Your next test will be November 14

1. Your next test will be November 14 Review session: Friday, Nov. 10, 5:30-7:30 pm Room 205 ENPH-Teaching wing

2. 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

3. 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!

4. HR Diagram of a Star Cluster

5. 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

6. Estimating the Age of a Cluster Age of a cluster = lifetime of stars on the turnoff point The lower on the MS the turn-off point, the older the cluster.

7. Fate of massive stars

8. Upper limit on white dwarf masses Pressure of degenerate gas cannot be increased indefinitely When particle velocities become relativistic, they cannot be increased anymore; Matter becomes “softer”: P ~ 4/3 The core gives in to gravity and collapses

9. Chandrasekhar limit: 1.4 Msun For a given mass, find the radius at which equilibrium is reached This is because gravitational pressure increases with mass. Electron pressure should also increase, and the only way to do it is to compress the star.

10. Death of massive stars What happens when the core is heavier than the Chandrasekhar limit?

12. Reactions proceed faster and faster, until …

13. Fig. 7-16, p. 126

14. The iron core of a giant star cannot sustain the pressure of gravity. It collapses inward in less than a second. The shock wave blows away outer layers of a star, creating a SUPERNOVA EXPLOSION!

15. Supernova in Centaurus A Precise mechanism – still unknown

16. Still many problems with SN scenario • Outward shock seems to get stalled by inward falling layers • Neutrinos carry away over 90% of the SN energy and deposit it to outer layers. However, computer models do not “explode”. Turbulent convection seems to help the outward shock to break through the infalling layers

17. Energy release due to radioactive decay of 56Ni and 56Co Type I and II Supernovae Core collapse of a massive star: Type II Supernova If an accreting White Dwarf exceeds the Chandrasekhar mass limit, it collapses, triggering a Type Ia Supernova. Type I: No hydrogen lines in the spectrum Type II: Hydrogen lines in the spectrum

18. Type Ia supernova: why there is no hydrogen? White dwarf gains mass beyond 1.4 Msun It collapses, and violent C-O fusion begins in the core Carbon deflagration: a white dwarf explodes

19. Type Ib supernova: why there is no hydrogen? Main-sequence blue giant that has lost its outer hydrogen-rich envelope Its remnant develops an iron core and collapses

20. Chemical elements in the UniverseHow did the elements form? • The Big Bang • Elements Formed: H, He, (Li) • Stellar Nucleosynthesis • Elements Formed: Almost all other elements • Supernovae Explosion • Elements Formed: Heaviest elements

21. All elements up to A ~ 250 are synthesized! S-processes: “slow” synthesis of elements up to iron R-processes (r = rapid): rapid neutron capture Supernova nucleosynthesis

22. Atomic nucleus n + (A,Z) ===> (A+1,Z) ===> (A+1,Z+1) + e + neutrino n + (A+1,Z+1) ===> (A+2,Z+1) ===> (A+2,Z+2) + e + neutrino And so on

23. Earth Cosmic abundance

24. Practically all heavy elements are due to stars We owe our very existence to SN explosions

25. Neutron Stars A supernova explosion of a M > 8 Msun star blows away its outer layers. The central core will collapse into a compact object of ~ a few Msun.

26. Formation of Neutron Stars Compact objects more massive than the Chandrasekhar Limit (1.4 Msun) collapse further. Pressure becomes so high that electrons and protons combine to form stable neutrons throughout the object: neutronization p + e-n + ne Neutron Star

27. Neutron Star Pressure of degenerate neutrons balances gravity ?? Strange matter? Quark-gluon plasma?? Neutron stars have been theoretically predicted in 30s. Landau, Oppenheimer, Zwicky, Baade

28. "spherical bastards” Fritz Zwicky 1898-1974 Walter Baade 1893-1960

29. Explained supernovae, discovered many of them, coined the term Predicted neutron star as a remnant of SN explosion; correctly suggested that it should be a star with the density of a nucleus resulting from gravitational collapse of a core Predicted that supernovae are the origin of the cosmic rays Discovered galaxy clusters Predicted dark matter Predicted gravitational lensing Predictions and discoveries

30. Properties of Neutron Stars Typical size: R ~ 10 km Mass: M ~ 1.4 – 3 Msun Density: r ~ 1015 g/cm3 Piece of neutron star matter of the size of a sugar cube has a mass of ~ 1 billion tons!!!

31. Density ~ 1015 g/cm3; One cubic cm weighs 109 ton!

32. Degenerate gas • The core is compressed until the inter-particle distance = de Broglie • wavelength • - One particle occupies finite volume in space and in momentum space • - Pauli exclusion principle permits only one particle per each state

33. Particle density mneutron ~ 2000 melectron Therefore, inter-particle distance can be 2000 times smaller and density 109 times higher! When particle velocities become relativistic, they cannot be increased anymore; Matter becomes “softer”: P ~ 4/3 The core gives in to gravity and collapses

35. Superfluidity Pyotr Kapitza (Nobel Prize 1978) discovered that liquid helium flows without friction when cooled below 2.17 K. This phenomenon is termed superfluidity. A superfluid shows several spectacular effects. For example, superfluid helium cannot be kept in an open vessel because then the fluid creeps as a thin film up the vessel wall and over the rim. Superfluid helium in a vessel does not rotate with it as a normal fluid does. Instead, a large number of whirlpools, called vortices, are formed.

36. Neutron stars have been theoretically predicted in 30s. Landau, Oppenheimer, Zwicky, Baade Isolated neutron stars are extremely hard to observe

37. Proper Motion of Neutron Stars Some neutron stars are moving rapidly through interstellar space. This might be a result of anisotropies during the supernova explosion forming the neutron star

38. Neutron stars should rotate extremely fast due to conservation of the angular momentum in the collapse They should have huge magnetic field due to conservation of the magnetic flux in the collapse However, there are two facts that can help:

39. Conservation of angular momentum: when radius decreases, rotation velocity goes up

41. Neutron star can make over 100 rotations per second! R R V  V B  B Conservation of magnetic field flux: BxR2 = const Magnetic field after collapse: B ~ 1012 – 1015 Gauss !!! Highest magnetic fields in the lab: 107 Gauss

42. Discovery of pulsars: Bell and Hewish, 1967 Jocelyn Bell

43. The enigma of pulsars Pulse repetition: from a few to 0.03 seconds Pulse duration: ~ 0.001 s Period extremely stable: it increases by less than 1 sec in a million years What could it be??? Only star rotation can be so stable. However: Centrifugal acceleration < gravitational acceleration It must be a neutron star!!

44. Lighthouse Model of Pulsars A Pulsar’s magnetic field has a dipole structure, just like Earth. Radiation is emitted mostly along the magnetic poles.

46. Neutron Star (SLIDESHOW MODE ONLY)

47. General idea of a pulsar emission

48. What is pulsar radiation? Synchrotron radiation of relativistic particles!

49. Pulsars can emit also in other EM ranges: optical, X-ray, etc.