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 T 4, 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 (10 10 ) 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

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) Luminosity Lifetime 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 Black HolesVery 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 SupernovaAlso 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  10 6 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!