Iron absorbs energy from gravitational energy Released during the collapse

2. Iron absorbs energy from gravitational energy Released during the collapse And Fe breaks apart releasing p+ that combine with e- of the star

3. Collapses in one second … what happens next is not completely understood

4. (in LMC) Explosion speeds up nuclear reactions, create elements more massive than iron. Enriched material spreads out and goes to the next generation of Stars

5. Rapid increase and fades over months

6. High energy e- are relativistic and the spiral motion creates this highly directional radiation

7. Properties of Synchrotron radiation • Electron’s spiral • Constant acceleration in circular • Motion gives off radiation • 3.Most radiation is admitted • In a small cone in the direction of • motion Note other properties

8. Guess where we find Black Holes and Pulsars ?

10. 0 The Remnants of Sun-Like Stars: White Dwarfs Sunlike stars build up a Carbon-Oxygen (C,O) core, which does not ignite Carbon fusion. He-burning shell keeps dumping C and O onto the core. C,O core collapses and the matter becomes degenerate. Formation of a White Dwarf What is degenerate matter??Later!

11. 0 White Dwarfs Degenerate stellar remnant (C,O core) Extremely dense: 3x106 g/cc ->1 teaspoon of WD material: mass ≈ 15 tons!!! Chunk of WD material the size of a beach ball would outweigh an ocean liner! White Dwarfs: Mass ~ Msun SurfaceTemp. ~ 25,000 K Luminosity ~ 0.01 Lsun (small area!)

12. Low luminosity; high temperature => White dwarfs are found in the lower left corner of the Hertzsprung-Russell diagram. 0 White Dwarfs (2) The more massive a white dwarf, the smaller it is! Pressure becomes larger with more mass, until electron degeneracy pressure (that which holds the white dwarf from collapsing-later!) can no longer hold up against gravity. WDs with more than ~ 1.4 solar masses can not exist! Since they would collapse.. To what professor? Later! Chandrasekhar Limit = 1.4 Msun

13. The Chandrasekhar Limit The more massive a white dwarf, the smaller it is. Pressure becomes larger, until electron degeneracy pressure can no longer hold up against gravity. WDs with more than ~ 1.4 solar masses can not exist!

14. Ie. Number per volume!

15. So..ideal gas P goes as T (kT) !

16. Pauli Exclusion principle…NO TWO ELECTRONS CAN BE IN THE SAME STATE! Electron spin in QM causes only one spin up and spin down e per state! RAISING T DOES NOT INCREASE P!

21. XXXXX

24. 0 Formation of Neutron Stars (2)

25. 0 Properties of Neutron Stars a piece of neutron star matter of the size of a sugar cube has a mass of ~ 100 million tons!!! Typical size: R ~ 10 km Mass: M ~ 1.4 – 3 Msun Density: r ~ 1014 g/cm3 A neutron star (more than the mass of the sun) would comfortably fit within the Capital Beltway!

26. 0 Discovery of Pulsars Angular momentum conservation => Collapsing stellar core spins up to periods of ~ a few milliseconds. Magnetic fields are amplified up to B ~ 109 – 1015 G. (up to 1012 times the average magnetic field of the sun) => Rapidly pulsed (optical and radio) emission from some objects interpreted as spin period of neutron stars

27. 0 Pulsars / Neutron Stars Neutron star surface has a temperature of~ 1 million K. Cas A in X-rays Wien’s displacement law, lmax = 3,000,000 nm / T[K] gives a maximum wavelength of lmax = 3 nm, which corresponds to X-rays.

28. 0 Pulsar Periods Over time, pulsars lose energy and angular momentum => Pulsar rotation is gradually slowing down. PERIOD INCREASES! GLITCHES..SUPPORT NEUTRON STAR MODEL OF PULSARS ? STARQUAKES (SOLID BULGING SURFACE CRACKS BECOMES ROUNDER AND SPEEDS UP THE ROTATION!

29. 0 Pulsar Winds Pulsars are emitting winds and jets of highly energetic particles. These winds carry away about 99.9 % of the energy released from the slowing-down of the pulsar’s rotation.

30. 0 Lighthouse Model of Pulsars A Pulsar’s magnetic field has a dipole structure, just like Earth. Radiation is emitted mostly along the magnetic poles.

31. 0 Images of Pulsars and Other Neutron Stars The vela Pulsar moving through interstellar space The Crab nebula and pulsar

32. 0 The Crab Pulsar Pulsar wind + jets Remnant of a supernova observed in A.D. 1054

33. 0 The Crab Pulsar (2) Visual image X-ray image

34. 0 Light Curves of the Crab Pulsar

35. 0 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

36. 0 Binary Pulsars Some pulsars form binaries with other neutron stars (or black holes). Radial velocities resulting from the orbital motion lengthen the pulsar period when the pulsar is moving away from Earth... …and shorten the pulsar period when it is approaching Earth.

37. 0 Neutron Stars in Binary Systems: X-ray Binaries Example: Her X-1 Star eclipses neutron star and accretion disk periodically 2 Msun (F-type) star Neutron star Orbital period = 1.7 days Accretion disk material heats to several million K => X-ray emission

38. 0 Pulsar Planets Some pulsars have planets orbiting around them. Just like in binary pulsars, this can be discovered through variations of the pulsar period. As the planets orbit around the pulsar, they cause it to wobble around, resulting in slight changes of the observed pulsar period.

42. I = MOMENT OF INERTIA w = ANGULAR VELOCITY Ie wsun / 2x109 IE. INS wns = Isunwsun ie conservation of Angular momentum

47. General Relativity A new description of gravity Postulate: Equivalence Principle: “Observers can not distinguish locally between inertial forces due to acceleration and uniform gravitational forces due to the presence of massive bodies.”

48. Another Thought Experiment Imagine a light source on board a rapidly accelerated space ship: Time Time a Light source a a a g As seen by a “stationary” observer As seen by an observer on board the space ship

49. Thought Experiment (2) For the accelerated observer, the light ray appears to bend downward! Now, we can’t distinguish between this inertial effect and the effect of gravitational forces Thus, a gravitational force equivalent to the inertial force must also be able to bend light!

50. Thought Experiment (Conclusion) This bending of light by the gravitation of massive bodies has indeed been observed: During total solar eclipses: The positions of stars apparently close to the sun are shifted away from the position of the sun. New description of gravity as curvature of space-time!