The Sun and Stars

1. The Sun and Stars

2. THIS WEEK • Chapters 11, 12, 13 • Review Tuesday, April 12 • Exam #2 Thursday, April 14 • Assigned question due Today: Question 3 from Chapter 12.

3. Nuclear Fusion • Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). • Why does this produce energy? • Before: the mass of 4 protons is 4 proton masses. • After: the mass of 2 protons and 2 neutrons is 3.97 proton masses. • Einstein: E = mc2. The missing mass went into energy! 4H ---> 1He + energy

4. Nuclear Fusion • Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

5. Nuclear Fusion • Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). • Extremely high temperatures and densities are needed! Images from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

6. Nuclear Fusion • Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). • Extremely high temperatures and densities are needed! The temperature is about 8,000,000K at the core of the Sun.

7. Nuclear Fusion • Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). • The details are a bit complex: Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

8. Nuclear Fusion • Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). • The details are a bit complex: • In the Sun, 6 hydrogen nuclei are involved in a sequence that produces two hydrogen nuclei and one helium nucleus. This is the proton-proton chain. • In more massive stars, a carbon nucleus is involved as a catalyst. This is the CNO cycle.

9. Nuclear Fusion • Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). • Why doesn’t the Sun blow up like a bomb?

10. Nuclear Fusion • Summary: 4 hydrogen nuclei (which are protons) combine to form 1 helium nucleus (which has two protons and two neutrons). • Why doesn’t the Sun blow up like a bomb? There is a natural “thermostat” in the core.

11. Controlled Fusion in the Sun • First, note that the rate of the p-p chain or CNO cycle is very sensitive to the temperature. • Rate ~ (temperature)4 for p-p chain. • Rate ~ (temperature)15 for the CNO cycle. • Small changes in the temperature lead to large changes in the fusion rate. • Suppose the fusion rate inside the Sun increased: • The increased energy heats the core and expands the star. But the expansion cools the core, lowering the fusion rate. The lower rate allows the core to shrink back to where it was before.

12. Models of the Solar Interior • The interior of the Sun is relatively simple because it is an ideal gas, described by three quantities: • Temperature • Pressure • Mass density

13. Models of the Solar Interior • The interior of the Sun is relatively simple because it is an ideal gas, described by three quantities: • Temperature • Pressure • Mass density • The relationship between these three quantities is called the equation of state.

14. Ideal Gas • For a fixed volume, a hotter gas exerts a higher pressure: Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

15. Hydrostatic Equilibrium • The Sun does not collapse on itself, nor does it expand rapidly.

16. Hydrostatic Equilibrium • The Sun does not collapse on itself, nor does it expand rapidly. Gravity and internal pressure balance: Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

17. Hydrostatic Equilibrium • The Sun does not collapse on itself, nor does it expand rapidly. Gravity and internal pressure balance. This is true at all layers of the Sun. Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

18. Models of the Solar Interior • The pieces so far: • Energy generation (nuclear fusion). • Ideal gas law (relation between temperature, pressure, and volume. • Hydrostatic equilibrium (gravity balances pressure). • Continuity of mass (smooth distribution throughout the star). • Continuity of energy (amount entering the bottom of a layer is equal to the amount leaving the top). • Energy transport (how energy is moved from the core to the surface).

19. Models of the Solar Interior • Solve these equations on a computer: • Compute the temperature and density at any layer, at any time. • Compute the size and luminosity of the star as a function of the initial mass. • Etc……. • It is possible to explain the temperature-luminosity diagrams of clusters (among other things).

20. Odds and Ends • Why does L vary like (mass)4? E.g., why is an O-star about 10,000 times more luminous than the Sun when its mass is only 20 times the solar mass?

21. Odds and Ends • Why does L vary like (mass)4? E.g., why is an O-star about 10,000 times more luminous than the Sun when its mass is only 20 times the solar mass? • More massive stars need hotter interiors to be stable. The increased temperature leads to large increase in energy generation (the rate varies like (temperature)15.) Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

22. Odds and Ends • Why are there no stars more massive than about 100 solar masses, and no stars with masses less than about 1/10 of a solar mass?

23. Odds and Ends • Why are there no stars more massive than about 100 solar masses, and no stars with masses less than about 1/10 of a solar mass? • At the high end, the pressure rises rapidly with mass, and is stronger than gravity when the mass gets near 100 solar masses.

24. Odds and Ends • Why are there no stars more massive than about 100 solar masses, and no stars with masses less than about 1/10 of a solar mass? • At the high end, the pressure rises rapidly with mass, and is stronger than gravity when the mass gets near 100 solar masses. The star is no longer stable!

