1. Part I: Black Holes and SpaceTime
July 23, 2004

2. Topics of the Day Properties of black holes
Mass
Spin
Size
A few words from Albert Einstein
Space Time
A few words from Stephen Hawking
Hawking radiation
Frame dragging
July 23, 2004

3. Black Hole Board Game Get into groups of six for board game.
Select a partner in this group of six.
This person is your spacecraft building teammate. (You did this yesterday)
You should have read the Mission Briefing and the Rules of the Game last night.
Now, play part 2 of the game.
July 23, 2004

4. Engage….. What do we know about black holes?
What do the students need to know about black holes?
What are some popular misconceptions about black holes?
What are some effective ways to teach this topic?
July 23, 2004

5. Black Hole Medley
Project for Prof. Cominsky’s Cosmology class several years ago
What would happen to the Earth if the Sun was instantaneously replaced by a BH of the same mass? (By the way, this can’t happen)
How many misconceptions can you find??
July 23, 2004

6. Properties of black holes
“Black Holes have no hair” – famous quote that alludes to the fact that (under GR), BH can be completely described by:
Charge (not expected to be seen)
Mass
Spin
July 23, 2004

7. Masses of Black Holes
Primordial – can be any size, including very small (If <1014 g, they would still exist) – none seen
“Stellar mass” black holes – must be at least 3 Mo (~1034 g) – many examples are well studied
Intermediate black holes – range from 100 to 1000 Mo - located in normal galaxies – many seen
Massive black holes – about 106 Mo – such as in the center of the Milky Way – many seen
Supermassive black holes – about Mo - located in Active Galactic Nuclei, often accompanied by jets – many seen
July 23, 2004

8. Black Hole Structure
BH are infamous for not letting light escape from within a certain radius (Schwarzschild, aka event horizon)
Using non-relativistic mechanics, how would you derive this radius?
Schwarzschild BH
July 23, 2004

9. Black Hole Structure Equate kinetic energy with potential energy
Kinetic energy of particle moving at light speed: ½ mc2
Potential energy at distance r: GMm/r
Rsch = 2GM/c2
July 23, 2004

10. Black Hole Structure Given: Rsch = 2GM/c2 where
G = × 10−11 N·m2/kg2
c = 3 x 108 m/s
1 Mo = 2 x 1030 kg
What is Rsch?
How does it scale?
July 23, 2004

11. Stellar Mass BH Often stars are formed in binary systems
Since they have unequal masses, the more massive star will evolve faster - and reach the end of its main sequence lifetime
In some cases, the supernova of the primary star will not disrupt the binary system and a COMPACT BINARY is formed
Mass transfer can then occur from the main sequence star onto the collapsed, compact companion star - which can be a WHITE DWARF, NEUTRON STAR or BLACK HOLE
July 23, 2004

12. White Dwarfs, Neutron Stars and Black Holes
White dwarfs are the size of the Earth and about 1 Mo
Neutron stars are 10 km in radius and about 1.4 Mo
One teaspoon of NS material weighs 100 million tons!
After supernova, if cores are larger than 3 Mo, a black hole will be formed
Mass transfer from normal star to compact object creates X-rays
July 23, 2004

13. Blondin X-ray Binary Simulation
This simulation by John Blondin (NCSU) shows a high mass star losing material to the compact object, and then forming an “accretion disk” of swirling material
July 23, 2004

14. Kepler’s third law a3 = GM(T/2p)2
where T is the orbital period and a is the semi-major axis of the orbit, G is the gravitational constant and M is the mass of the central object.
So – how would you use X-ray data to figure out if a black hole existed in a binary?
July 23, 2004

15. The First Black Hole Cygnus X-1 binary system Most likely mass is
Mass determined by Doppler shift measurements of optical lines
July 23, 2004

16. Measuring Mass At least 12 stellar mass BH have been well studied
Easiest to measure Doppler shift accurately when X-rays are not heating the accretion disk
X-ray “novae”
kepler
July 23, 2004

17. Intermediate mass BH
Recent simulations of starburst galaxy M82 have shown that collisions in the early life of a star cluster near the galaxy’s center can form a BH with mass Mo and replicate the Chandra observations
The BH is offset from the center of the galaxy by about 600 light years
July 23, 2004

