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Black Holes and Close Binary Star Systems

Black Holes and Close Binary Star Systems. Black Holes (continued…) Gravity in a close binary system Accretion Disks White Dwarfs in semi-detached binaries Type IA Supernovae. Final Exam. Take-home will be handed out in class on Tuesday April 23.

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Black Holes and Close Binary Star Systems

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  1. Black Holes and Close Binary Star Systems • Black Holes (continued…) • Gravity in a close binary system • Accretion Disks • White Dwarfs in semi-detached binaries • Type IA Supernovae

  2. Final Exam • Take-home will be handed out in class on Tuesday April 23. • To be submitted on Wednesday May 1 at 10:30AM in 210 JFB (regularly schedule final exam meeting time). • Comprehensive , Slight emphasis on material in chapters 13-18. • A study “guide/review” is on the website as Lecture 27.

  3. The Schwarzschild metric • Consider a sphere of radius R and mass M placed at the origin of the coordinate system. The coordinate r does NOT represent distance from the origin. A concentric sphere whose surface is at r would have a surface area 4r2. • A Flamm paraboloid helps “visualize” this curvature. Remember that “you” would be contained in the curved spacetime and you cannot directly “view” the curvature into the 4th dimension…. • Proper distance along a radial line • Proper Time at radial coordinate r • http://en.wikipedia.org/wiki/Schwarzschild_metric • http://casa.colorado.edu/~ajsh/schwp.html • http://people.hofstra.edu/Stefan_Waner/diff_geom/Sec15.html http://channel.nationalgeographic.com/episode/journey-to-the-edge-of-the-universe-3023/Overview#tab-interactive

  4. Black Holes • In 1783 John Mitchell pondered that the escape velocity from the surface of a star 500 times larger than the sun with the same average density would equal the speed of light. • Light would not be able to escape from such a star!!!! • Naïve solution of Newtonian escape velocity equation for c gives a radius of R=2GM/c2 for a star whose escape velocity equals the speed of light. • R=2.95(M/M) km….kinda small!!! In 1939 J. Robert Oppenheimer and Hartland Snyder described the ultimate gravitational collapse of a massive star that has exhausted its sources of nuclear fusion. They pondered what happened to the cores of stars whose mass exceeded the limit of neutron stars.. In 1967 the term “black hole” was coined By John Archibald Wheeler

  5. The Schwarzschild Radius • Consider the Schwarzschild metric • When the radial coordinate of the star’s surface has collapsed to RS=2GM/c2 the square roots in the metric go to zero. RS is known as the Schwarzschild Radius. • At r=RS the behavior of space and time is “remarkable”…. • The proper time measured by a clock here is d=0. • Time has slowed to a complete stop! As measured from a vantage point far away. From this viewpoint nothing ever happens at the Scwarzschild radius • Does this mean that even light is frozen in time??? • The speed of light by an observer suspended above the star must always be c. But from far away we can determine that light is delayed as it moves through curved spacetime… • The apparent speed of light, the rate at which the spatial coordinates of a photon change, is called the coordinate speed of light. For light ds=0. • For dd=0, we have • In flat spacetime dr/dt~c, however at r=RS dr/dt=0 • Light does appear frozen in time at the Schwarzschild radius!!!

  6. The Schwarzschild Radiusand Event Horizon • A non-rotating black hole would have a particularly simple structure!!! • At the center is a Singularity. A point of zero volume and infinite density where all of the black hole’s mass is located. • Spacetime is infinitely curved at the singularity. • Cloaking the central singularity is the event horizon, so the singularity can never be observed • “Law of Cosmic Censorship” that forbids a naked singularity from appearing unclothed… • A star that has collapsed within the Schwarzschild radius is called a Black Hole. • It is enclosed by the Event Horizon located at r=RS. • The region inside of the event horizon is forever hidden from view of the rest of the universe!!! • However the properties of the Black Hole may be calculated. • Its gravitational effects are still felt… • Note that the event horizon is a “mathematical surface” and does not necessarily coincide with any physical surface

  7. A Trip into a Black Hole • What happens to an object (indestructible person) that free falls into a black hole? • She shines a monochratic flashlight back at us once per second. • These light signals arrive farther and farther apart for several reasons… • Subsequent signals must travel farther as she accelerates • Her proper time is running slower at ther location due to gravitational time dilation and her motion special relativity time dilation • The coordinate speed of light become slower as she approaches the black hole • The frequency of light becomes increasingly redshifted • Due to her acceleration away from us • And gravitational redshift • The light is redshifted and dimmed to invisibility • Imagine an attempt to investigate a black hole from a safe distance and reflecting a radio photon (or any photon) from an object at the event horizon. • Travel time between radial coordinates r1<r2. • If r1=RS…t=infinity • Any object falling to the horizon will appear frozen there (in the infinite future). Even the collapsing star.