25. Odds and Ends • Why are there no stars more massive than about 100 solar masses, and no stars with masses less than about 1/10 of a solar mass? • At the low end, the core temperature does not get high enough to fuse hydrogen since the gravitational force is relatively weak.

26. Odds and Ends • Why are there no stars more massive than about 100 solar masses, and no stars with masses less than about 1/10 of a solar mass? • At the low end, the core temperature does not get high enough to fuse hydrogen since the gravitational force is relatively weak. “Brown dwarfs” are such low-mass objects.

27. Temperature-Luminosity Diagrams • Most of the stars are in the “main sequence”. We can understand these stars pretty well. Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

28. Temperature-Luminosity Diagrams • Most of the stars are in the “main sequence”. We can understand these stars pretty well. • What about these “giants” and “white dwarfs”? Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

29. Temperature-Luminosity Diagrams • Most of the stars are in the “main sequence”. We can understand these stars pretty well. • What about these “giants” and “white dwarfs”? • These are stars in a much later stage of evolution… Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

30. Stellar Evolution and the Life Cycles of the Stars

31. Stellar Evolution • There are several distinct phases in the life cycle of a star. The evolutionary path depends on the initial mass of the star.

32. Stellar Evolution • There are several distinct phases in the life cycle of a star. The evolutionary path depends on the initial mass of the star. • Although there is a continuous range of masses, we often talk about “lightweight” stars (masses similar to the Sun) and “heavyweight” stars (masses about about 10 solar masses).

33. Stellar Evolution

34. Stellar Evolution • The basic steps are: • Gas cloud • Main sequence • Red giant • Rapid mass loss (planetary nebula or supernova explosion) • Remnant

35. Stellar Evolution • The basic steps are: • Gas cloud • Main sequence • Red giant • Rapid mass loss (planetary nebula or supernova explosion) • Remnant • The length of time spent in each stage, and the details of what happens at the end depend on the initial mass.

36. Star Formation • The starting point is a giant molecular cloud. The gas is relatively dense and cool, and usually contains dust.

37. Star Formation • The starting point is a giant molecular cloud. The gas is relatively dense and cool, and usually contains dust. • A typical cloud is several light years across, and can contain up to one million solar masses of material.

38. Star Formation • The starting point is a giant molecular cloud. The gas is relatively dense and cool, and usually contains dust. • A typical cloud is several light years across, and can contain up to one million solar masses of material. • Thousands of clouds are known.

39. Side Bar: Observing Clouds • Ways to see gas:

40. Side Bar: Observing Clouds • Ways to see gas: • By “reflection” of a nearby light source. Blue light reflects better than red light, so “reflection nebulae” tend to look blue.

41. Side Bar: Observing Clouds • Ways to see gas: • By “reflection” of a nearby light source. Blue light reflects better than red light, so “reflection nebulae” tend to look blue. • By “emission” at discrete wavelengths. A common example is emission in the Balmer-alpha line of hydrogen, which appears red.

42. Side Bar: Observing Clouds • Ways to see dust:

43. Side Bar: Observing Clouds • Ways to see dust: • If the dust is “warm” (a few hundred degrees K) then it will emit light in the long-wavelength infrared region or in the short-wavelength radio.

44. Side Bar: Observing Clouds • Ways to see dust: • If the dust is “warm” (a few hundred degrees K) then it will emit light in the long-wavelength infrared region or in the short-wavelength radio. • Dust will absorb light: blue visible light is highly absorbed; red visible light is less absorbed, and infrared light suffers from relatively little absorption.

45. Side Bar: Observing Clouds • Ways to see dust: • If the dust is “warm” (a few hundred degrees K) then it will emit light in the long-wavelength infrared region or in the short-wavelength radio. • Dust will absorb light: blue visible light is highly absorbed; red visible light is less absorbed, and infrared light suffers from relatively little absorption. Dust causes “reddening”.

46. Giant Molecular Clouds • This nebula is in the sword of Orion. It is about 29 light years across and 1500 light years away. • Dark regions are apparent (obscuration by dust), as well as regions of glowing gas (heated by a nearby hot star). Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

47. Giant Molecular Clouds • This nebula is in the belt of Orion. Dark dust lanes and also glowing gas are evident.

48. The Protostar • A giant molecular cloud is in rough hydrostatic equilibrium: gravity balances internal pressure.

49. The Protostar • A giant molecular cloud is in rough hydrostatic equilibrium: gravity balances internal pressure. • An external disturbance can cause the cloud to collapse:

50. The Protostar • A giant molecular cloud is in rough hydrostatic equilibrium: gravity balances internal pressure. • An external disturbance can cause the cloud to collapse: • The material collapses to a rotating disk, and friction drives material into the center, where it builds up. • The central object heats up as the cloud collapses. Eventually, the temperature gets hot enough for nuclear fusion to occur.