Black Holes and SpaceTime

1. 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

3. 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?

4. 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??

5. Common Misconceptions • Black holes are black because they don’t emit any light or suck up all light • BH are a source of gravity or 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

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

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 109-10 Mo - located in Active Galactic Nuclei, often accompanied by jets – many seen

8. Schwarzschild BH 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?

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

10. Black Hole Structure • Given: Rsch = 2GM/c2 where G =6.6742 × 10−11 N·m2/kg2 c = 3 x 108 m/s 1 Mo = 2 x 1030 kg • What is Rsch? • How does it scale?

11. Compact Binaries and Supernovae • 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

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

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

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?

15. The First Black Hole • Cygnus X-1 binary system • Most likely mass is 16 (+/- 5) Mo • Mass determined by Doppler shift measurements of optical lines

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”

17. Milky Way’s Black Hole • Best evidence comes from measurements of star positions 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

18. 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

19. Chandra deep field Chandra finds black holes are everywhere! Black holes in empty space Empty Black holes in“normal” galaxies Galaxy Black holes in quasars QSO

20. 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

21. 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." • (http://rescomp.stanford.edu/~cheshire/EinsteinQuotes.html)

22. Einstein Centenary • Simon and Erika • break

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 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

25. Einstein’s GR equation Gab = 8 p G Tab c2 where Gabdescribes the geometry of spacetime and Tabdescribes 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

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

27. Motion in spacetime • What is the motion of a particle in spacetime? • Do particles follow straight lines?

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?

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

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.

31. Bob Nemiroff’s black hole movies • Approaching a black hole • Circling the black hole

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

33. Measuring spin Two views of matter spinning around BH

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?

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?

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

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

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.

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

40. Frame dragging activity • Paper plate, honey, peppercorns, food dye, superball • What happens when the ball spins? movie

41. 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

42. 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

43. Reflection and Debrief • What are some of the effective ways to teach these topics? • Standards (add some here – 2061)

44. Web Resources • Astronomy picture of the Dayhttp://antwrp.gsfc.nasa.gov/apod/astropix.html • Imagine the Universehttp://imagine.gsfc.nasa.gov • Relativity animations http://www.pbs.org/wgbh/nova/einstein/relativity/index.html • NCSA’s Unveiling the Hidden Universehttp://www.ncsa.uiuc.edu/Cyberia/Bima/BimaHome.html#Unveiling • Jim Brau at the U of Oregon Astro 122 noteshttp://blueox.uoregon.edu/~jimbrau/astr122

45. Web Resources • Pictures from the Hubble Space Telescope http://oposite.stsci.edu/pubinfo/pictures.html • Chris Hillman’s Relativity Pagehttp://www.math.washington.edu/~hillman/relativity.html • Andrew Hamilton’s Black Hole Flight Simulator http://casa.colorado.edu/~ajsh/bhfs/screenshots/ • Stephen Hawking’s Home page http://www.hawking.org.uk/ • Genzel Group Milky Way BH video http://www.eso.org/outreach/press-rel/pr-2002/pr-17-02.html#vid-02-02

46. Web Resources • Rossi X-ray Timing Explorerhttp://oposite.stsci.edu/pubinfo/pictures.html • Gravity Probe B http://einstein.stanford.edu • Micro-Arcsecond X-ray Imaging Mission http://maxim.gsfc.nasa.gov • Laser Interferometric Space Array http://lisa.nasa.gov • Bob Nemiroff’s black hole movieshttp://antwrp.gsfc.nasa.gov/htmltest/rjn_bht.html • ROSAT X-ray imageshttp://wave.xray.mpe.mpg.de/rosat/calendar/2000/oct

47. Move slides • The following slides go to 7/28

48. Constellation X • Four X-ray satellites that point at the same place • Launched two at a time • High resolution x-ray spectra • Large collecting area • Delayed until at least 2013

49. Comparison of Line Profiles from Constellation-X Energy (keV) Measuring spin Constellation X will be able to tell spinning (Kerr) black holes from non-spinning (Schwarzschild) black holes

50. The strongest signal comes from two orbiting black holes Black hole mergers in distant galaxies will test General Relativity in the extreme Gravitational Radiation • General Relativity predicts the existence of gravitational radiation  waves of gravity that travel at the speed of light