18. Milky Way’s Massive BH
Best evidence comes from measurements of star motions in infrared images of central Milky Way by Ghez et al. and Genzel et al.
S2, the closest star to Sgr A* (the radio source at the exact center of the Milky Way) indicates a mass of 2.6 million +/- 0.2 Mo
S2 is at a distance of 17 light-hours from Sgr A* - whose event horizon is 26 light seconds
movie
July 23, 2004

19. NGC 4261 – best HST photo 100 million light years away
1.2 billion Mo black hole in a region the size of our Solar System
Mass of disk is 100,000 Mo
Disk is 800 light years across
July 23, 2004

20. Chandra finds supermassive BH everywhere!
Chandra deep field
Black holes in empty space
Empty
Black holes in“normal” galaxies
Galaxy
Black holes in quasars
QSO
July 23, 2004

21. God does not play dice with the Universe
Albert Einstein
“I want to know God's thoughts...the rest are details.”
“Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world.”
“With fame I become more and more stupid, which of course is a very common phenomenon.”
God does not play dice with the Universe
July 23, 2004

22. Break: What do you know about Einstein?
Why is 2005 the World Year of Physics?
Can you name 3 of Einstein’s most famous contributions to physics?
Everything should be made as simple as possible, but not simpler
Education is what remains after one has forgotten everything he learned in school
Two things are infinite: the universe and human stupidity; and I'm not sure about the the universe." (
July 23, 2004

23. Einstein and Relativity
1905 – Theory of Special Relativity
Applies to objects at a constant velocity
Time dilation and length contraction
Space and time are intertwined
Matter and energy are equivalent
Length contraction and time dilation
July 23, 2004
movie

24. Einstein and Relativity
1916 – Theory of General Relativity
Applies to objects that are accelerated
Describes the effects of gravity on spacetime
Spacetime
Acceleration
July 23, 2004

25. Einstein’s GR equation
Gab = 8 p G Tab c2
where Gab describes the geometry of spacetime and Tab describes the flow of energy and momentum through spacetime
Gab and Tab are tensors
“Matter tells spacetime how to curve and spacetime tells matter how to move”
-- J. A. Wheeler
July 23, 2004

26. Solutions to GR equations
Non-rotating, spherical black hole (Schwarzschild)
Rotating, axisymmetric BH (Kerr)
White holes
Wormholes
July 23, 2004

27. Motion in spacetime What is the motion of a particle in spacetime?
Do particles follow straight lines?
July 23, 2004

28. Spacetime activity Bedsheet, small balls and heavy weight
Try rolling the balls across the sheet with and without the weight
Can you make a small ball curve in an orbit around the weight?
July 23, 2004

29. Hamilton’s black hole trajectory
Minimum stable orbit is at 3 Schwarzschild radii or 300 km for this 30 Mo black hole
In order to orbit any closer, you must fire thrusters to maintain forward motion
July 23, 2004

30. Hamilton’s orbiting a black hole
Orbiting the black hole at close to the photon sphere. We are moving at almost the speed of light, so the relativistic beaming effects are quite strong.
July 23, 2004

31. Bob Nemiroff’s black hole movies
Approaching a black hole
Circling the black hole
July 23, 2004

32. Hamilton’s Wormhole
Complete Schwarzschild geometry consists of a black hole, a white hole, and two Universes connected at their horizons by a wormhole, also known as the Einstein-Rosen bridge
July 23, 2004

33. Measuring spin
Two views of matter spinning around BH
July 23, 2004

34. Active Galaxy Activity #3
Do you know how astronomers use light to compute the size of a black hole?
Here is a time history of flux from an active galaxy.
What is happening here?
What does this tell you about the size of the black hole?
July 23, 2004

35. Measuring size
The size of an object is related to the light variations seen from an object by
Size = c Dt
where c is the speed of light
and Dt is the timescale of the fastest variations seen from the object
Why do we use the fastest variations?
How does this work?
July 23, 2004

