A100 Exploring the Universe: Black holes. Martin D. Weinberg UMass Astronomy
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1 A100 Exploring the Universe: Black holes Martin D. Weinberg UMass Astronomy October 30, 2014 Read: S2, S3, Chap 18 10/30/14 slide 1
2 Sizes of s The solar neighborhood visualized! Thanks to Raymond Phoung Read: S2, S3, Chap 18 10/30/14 slide 2
3 Sizes of s The solar neighborhood visualized! Thanks to Raymond Phoung Exam #2: November 04 Covers Chaps: S4, 14, 15, (16), 17, 18 Read: S2, S3, Chap 18 10/30/14 slide 2
4 Sizes of s The solar neighborhood visualized! Thanks to Raymond Phoung Exam #2: November 04 Covers Chaps: S4, 14, 15, (16), 17, 18 Today 1. Black holes What they are What they are NOT Theories of relativity Read: S2, S3, Chap 18 10/30/14 slide 2
5 Sizes of s The solar neighborhood visualized! Thanks to Raymond Phoung Exam #2: November 04 Covers Chaps: S4, 14, 15, (16), 17, 18 Today 1. Black holes What they are What they are NOT Theories of relativity Questions? Read: S2, S3, Chap 18 10/30/14 slide 2
6 Stellar evolution Black Holes Sizes of s A star with M > 18M Sun would leave behind an iron core more massive than 2-3 M Sun Neutron degeneracy pressure would fail with nothing to stop its gravitational collapse Core would collapse into a singularity! Gravity becomes so strong that nothing, not even light, can escape Infalling matter is shredded by powerful tides Black hole! Black because they neither emit nor reflect light Hole because nothing entering can ever escape Read: S2, S3, Chap 18 10/30/14 slide 3
7 is conserved: a quick review Sizes of s Definition: is the capacity of a physical system to do work Definition: Work is application of force over a distance Read: S2, S3, Chap 18 10/30/14 slide 4
8 Kinetic energy Sizes of s Example: kinetic energy from accelerating an object m v=0 d d m Push object with constant force over distance d Final velocity v f Average velocity: v = v f 2 = d t Force required: F = ma = m v f t Work done (energy): E = Fd = mv fd t v=v f = 1 2 mv2 f Read: S2, S3, Chap 18 10/30/14 slide 5
9 Kinetic energy Sizes of s Example: kinetic energy from accelerating an object m v=0 d d m Push object with constant force over distance d Final velocity v f Average velocity: v = v f 2 = d t Force required: F = ma = m v f t Work done (energy): E = Fd = mv fd t v=v f = 1 2 mv2 f Read: S2, S3, Chap 18 10/30/14 slide 5
10 Kinetic energy Sizes of s Example: kinetic energy from accelerating an object m v=0 d d m Push object with constant force over distance d Final velocity v f Average velocity: v = v f 2 = d t Force required: F = ma = m v f t Work done (energy): E = Fd = mv fd t v=v f = 1 2 mv2 f Read: S2, S3, Chap 18 10/30/14 slide 5
11 Kinetic energy Sizes of s Example: kinetic energy from accelerating an object m v=0 d d m Push object with constant force over distance d Final velocity v f Average velocity: v = v f 2 = d t Force required: F = ma = m v f t Work done (energy): E = Fd = mv fd t v=v f = 1 2 mv2 f Read: S2, S3, Chap 18 10/30/14 slide 5
12 Potential energy Example: potential energy is energy that can be converted to kinetic energy by moving in a force field v=0 v=vf Ground level Potential energy is positive to start Kinetic energy is gained as ball rolls down hill Potential energy is zero at bottom of hill Read: S2, S3, Chap 18 10/30/14 slide 6
13 Potential energy Example: potential energy is energy that can be converted to kinetic energy by moving in a force field v=0 Ground level v=vf v=0 Potential energy is zero at top of well Kinetic energy is gained as ball rolls into well v=vf Potential energy is negative at bottom of well Total energy (kinetic plus potential) is conserved Read: S2, S3, Chap 18 10/30/14 slide 6
14 Sizes of s Need a critical value of velocity to escape the surface of a gravitating body To escape the gravitational pull of a planet, need an initial velocity that will make your total mechanical energy be unbound Total mechanical energy of a blob the energy of motion added to the energy given up by falling in: E = KE +PE = 1 2 mv2 GMm R Read: S2, S3, Chap 18 10/30/14 slide 7
15 Sizes of s must be greater than zero to be unbound: 0 = 1 2 mv2 GMm R 2GM v esc = R [Just like ball rolling in the potential well] Examples: Earth: v esc = 11.2 km/s Moon: v esc = 2.4 km/s Read: S2, S3, Chap 18 10/30/14 slide 8
