Homework #10

1. Homework #10 • Cosmic distance ladder III: Use formula and descriptions given in question text • Q7: Luminosity, temperature and area of a star are related by the Stefan-Boltzmann-Law: L = b A T4, so use scaling arguments to figure out L from R,T and R from L,T

2. Homework #10 • Q9: Estimate life expectancy from energy production rate and available fuel (mass) • Example: Star with 4L and 3M uses 4 times more mass for energy production, but has 3 times more mass, so it life time is a factor ¾=0.75 compared to the sun: 7.5 billion years • Q8: Given are m and M, so use the distance formula d(m,M) from Q5.

3. The Fundamental Problem in studying the stellar lifecycle • We study the subjects of our research for a tiny fraction of its lifetime • Sun’s life expectancy ~ 10 billion (1010) years • Careful study of the Sun ~ 370 years • We have studied the Sun for only 1/27 millionth of its lifetime!

4. Suppose we study human beings… • Human life expectancy ~ 75 years • 1/27 millionth of this is about 74 seconds • What can we learn about people when allowed to observe them for no more than 74 seconds?

5. Theory and Experiment • Theory: • Need a theory for star formation • Need a theory to understand the energy production in stars  make prediction how bight stars are when and for how long in their lifetimes • Experiment:observe how many stars are where when and for how long in the Hertzsprung-Russell diagram •  Compare prediction and observation

6. Hydrostatic Equilibrium • Two forces compete: gravity (inward) and energy pressure due to heat generated (outward) • Stars neither shrink nor expand, they are in hydrostatic equilibrium, i.e. the forces are equally strong Heat Gravity Gravity

7. Star Formation & Lifecycle • Contraction of a cold interstellar cloud • Cloud contracts/warms, begins radiating; almost all radiated energy escapes • Cloud becomes dense  opaque to radiation  radiated energy trapped  core heats up

8. Example: Orion Nebula • Orion Nebula is a place where stars are being born

9. Protostellar Evolution • increasing temperature at core slows contraction • Luminosity about 1000 times that of the sun • Duration ~ 1 million years • Temperature ~ 1 million K at core, 3,000 K at surface • Still too cool for nuclear fusion! • Size ~ orbit of Mercury

10. Path in the Hertzsprung-Russell Diagram Gas cloud becomes smaller, flatter, denser, hotter  Star

11. Protostellar Evolution • increasing temperature at core slows contraction • Luminosity about 1000 times that of the sun • Duration ~ 1 million years • Temperature ~ 1 million K at core, 3,000 K at surface • Still too cool for nuclear fusion! • Size ~ orbit of Mercury

12. Path in the Hertzsprung-Russell Diagram Gas cloud becomes smaller, flatter, denser, hotter  Star

13. A Newborn Star • Main-sequence star; pressure from nuclear fusion and gravity are in balance • Duration ~ 10 billion years (much longer than all other stages combined) • Temperature ~ 15 million K at core, 6000 K at surface • Size ~ Sun

14. Mass Matters • Larger masses • higher surface temperatures • higher luminosities • take less time to form • have shorter main sequence lifetimes • Smaller masses • lower surface temperatures • lower luminosities • take longer to form • have longer main sequence lifetimes

15. Mass and the Main Sequence • The position of a star in the main sequence is determined by its mass All we need to know to predict luminosity and temperature! • Both radius and luminosity increase with mass

16. Stellar Lifetimes • From the luminosity, we can determine the rate of energy release, and thus rate of fuel consumption • Given the mass (amount of fuel to burn) we can obtain the lifetime • Large hot blue stars: ~ 20 million years • The Sun: 10 billion years • Small cool red dwarfs: trillions of years The hotter, the shorter the life!

17. Main Sequence Lifetimes Mass(in solar masses)LuminosityLifetime 10 Suns 10,000 Suns 10 Million yrs 4 Suns 100 Suns 2 Billion yrs 1 Sun 1 Sun 10 Billion yrs ½ Sun 0.01 Sun 500 Billion yrs

18. Is the theory correct? Two Clues from two Types of Star Clusters  Open Cluster Globular Cluster 

19. Star Clusters • Group of stars formed from fragments of the same collapsing cloud • Same age and composition; only mass distinguishes them • Two Types: • Open clusters (young  birth of stars) • Globular clusters (old  death of stars)

20. What do Open Clusters tell us? • Hypothesis: Many stars are being born from a interstellar gas cloud at the same time • Evidence: We see • “associations” of stars • of same age •  Open Clusters

21. Why Do Stars Leave the Main Sequence? • Running out of fuel

22. Stage 8: Hydrogen Shell Burning • Cooler core  imbalance between pressure and gravity core shrinks • hydrogen shell generates energy too fast  outer layers heat up star expands • Luminosity increases • Duration ~ 100 million years • Size ~ several Suns

23. Stage 9: The Red Giant Stage • Luminosity huge (~ 100 Suns) • Surface Temperature lower • Core Temperature higher • Size ~ 70 Suns (orbit of Mercury)

24. Lifecycle • Lifecycle of a main sequence G star • Most time is spent on the main-sequence (normal star)

25. The Helium Flash and Stage 10 • The core becomes hot and dense enough to overcome the barrier to fusing helium into carbon • Initial explosion followed by steady (but rapid) fusion of helium into carbon • Lasts: 50 million years • Temperature: 200 million K (core) to 5000 K (surface) • Size ~ 10  the Sun

26. Stage 11 • Helium burning continues • Carbon “ash” at the core forms, and the star becomes a Red Supergiant • Duration: 10 thousand years • Central Temperature: 250 million K • Size > orbit of Mars

27. Deep Sky Objects: Globular Clusters • Classic example: Great Hercules Cluster (M13) • Spherical clusters • may contain millions of stars • Old stars • Great tool to study stellar life cycle

28. Observing Stellar Evolution by studying Globular Cluster HR diagrams • Plot stars in globular clusters in Hertzsprung-Russell diagram • Different clusters have different age • Observe stellar evolution by looking at stars of same age but different mass • Deduce age of cluster by noticing which stars have left main sequence already

29. Catching Stellar Evolution “red-handed” Main-sequence turnoff

30. Type of Death depends on Mass • Light stars like the Sun end up as White Dwarfs • Massive stars (more than 8 solar masses) end up as Neutron Stars • Very massive stars (more than 25 solar masses) end up as Black Holes

31. Reason for Death depends on Mass • Light stars blow out their outer layers to form a Planetary Nebula • The core of a massive star (more than 8 solar masses) collapses, triggering the explosion of a Supernova • Also the core of a very massive stars (more than 25 solar masses) collapses, triggering the explosion Supernova

32. Light Stars: Stage 12 - A Planetary Nebula forms • Inner carbon core becomes “dead” – it is out of fuel • Some helium and carbon burning continues in outer shells • The outer envelope of the star becomes cool and opaque • solar radiation pushes it outward from the star • A planetary nebula is formed Duration: 100,000 years Central Temperature: 300  106 K Surface Temperature: 100,000 K Size: 0.1  Sun

33. Deep Sky Objects: Planetary Nebulae • Classic Example: Ring nebula in Lyra (M57) • Remains of a dead, • exploded star • We see gas expanding in a sphere • In the middle is the dead star, a “White Dwarf”

34. Stage 13: White Dwarf • Core radiates only by stored heat, not by nuclear reactions • core continues to cool and contract • Size ~ Earth • Density: a million times that of Earth – 1 cubic cm has 1000 kg of mass!

35. Stage 14: Black Dwarf • Impossible to see in a telescope • About the size of Earth • Temperature very low  almost no radiation  black!