1. Black Holes A stellar mass black hole accreting material from a companion star 1

2. Black Holes and General Relativity 1. The Equivalence Principle In an elevator with no windows, there is no way to distinguish effects of gravity from the effects of the elevator being accelerated General Relativity: Einstein's description of gravity (extension of Newton's). Published in 1915. It begins with: 2

3. 2. Gravitational Redshift Consider accelerating elevator in free space (no gravity). time zero, speed=0 later, speed > 0 light received when elevator receding at some speed. light emitted when elevator at rest. Received light has longer wavelength (or shorter frequency) because of Doppler Shift ("redshift"). Gravity must have same effect! Verified in Pound-Rebka experiment. 3

4. 3. Gravitational Time Dilation A photon moving upwards in gravity is redshifted. Since the photon's period gets longer. Observer 1 will measure a longer period than Observer 2. So they disagree on time intervals. Observer 1 would say that Observer 2's clock runs slow! 1 2 All these effects are unnoticeable in our daily experience! They are tiny in Earth’s gravity, but large in a black hole’s. 4

5. Escape Velocity Velocity needed to escape the gravitational pull of an object. v esc = 2GM R Escape velocity from Earth's surface is 11 km/sec. If Earth were crushed down to 1 cm size, escape velocity would be speed of light. Then nothing, including light, could escape Earth. This special radius, for a particular object, is called the Schwarzschild Radius, R S. R S  M. 5

6. Black Holes If core with about 3 M Sun or more collapses, not even neutron pressure can stop it (total mass of star about 25 M Sun ). Core collapses to a point, a "singularity". Gravity is so strong that nothing can escape, not even light => black hole. Schwarzschild radius for Earth is 1 cm. For a 3 M Sun object, it’s 9 km. 6

7. Event horizon: imaginary sphere around object with radius equal to Schwarzschild radius. Event horizon Schwarzschild Radius Anything crossing over to inside the event horizon, including light, is trapped. We can know nothing more about it after it does so. 7

8. Like a rubber sheet, but in three dimensions, curvature dictates how all objects, including light, move when close to a mass. Black hole achieves this by severely curving space. According to Einstein's General Relativity, all masses curve space. Gravity and space curvature are equivalent. 8

9. Curvature at event horizon is so great that space "folds in on itself", i.e. anything crossing it is trapped. 9

10. Approaching a Black Hole: 10

11. Circling a Black Hole at the Photon Sphere: 11

12. Effects around Black Holes 1) Enormous tidal forces. 2) Gravitational redshift. Example, blue light emitted just outside event horizon may appear red to distant observer. 3) Time dilation. Clock just outside event horizon appears to run slow to a distant observer. At event horizon, clock appears to stop. 12

13. Black Holes have no Hair Properties of a black hole: - Mass - Spin (angular momentum) - Charge (tends to be zero) 13

14. Black Holes can have impact on their environments 14

15. Do Black Holes Really Exist? Good Candidate: Cygnus X-1 - Binary system: 30 M Sun star with unseen companion. - Binary orbit => companion > 7 M Sun. - X-rays => million degree gas falling into black hole. 15

16. Supermassive (3 million solar mass) Black Hole at the Galactic Center 16

18. The Milky Way Galaxy a b c d

19. Artist's Conception Take a Giant Step Outside the Milky Way Example (not to scale)

20. Artist's Conception Take a Giant Step Outside the Milky Way Example (not to scale)

21. from above ("face-on") see disk and bulge from the side ("edge-on") Orion arm Perseus arm Cygnus arm Carina arm Sun

22. Another galaxy: NGC 4414. The Milky Way roughly resembles it.

23. M31

24. The Three Main Structural Components of the Milky Way 1. Disk - 30,000 pc diameter (or 30 kpc) - contains young and old stars, gas, dust. Has spiral structure - vertical thickness roughly 100 pc - 2 kpc (depending on component. Most gas and dust in thinner layer, most stars in thicker layer) 2. Halo - at least 30 kpc across - contains globular clusters, old stars, little gas and dust, much "dark matter" - roughly spherical

25. 3. Bulge - About 4 kpc across - old stars, some gas, dust - central black hole of 3 x 10 6 solar masses - spherical

26. Shapley (1917) found that Sun was not at center of Milky Way Shapley used distances to variable “ RR Lyrae ” stars (a kind of Horizontal Branch star) in Globular Clusters to determine that Sun was 16 kpc from center of Milky Way. Modern value 8 kpc.

27. Stellar Orbits Halo: stars and globular clusters swarm around center of Milky Way. Very elliptical orbits with random orientations. They also cross the disk. Bulge: similar to halo. Disk: rotates.

28. Precise Distance to Galactic Center Distance = 7.94 +/- 0.42 kpc Eisenhauer et al. 2003 Orbital motion 6.37 mas/yr SgrA*

29. Rotation of the Disk Sun moves at 225 km/sec around center. An orbit takes 240 million years. Stars closer to center take less time to orbit. Stars further from center take longer. The "rotation curve" of the Milky Way => rotation not rigid like a phonograph record or a merry-go-round. Rather, "differential rotation". Over most of disk, rotation velocity is roughly constant.

31. Spiral Structure of Disk Spiral arms best traced by: Young stars and clusters Emission Nebulae HI Molecular Clouds (old stars to a lesser extent) Disk not empty between arms, just less material there.

32. Problem: How do spiral arms survive? Given differential rotation, arms should be stretched and smeared out after a few revolutions (Sun has made 20 already): The Winding Dilemma

33. The spiral should end up like this: Real structure of Milky Way (and other spiral galaxies) is more loosely wrapped.

34. Proposed solution: Arms are not material moving together, but mark peak of a compressional wave circling the disk: A Spiral Density Wave Traffic-jam analogy:

35. Now replace cars by stars and gas clouds. The traffic jams are actually due to the stars' collective gravity. The higher gravity of the jams keeps stars in them for longer. Calculations and computer simulations show this situation can be maintained for a long time. Traffic jam on a loop caused by merging

36. Molecular gas clouds pushed together in arms too => high density of clouds => high concentration of dust => dust lanes. Also, squeezing of clouds initiates collapse within them => star formation. Bright young massive stars live and die in spiral arms. Emission nebulae mostly in spiral arms. So arms always contain same types of objects, but individual objects come and go.

37. 90% of Matter in Milky Way is Dark Matter Gives off no detectable radiation. Evidence is from rotation curve: Rotation Velocity (AU/yr) Solar System Rotation Curve: when almost all mass at center, velocity decreases with radius ("Keplerian") R (AU) 10 5 1 1 20 30 Curve if Milky Way ended where visible matter pretty much runs out. observed curve Milky Way Rotation Curve

38. Not enough radiating matter at large R to explain rotation curve => "dark" matter! Dark matter must be about 90% of the mass! Mass of Milky Way 6 x 10 11 solar masses within 40 kpc of center. Composition unknown. Probably mostly exotic particles that don't interact with ordinary matter at all (except gravity). Some may be brown dwarfs, dead white dwarfs … Most likely it's a dark halo surrounding the Milky Way.

39. Seeing into the center of the Milky Way