16 Sizes of s must be greater than zero to be unbound: 0 = 1 2 mv2 GMm R 2GM v esc = R [Just like ball rolling in the potential well] Examples: Earth: v esc = 11.2 km/s Moon: v esc = 2.4 km/s Neutron star: v esc = 160,000 km/s = 0.53 c! Read: S2, S3, Chap 18 10/30/14 slide 8
17 Radius Sizes of s For a given escape velocity and mass, we can compute the radius we need to just escape: R = 2GM v 2 esc Read: S2, S3, Chap 18 10/30/14 slide 9
18 Radius Sizes of s For a given escape velocity and mass, we can compute the radius we need to just escape: R = 2GM v 2 esc Nothing moves faster than the speed of light... Read: S2, S3, Chap 18 10/30/14 slide 9
19 Radius Sizes of s For a given escape velocity and mass, we can compute the radius we need to just escape: R = 2GM v 2 esc Nothing moves faster than the speed of light... Light cannot escape from a Black Hole if it comes from a radius closer than the Radius, R s : R s = 2GM c 2 where M is the mass of the hole. Read: S2, S3, Chap 18 10/30/14 slide 9
20 Sizes of s Sizes of black holes Some comparisons: Radius R s = 2GM c M Sun White Dwarf: radius of 1 R earth = 6370 km 1.4 M Sun Neutron Star: radius of 10 km A with a mass of 1 M Sun has R s =3 km Read: S2, S3, Chap 18 10/30/14 slide 10
21 Sizes of s Newton s law of gravity tell us how to compute gravitational force. Suppose that the distribution of mass changes in one part of the Universe. How quickly does this information travel to another part of the Universe? (A) Instantaneously. (B) At the speed of light. (C) At some speed slower than the speed of light. Read: S2, S3, Chap 18 10/30/14 slide 11
22 Sizes of s Newton s law of gravity tell us how to compute gravitational force. Suppose that the distribution of mass changes in one part of the Universe. How quickly does this information travel to another part of the Universe? (A) Instantaneously. [According to Newton] (B) At the speed of light. (C) At some speed slower than the speed of light. Read: S2, S3, Chap 18 10/30/14 slide 11
23 Sizes of s Newton s law of gravity tell us how to compute gravitational force. Suppose that the distribution of mass changes in one part of the Universe. How quickly does this information travel to another part of the Universe? (A) Instantaneously. (B) At the speed of light. [According to Einstein] (C) At some speed slower than the speed of light. Read: S2, S3, Chap 18 10/30/14 slide 11
24 Implications for the Laws of Physics Sizes of s Newton s theory gravity implies that the force propagates infinitely fast (action at a distance) Read: S2, S3, Chap 18 10/30/14 slide 12
25 Implications for the Laws of Physics Sizes of s Newton s theory gravity implies that the force propagates infinitely fast (action at a distance) Need to modify laws of motion to think about velocities near the speed of light () Read: S2, S3, Chap 18 10/30/14 slide 12
26 Implications for the Laws of Physics Sizes of s Newton s theory gravity implies that the force propagates infinitely fast (action at a distance) Need to modify laws of motion to think about velocities near the speed of light () Also need to modify law of gravity to incorporate new laws of motion Read: S2, S3, Chap 18 10/30/14 slide 12
27 Implications for the Laws of Physics Sizes of s Newton s theory gravity implies that the force propagates infinitely fast (action at a distance) Need to modify laws of motion to think about velocities near the speed of light () Also need to modify law of gravity to incorporate new laws of motion : Einstein s theory of gravitation (1915) First solutions by Karl (1916) Not taken seriously until the 1960s Read: S2, S3, Chap 18 10/30/14 slide 12
28 New theory of motion Sizes of s Thought experiment... Q: Two cars have a head-on collision. Each is moving at 45 mph. What is their relative speed? Read: S2, S3, Chap 18 10/30/14 slide 13
29 New theory of motion Sizes of s Thought experiment... Q: Two cars have a head-on collision. Each is moving at 45 mph. What is their relative speed? A: 90 mph Read: S2, S3, Chap 18 10/30/14 slide 13
30 New theory of motion Sizes of s Thought experiment... Q: Two cars have a head-on collision. Each is moving at 45 mph. What is their relative speed? A: 90 mph Q: Two spaceships have a head-on collision. Each is moving at 0.9 c. What is their relative speed? Read: S2, S3, Chap 18 10/30/14 slide 13
31 New theory of motion Sizes of s Thought experiment... Q: Two cars have a head-on collision. Each is moving at 45 mph. What is their relative speed? A: 90 mph Q: Two spaceships have a head-on collision. Each is moving at 0.9 c. What is their relative speed? A: 1.8 c? No, it is 0.99 c (according to special relativity) Read: S2, S3, Chap 18 10/30/14 slide 13