  8. A Trip into a Black Hole

  9. A Trip into a Black Hole

  10. The Discomforts Associated with a Trip into a Black Hole • Differential Tidal Forces… • Rip and Squeeze… • Ripped apart several hundred kilometers from the Black Hole • In just 2 milliseconds she would fall the final few hundred kilometers to the event horizon …and crosses it!!! • Her proper time continues normally and she encounters no frozen stellar surface since it has fallen through long ago. • However once inside the event horizon….. • (ds)2=(c dt)2(1-Rs/r)<0 • Spacelike interval • Drawn to the singularity within 6.6 x 10-5 s

  11. Mass Range of Black Holes • Stellar-Mass Black holes: 3-15 M may form directly or indirectly as a consequence of the core collapse of a sufficiently massive supergiant star. Could also form when a neutron star stips away enough mass from a companion. • Intermediate Mass Black Holes: may exist in a range of 100 to in excess of 1000 M . Ultraluminous X-ray Sources. • Supermassive Black Holes: are known to exist at the center of many (probably most) galaxies. Range in mass from 105-109M. The milky way has one that is about 3.7 x 106 M. • Primordial Black Holes: from 10-8kg to 105M. The only criterion for a black hole is that its entire mass must lie within the Schwarzschild radius. • Schwarzschild radius of proton: RS=2Gmp/c2=2.47x10-54m • Schwarzschild radius of electron: RS=2Gmp/c2=1.34x10-57m

  12. Black Holes Have No Hair! • Completely described by • Mass • Angular Momentum • Electric Charge • Upper limit to black hole’s angular momentum • Lmax=GM2/c

  13. Kerr Metric

  14. Kerr-Newman Metric

  15. Spacetime Frame Dragging • Rotation distorts the central singularity from a point to a flat ring. • The event horizon assumes the shape of an ellipsoid. • As a massive object spins, it induces a rotation in the surrounding spacetime Spacetime Frame Dragging • Ergosphere: a nonspherical region outside the event horizon where any particle must move in the same direction that the black hole rotates. Spacetime within the ergosphere is so rapidly rotating that a particle would have to move more rapidly than c to remain at the same angular coordinate. • Even earth generates frame dragging..!!!

  16. Tunnels in Spacetime: “Wormholes” • There are some vacuum solutions to Einstein’s equations that admit tunnels in space-time. • Also the realm of science-fiction….

  17. Stellar-Mass Black Hole Candidates • Evidence for Stellar Mass Black holes • X-ray binaries with massive compact objects of M>3 M • Cygnus X-1 • LMC X-3 • V404 Cygni

  18. Hawking Radiation

  19. Hawking Radiation • Hawking predicted that black holes can radiate away energy - evaporate by a process where particle anti-particle pairs appear as a fluctuation out of the vacuum near an event horizon. Normally the pair would annihilate and disappear. However near the horizon one of the pair can disappear within the event horizon alllowing the other to escape… Slow Evaporation!!!! The End….

  20. Super Massive Black Holes http://en.wikipedia.org/wiki/Supermassive_black_hole http://en.wikipedia.org/wiki/File:A_Black_Hole%E2%80%99s_Dinner_is_Fast_Approaching_-_Part_2.ogv

  21. Super Massive Black Holes

  22. Super Massive Black Holes

  23. Gravity in a close binary system

  24. Lagrangian Points and Equipotential Surfaces • Lagrange points: no net force on a test mass

  25. Classes of Binary SystemsRoche Lobes • Tear drop shaped region of space of the equipotential surface

  26. Mass Transfer Rates

  27. Mass Transfer Rates

  28. Energy Release through “falling”…

  29. Energy Release through “falling”…

  30. Accretion Disks • What is the temperature of Disk? • What is its Luminosity?

  31. Accretion Disks

  32. Accretion Disks

  33. Accretion Disks

  34. Accretion Disks

  35. Evolution of a Binary System

  36. Types of Interacting Binaries

  37. Types of Interacting Binaries

  38. Types of Interacting Binaries

  39. White Dwarfs in Semidetached Binaries Cataslysmic Variables Dwarf or Classical Nova: Survives its Energy Release Supernova Type IA White Dwarf is destroyed…

  40. Dwarf Novae

  41. Dwarf Novae

  42. Dwarf Novae

  43. Type IA SupernovaeObservations “Remarkably” consistent in their light output Standard Candle…

  44. Type IA SupernovaeModels • Double degenerate: two white dwarfs • Single Degenerate: One white dwarf • Complete destruction of white dwarf • Accumulation of helium deposit on surface triggers a helium flash. Shock wave triggering ignition of Carbon and Oxygen ignition….

  45. Type IA SupernovaeModels

  46. Type IA SupernovaeApplications • Map the Universe!!! • Determine that expansion of Universe is accelerating

  47. Neutron Stars and Black Holes in Binaries • X-ray systems !!!

  48. Binary X-ray Pulsars

  49. Alfven Radius and infall channeling towards poles

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