuclear fuels such as carbon? a. They never get hot enough. b. They did not accumulate enough carbon when they formed. c. Beryllium is highly unstable. d. Carbon has too many neutrons in its nucleus. e. Both a and d above.

Quiz Questions 16. How do star clusters confirm that stars are evolving? a. The H-R diagram of a star cluster is missing the upper part of the main sequence. b. The H-R diagram of a star cluster is missing the lower part of the main sequence. c. The relative motion of stars in a cluster can be estimated by their Doppler shifts. d. Pulsating variable stars in globular clusters display a period-luminosity relationship. e. Star clusters occasionally lose members.

Quiz Questions 17. How are the ages of star clusters related to their turn-off points? a. The age of a cluster is the life expectancy of stars at its turn-off point. b. The higher the turn-off point, the older the star cluster. c. The lower the turn-off point, the older the star cluster d. Both a and b above. e. Both a and c above.

Quiz Questions 18. What is the general trend in the ages of the two types of star clusters? a. Globular clusters are young and open clusters are old. b. Globular clusters are old, and open clusters are both young and old. c. All star clusters are very young d. All star clusters are very old. e. The two types of star clusters have both very young and very old members.

Quiz Questions 19. From Figure 12-13, what is the absolute magnitude of a Type II Cepheid with a period of 30 days? a. -5 b. -4 c. -3 d. -2 e. -1

Quiz Questions 20. The period of a Cepheid variable star and the time of one recent maximum can be used to predict the time of a future maximum. Suppose that you calculate the time of future maximum brightness and then make measurements to observe this maximum. After the correction for Earth's orbital position has been made, you find that the maximum occurred a few minutes later than predicted. What does this tell you about this star? a. The star is moving toward Earth. b. The star is moving away from Earth. c. The star is slowly contracting. d. The star is slowly expanding. e. The star is not a Cepheid variable.

Answers 1. c 2. b 3. c 4. d 5. d 6. e 7. b 8. c 9. b 10. e 11. b 12. c 13. e 14. b 15. a 16. a 17. d 18. b 19. d 20. d

Evolution of Stars (SLIDESHOW MODE ONLY)