32 Sizes of s What is the medium that propagates light? c. 1900: scientists look for differences in the speed of light in different directions Michelson-Morley experiment: no difference Einstein showed that this can be explained assuming the speed of light is constant for all observers Read: S2, S3, Chap 18 10/30/14 slide 14
33 Sizes of s What is the medium that propagates light? c. 1900: scientists look for differences in the speed of light in different directions Michelson-Morley experiment: no difference Einstein showed that this can be explained assuming the speed of light is constant for all observers Two principles: The laws of physics must be the same in all reference frames (True in Galilean relativity, Newtons Laws, too) Speed of light must be constant in all reference frames (New!) Read: S2, S3, Chap 18 10/30/14 slide 14
34 of Sizes of s c Consider two observers moving at near the speed of light relative to each other At the instant that they are at the same place, one observer fires a flash bulb or strobe Sphere of light propagates from this point c A B v=0.8 c c What does each observer see? c Read: S2, S3, Chap 18 10/30/14 slide 15
35 of Sizes of s Each observer must see a sphere of light. How can this be? Stationary observer A sees B s length contracts: L = L o 1 v 2 /c 2 B s clock dialates: T = T o / 1 v 2 /c 2 B s energy increases: E = E o / 1 v 2 /c 2 From B s point of view, the same thing happens to A. Both observers A & B see light sphere from the flash bulb. Read: S2, S3, Chap 18 10/30/14 slide 16
36 Sizes of s Laser source Photon Clock 1.5 m Photocell detector Clock ticks when pulse arrives, sends new pulse Pulse from laser travels 3 meters to receiver t = 3m/ m/s = 10 8 s Read: S2, S3, Chap 18 10/30/14 slide 17
37 s in moving frames Sizes of s As seen by spaceship pilot (B) at v = 0.8c Read: S2, S3, Chap 18 10/30/14 slide 18
38 s in moving frames Sizes of s v=0.8 c As seen by mission control (A) Read: S2, S3, Chap 18 10/30/14 slide 18
39 Sizes of s More consequences Lengths and clocks Simultaneous events in one frame are not simultaneous in another Pole and barn paradox Read: S2, S3, Chap 18 10/30/14 slide 19
40 Sizes of s More consequences Lengths and clocks Simultaneous events in one frame are not simultaneous in another Pole and barn paradox 80 m pole, 40 m barn with doors at both ends Runner runs through barn at v = 0.5c In barn frame: L = = 34.9 m Runner: barn is L = = 17.4 m Barn doors close and open simultaneously in barn s frame but not in Runner s frame Twin paradox Read: S2, S3, Chap 18 10/30/14 slide 19
41 Sizes of s More consequences Lengths and clocks Simultaneous events in one frame are not simultaneous in another Pole and barn paradox Twin paradox Read: S2, S3, Chap 18 10/30/14 slide 19
42 Sizes of s More consequences Lengths and clocks Simultaneous events in one frame are not simultaneous in another Pole and barn paradox Twin paradox One twin travels at 0.99c to star 10 ly away Travelling twin sees length to star contracted: L = 10 ly = 1.41 ly Time to get there and back: T = ly/c = 2.82 years Twin on Earth sees: 2 10 ly/c = 20 years Read: S2, S3, Chap 18 10/30/14 slide 19
43 A uniform gravitational field (like that near the Earth) is equivalent to a uniform acceleration A person cannot tell the difference between 1. Standing on the Earth, feeling the effects of gravity as a downward pull 2. Standing in a very smooth elevator that is accelerating upwards at g (32 feet per second per second) Read: S2, S3, Chap 18 10/30/14 slide 20
44 Sizes of s Back to action at a distance! Led Einstein to come up with a new way of describing gravity 1. Space-time is curved by mass 2. The motion of the mass is determined by the curvature of space-time In this view, gravity is no longer a force! Trajectories of objects in space-time move along the shortest path Read: S2, S3, Chap 18 10/30/14 slide 21
45 Sizes of s Back to action at a distance! Led Einstein to come up with a new way of describing gravity 1. Space-time is curved by mass 2. The motion of the mass is determined by the curvature of space-time In this view, gravity is no longer a force! Trajectories of objects in space-time move along the shortest path Read: S2, S3, Chap 18 10/30/14 slide 21
