Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Chapter 23: Black Holes March 7, 2006 Astronomy 2010 1 Fact, Fiction, or Unknown This is a game where you (or I) make statements about black holes (or wormholes) and then we discuss whether these are fact, fiction, or unknown. March 7, 2006 Astronomy 2010 2 General Relativity To understand what black holes are, we begin with an introduction to Einstein’s theory of general relativity. It improves on Newton’s theory of gravity. Newton’s gravity works well in most situations (planetary orbits, binary stars) but fails when: Gravity becomes extremely intense. Large masses move rapidly. Light is effected by a large mass. March 7, 2006 Astronomy 2010 3 The Equivalence Principle The equivalence principle says that an object will behave the same whether in gravity or accelerating at an equivalent rate. No experiment can distinguish between gravity and acceleration. We must get the same result. Astronauts feel weightless in orbit because their acceleration cancels gravity. March 7, 2006 Astronomy 2010 4 Here’s the Rub Aim a laser beam from the rear to front of a shuttle. In zero gravity the laser will hit the front center of the shuttle. In free fall around the Earth, the laser must hit the same spot -- but from the time the light leaves the laser until it reaches the front, the shuttle has moved! The light is bent by gravity to hit the front center! March 7, 2006 Astronomy 2010 5 General Relativity: Warped Space March 7, 2006 Astronomy 2010 6 Light “Bends” March 7, 2006 Astronomy 2010 7 Tests of General Relativity Einstein’s theory says that the presence of matter warps space and time. Gravity is replaced by warping of space-time. Predictions: Precession of the perihelion of Mercury Light will be bent when passing near large objects Time will slow down near a large mass Gravitational redshift of light Massive objects will collapse to a singularity (black hole). March 7, 2006 Astronomy 2010 8 Deflection of Light Arthur Eddington mounted two expeditions in 1919, one to Brazil and the other to West Africa, to view a total eclipse and measure the deflection of starlight passing near the Sun. Both obtained measurements that agreed with GR predictions fame for Einstein & Eddington. Gravitational lensing is now a tool: multiple images of distant objects microlensing: one image but brightness changes March 7, 2006 Astronomy 2010 9 gravitational lens -- gravity can bend light around a very heavy obstacle possible gravitational lens observed March 7, 2006 Astronomy 2010 10 Lensing of Distant Galaxies Hubble picture of distant galaxies lensed by nearer galaxy (bright fuzzy structure). Lensed galaxies appear as arcs in the picture. Can be used to estimate the mass of the intermediate galaxy. March 7, 2006 Astronomy 2010 11 Gravity's Final Victory A star more massive than about 18 Msun leaves behind a core larger than 3 Msun Neutron degeneracy pressure fails Nothing can stop its gravitational collapse. Core collapses to a singularity: zero radius infinite density Near the singularity gravity is so strong that not even light can escape. March 7, 2006 Astronomy 2010 12 Escape Velocity: Rocket Analogy light: 299,792 km/s Black Holes: Key Concepts Black Holes are totally collapsed objects gravity so strong not even light can escape predicted by General Relativity Find them by their Gravity – Binary stars Orbit of visible partner Accretion disk – matter sucked in from partner X-ray Binaries Gravitational microlensing March 7, 2006 Astronomy 2010 16 Black Hole Formation Supernovae explosion collapsing core passes through a neutron star stage neutron star not stable degeneracy pressure insufficient Core becomes a Black Hole: "Black" because it neither emits nor reflects light. "Hole" because nothing entering can ever escape. Only its enormous mass remains March 7, 2006 Astronomy 2010 17 Near the Singularity Gravity is so strong that nothing, not even light, can escape. Infalling matter is shredded by powerful tides and crushed to infinite density. March 7, 2006 Astronomy 2010 18 Schwarzschild Radius Light cannot escape from a Black Hole if it comes from a radius closer than the Schwarzschild radiius M = Mass of the Black Hole, c = speed of light, G = newton’s constant At this distance: escape velocity = speed of light Light speed is the fastest possible speed! mass of 1 Msun a Schwarzschild Radius of 3 km. March 7, 2006 Astronomy 2010 19 Event Horizon Schwarzschild radius marks the Event Horizon surrounding the black hole's singularity: Events occurring inside are invisible to the outside universe. Anything closer to the singularity can never leave the black hole The Event Horizon hides the singularity from the outside universe. “Point of No Return” for objects falling into a black hole. March 7, 2006 Astronomy 2010 20 Gravity Around Black Holes Far away from a black hole: Gravity is the same as for a star of the same mass. If the Sun became a Black Hole, all the planets would continue in the same orbits. Close to a black hole: R < 3 RS, there are no stable orbits - all matter eventually gets sucked in. March 7, 2006 Astronomy 2010 21 Simulated Views of a Black Hole far away up close Falling into a Black Hole Falling toward a black hole wouldn’t be a pleasant experience… Falling feet-first, your body would be scrunched sideways and stretched along the length of your body by the tidal forces of the black hole. Your body would look like a spaghetti noodle! Stretching happens because your feet would be pulled much more strongly than your head. Sideways scrunching happens because all points of your body would be pulled toward the center of the black hole. Your shoulders would be squeezed closer together as you fell closer to the center of the black hole. Tidal stretching/squeezing of anything falling into a B.H. is conveniently forgotten in Hollywood movies. March 7, 2006 Astronomy 2010 23 Falling into a Black Hole A friend watching you as you enter a B.H., would see your clock