36. Micro-Arcsecond X-ray Imaging Mission
Image a Black Hole!
0.1 arc sec resolution
HST Image
M87
Close to the event horizon the peak energy is emitted in X-rays
MAXIM
0.1 micro arc sec resolution
4-8 m arc sec
Micro-Arcsecond X-ray Imaging Mission
July 23, 2004

37. Stephen Hawking
“God not only plays dice, he also sometimes throws the dice where they cannot be seen.”
“My goal is simple. It is complete understanding of the universe, why it is as it is and why it exists at all.”
“It is not clear that intelligence has any long-term survival value.”
Proved that if GR is true and the universe is expanding, then a singularity existed at the birth of the universe
July 23, 2004

38. Hawking Radiation
Hawking radiation results from the formation of virtual particle pairs near the black hole’s event horizon. The total energy of the pair, E1 + E2 =0.
According to quantum mechanics, virtual pairs of particles are always being created from the vacuum – they usually annihilate, disappearing back into the vacuum
However, if the pair is formed near a black hole, one particle can become real (E1>0) and escape, while the other falls into the black hole
The escaping particle makes Hawking radiation, while to conserve energy, the particle that falls in has to have E2<0, which lowers the energy of the black hole, and eventually causes it to evaporate.
July 23, 2004

39. Hawking radiation from a very small black hole
Bigger black holes are colder and fainter
Hawking radiation will eventually lead to the death of all BHs at the end of time
Evaporation of mini-black hole in a gamma-ray burst
July 23, 2004

40. Information escapes a BH?
Hawking radiation produces a paradox:
He previously claimed that no information can escape from a BH
Yet, the escaping particle carries away the information about its partner – as charge, etc. must be conserved in pair production
He has now (as of last week) concluded that information can escape from a BH
Details were released yesterday (7/21)
July 23, 2004

41. Frame dragging activity
Paper plate, honey, peppercorns, food dye, superball
What happens when the ball spins?
movie
July 23, 2004

42. Frame Dragging Predicted by Einstein’s theory of General Relativity
Rotating bodies drag space and time around themselves as they rotate – like a spinning object stuck in molasses
It may have been observed by RXTE in neutron star and black hole binaries in oscillations caused by matter in precessing accretion disks
Precessing top
July 23, 2004

43. These two effects are at right angles to each other
Frame Dragging
Gravity Probe B –now launched!
Will test 2 predictions of GR using 4 extremely accurate gyroscopes
Measure space-time reference frame of Earth – gyroscopes will move 6.6 arcseconds per year
Measure frame dragging of Earth – gyroscopes will move by 42 milliarcseconds per year
These two effects are at right angles to each other
July 23, 2004

44. Reflection and Debrief
July 23, 2004

45. Reflection and Debrief (Evaluate)
Now what do we know?
What are the big ideas here?
What do our students need to know?
Is there anything else we need to know?
Misconceptions
(take notes)
July 23, 2004

46. Common Misconceptions
Black holes are black because they don’t emit any light or suck up all light
BH are emitting gravity or are the definition of gravity
BH travel through space acting like cosmic vacuum cleaners
BH are wormholes = time travel machines
If we had a BH at the location of the Sun, it would suck in the Earth
July 23, 2004

47. Reflection and Debrief (Evaluate)
What are some of the effective ways to teach these topics?
Standards???
(take notes)
July 23, 2004

48. Web Resources
Astronomy picture of the Day
Imagine the Universe
Relativity animations
NCSA’s Unveiling the Hidden Universe
Jim Brau at the U of Oregon Astro 122 notes
Intermediate mass black hole
July 23, 2004

49. Web Resources
Pictures from the Hubble Space Telescope
Chris Hillman’s Relativity Page
Andrew Hamilton’s Black Hole Flight Simulator
Stephen Hawking’s Home page
Genzel Group Milky Way BH video html#vid-02-02
July 23, 2004

50. Web Resources
Rossi X-ray Timing Explorer
Gravity Probe B
Micro-Arcsecond X-ray Imaging Mission
Laser Interferometric Space Array
Bob Nemiroff’s black hole movies
ROSAT X-ray images
July 23, 2004