46 Sizes of s Back to action at a distance! Led Einstein to come up with a new way of describing gravity 1. Space-time is curved by mass 2. The motion of the mass is determined by the curvature of space-time In this view, gravity is no longer a force! Trajectories of objects in space-time move along the shortest path Read: S2, S3, Chap 18 10/30/14 slide 21
47 Sizes of s Read: S2, S3, Chap 18 10/30/14 slide 22
48 Sizes of s Read: S2, S3, Chap 18 10/30/14 slide 22
49 Sizes of s Back to Black holes If the Sun shrank into a, its gravity would be different only near the event horizon Read: S2, S3, Chap 18 10/30/14 slide 23
50 Sizes of s Back to Black holes Black holes do not suck! If the Sun shrank into a, its gravity would be different only near the event horizon Read: S2, S3, Chap 18 10/30/14 slide 23
51 Sizes of s R s defines the Event Horizon surrounding the s singularity: Events occurring inside R s are invisible to the outside universe Anything closer to the singularity than R s can never leave the The Event Horizon hides the singularity from the outside universe The Event Horizon marks the Point of No Return for objects falling into a Black Hole. Read: S2, S3, Chap 18 10/30/14 slide 24
52 Sizes of s Black holes do not suck! Far away from a : Gravity is the same as a star of the same mass. If the Sun became a Black Hole, the planets would all orbit the same as before. Close to a : R < 3R s, there are no stable orbits matter falls in At R = 1.5R s, photons would orbit in a circle! Read: S2, S3, Chap 18 10/30/14 slide 25
53 Wavelength of light increases when climbing out of a gravitational well Think of a baseball hit high into the air, slowing as it climbs Photon also loses energy Read: S2, S3, Chap 18 10/30/14 slide 26
54 Wavelength of light increases when climbing out of a gravitational well Think of a baseball hit high into the air, slowing as it climbs Photon also loses energy is observable: 1960, observed in elevator shaft Jefferson Tower physics building at Harvard University Observed in solar radiation, neutron stars GPS system! Read: S2, S3, Chap 18 10/30/14 slide 26
55 How to find a? Sizes of s Look for the effects of their gravity on their surroundings Search for stellar-mass s in binary star systems by looking for: A star orbiting around an unseen massive companion X-rays emitted by gas heated to extreme temperatures as it falls into the High velocities Read: S2, S3, Chap 18 10/30/14 slide 27
56 How to find a? Sizes of s X-Ray Binaries Bright, variable X-ray sources identified by X-ray observatory satellites: Spectroscopic binary with only one set of spectral lines - the second object is invisible. Gas from the visible star is dumped on the companion, heats up, and emits X-rays. Estimate the mass of the unseen companion from the parameters of its orbit. Read: S2, S3, Chap 18 10/30/14 slide 28
57 How to find a? Sizes of s Some X-ray binaries contain compact objects of mass exceeding 3M Sun which are likely to be s Read: S2, S3, Chap 18 10/30/14 slide 29
58 Black Holes are not really Black! Sizes of s Classical says: Black Holes are totally black Can only grow in mass and size Last forever (nothing gets out once inside) But: does not include the effects of Quantum Mechanics! Read: S2, S3, Chap 18 10/30/14 slide 30
59 Black Holes are not really Black! Sizes of s Stephen Hawking looked at the problem by considering quantum effects occurring near the event horizon of a Black Hole. He showed that: Black holes slowly leak particles with a blackbody spectrum. Each particle carries off a little of the s mass The smaller the mass of the, the faster it leaks. Read: S2, S3, Chap 18 10/30/14 slide 31
60 Evaporating Black Holes Sizes of s Evaporating Holes Black Holes evaporate slowly by emitting subatomic particles and photons via Hawking Radiation. The smaller the mass, the faster the evaporation. For s in the real universe, the evaporation rate is VERY slow: A 3 M Sun would require about years to completely evaporate. This is about times the present age of the Universe. Read: S2, S3, Chap 18 10/30/14 slide 32
61 Sizes of s White holes? Wormholes? A theoretical possibility. Practical impossibility! Read: S2, S3, Chap 18 10/30/14 slide 33
62 Sizes of s White holes? Wormholes? A theoretical possibility. Practical impossibility! Can the whole universe be curved? Definitely... see cosmology. Read: S2, S3, Chap 18 10/30/14 slide 33
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