run slower and slower (than his) as you approached the event horizon. This is the effect of "time dilation". Your friend would see you take an infinite amount of time to cross the event horizon time would appear to stand still. However, in your reference frame your clock would run forward normally and you would reach the center very soon. March 7, 2006 Astronomy 2010 24 Gravitational Redshift If you beamed back the progress of your journey into a black hole, your friend would have to tune to progressively longer wavelengths (lower frequencies) as you approached the event horizon. This is the effect of gravitational redshift. Eventually, the photons would be stretched to infinitely long wavelengths. March 7, 2006 Astronomy 2010 25 Seeing the Invisible Question: If no light gets out of a black hole, how can we ever hope to find one? Answer: Look for the effects of their gravity on nearby objects. For example, search for black holes in binary star systems: A star orbiting around an unseen massive companion. X-rays emitted by gas heated to extreme temperatures as it falls into the black hole. March 7, 2006 Astronomy 2010 26 March 7, 2006 Astronomy 2010 27 What if a Binary Partner is a Black Hole? black hole and visible star orbit around a center of mass motion of visible companion betrays black hole Kepler's 3rd law total mass of the system. If the mass of the unseen object is too big for a neutron star or a white dwarf, then it is very likely a black hole! orbit depends mass of two objects March 7, 2006 Astronomy 2010 28 Accretion from Binary Partner Motion of Accretion Disk from Doppler Shift Measure Black Hole mass X-Ray Binaries Bright, variable X-ray sources identified by Xray 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. March 7, 2006 Astronomy 2010 32 X-Ray Emission Visible Star black hole accretion disk Gas pulled off Gas temperature increases closer to BH. Gas near BH emits x-rays. Chandra X-ray Observatory Detects/images X-ray sources that are billions of LY away. Chandra’s mirrors are the largest, most precisely shaped and aligned, and smoothest mirrors ever constructed. Images 25 times sharper than the best previous X-ray telescope. Launched by Space Shuttle Columbia on July 23, 1999. One of NASA's Great Observatories. This focusing power is equivalent to the ability to read a newspaper at a distance of half a mile. Chandra's improved sensitivity is making possible more detailed studies of black holes, supernovae, and dark matter. March 7, 2006 Astronomy 2010 34 March 7, 2006 Astronomy 2010 35 X-Ray Emission Visible star close loses some of its gas to the black hole Gas material forms an accretion disk as it spirals onto the black hole gas particles in the disk rub against each and heat up from friction friction increases inward causing increasing temperature closer to the event horizon near event horizon, the disk is hot enough to emit X-rays. March 7, 2006 Astronomy 2010 36 Black Hole Candidates A number of X-ray binaries have been found with unseen companions with masses > 3 Msun, too big for a neutron star. Some Candidates: Cygnus X-1: M = 6-10 Msun V404 Cygni: M > 6 Msun LMC X-3: M = 7-10 Msun None are as yet iron-clad cases, but in general things are looking pretty good. March 7, 2006 Astronomy 2010 37 Black Hole Theory Modern physics has two basic sets of laws for the universe: General relativity -- macro-scale Quantum field theory -- micro-scale The two are not compatible! Most problems fall into one category only. Black holes need both. micro-size and macro-mass The study of black holes (on paper) helps understand how to combine the two theories. March 7, 2006 Astronomy 2010 38 Black Hole Theory (cont’d) Black holes are “simple” objects described by their mass, spin, and electric charge. Black holes have no hair. All event horizons are spherical, no matter what the mass looked like before collapse. Black holes have no magnetic field (internal). Black holes have entropy (a measure of disorder) that is proportional to the size of the event horizon. Black holes have a temperature black body March 7, 2006 Astronomy 2010 39 Stephen Hawking Black holes slowly "leak" particles – Hawking radiation Stephen W. Hawking (b1942) quantum mechanics near the event horizon of a black hole. Each particle carries off a little of the black hole's mass The smaller the mass of the black hole, the faster it leaks. Hawking radiation is equivalent to black body radiation. Evaporating Black Holes Black Holes evaporate slowly by emitting “Hawking radiation” Black Holes will eventually vanish The smaller the mass, the faster the evaporation Questions Remain about Black Holes: Is the information that falls into a Black Hole lost forever? What is inside a black hole? Can wormholes be produced to travel in time and/or space? March 7, 2006 Astronomy 2010 41 Super Massive Black Holes Observation of so-called active galaxies provides strong evidence for the existence of super massive black holes which provide a simple explanation for the extremely energetic nuclei. See Chapter 26. March 7, 2006 Astronomy 2010 49 Discussion Question Discuss the following question with a classmate then write down your short answer: What would happen to the Earth’s orbit if the Sun were suddenly replaced by a black hole with the same mass as the Sun? Of course the Earth would become dark and cold. I want you to discuss what would happen to the Earth’s orbit. March 7, 2006 Astronomy 2010 50 Hollywood and Reality Black holes are portrayed as cosmic vacuum cleaners in TV and films, sucking up everything around them. Black holes are dangerous only if something gets too close to them. Because all of their mass is compressed to a point, it is possible to get very close where the gravity gets very large. Objects far enough away will not sense anything unusual. If the Sun were replaced by a black hole of the same mass, the orbits of the planets would remain unchanged It would however be darker and colder. March 7, 2006 Astronomy 2010 51