Transcript Black Holes
Black Holes Astronomy 315 Professor Lee Carkner Lecture 16 Relativity Relativity asks the question: How do physical phenomena depend on the observer’s frame of reference? Most effects are hard to see except at high speeds or near large masses n.b. The Theory of Relativity does not mean, “Everything is relative.” Special Relativity Two postulates The speed of light is the same for everyone c = 3X108 m/s This is the fastest anything can travel Laser Clock The beam then bounces back down into a detector mounted next to the laser on the floor If the distance between the floor and the ceiling is d0, the time from laser firing to detection can be found velocity = distance /time t0 = 2d0/v This is for a clock at rest d0 Moving Clock Someone standing outside the train would see the mirror and detector moving Since the moving laser beam has farther to travel (d > d0) so the time seen outside the train is Compared to a clock at rest t0 = 2d0/c t > t0 d Time Dilation Each tick takes longer for the moving clock Less time passes on the train Called time dilation Time dilation is very small unless you are moving very fast Twin Paradox Imagine a pair of twins One making a round trip to alpha Centauri on a spaceship traveling 0.99c Twin on ship would feel 1 year pass Earth twin is now 5 years older! General Relativity Key idea: Mass and energy are the same thing This means that light near a large mass is affected the same way a solid object is Curved Spacetime The star would pull on the ball causing the path to bend Spacetime is curved near a mass Mass causes light to bend Graviatational Red Shift The ball slows down and loses energy The frequency of light changes as it moves near a mass Gravitational Time Dilation The curved spacetime near a mass affects light similar to the way our moving train did More time passes near a mass If you jump into a black hole, to people watching you it would take a long time for you to get anywhere Black Hole Mass: Size: singularity Density: Supported by: unsupported Progenitor: Example: high mass X-ray binaries Limits of Neutron Degeneracy There is no force that can stop the collapse, so the core contracts to an infinitely small point called a singularity The object is called a black hole Escape Velocity Must have the escape velocity Velocity is related to kinetic energy (KE = ½mv2) , so the object must have more kinetic energy than the gravitational energy that holds it back High mass, small radius means you need a high velocity to escape Escaping a Black Hole Thus, light has to fight gravity to escape from a mass If the escape velocity of an object is greater than the speed of light (c=3X108 m/s), the light cannot escape and the object is a black hole If light can’t escape, nothing can Light is gravitationally red shifted to zero Structure of a Black Hole Once you get closer to a black hole than the event horizon, you can never get back out The radius of the event horizon is called the Schwarzschild radius: RS = (2GM/c2) This is the definition of a black hole Tidal Force F = GMm/r2 The smaller r is, the greater the force Imagine you are falling feet first into a black hole If the difference is large enough, you will be pulled apart Nothing can get to the event horizon intact X-ray Binary Material from the normal star gets pulled onto the compact object Material falling onto a compact object gets very hot and produces high energy radiation Why? Tidal forces and friction heat the disk X-ray binary Finding Black Holes By getting the Doppler shifts for the stars we can find the orbital parameters Even though the black holes are invisible, they manifest themselves by their strong gravitational fields Cygnus X-1 Matches up with a bright O star with an unseen companion Mass of companion about 9 Msun X-ray emission varies rapidly, implying emitting region is very small Produces a pair of jets out through the poles One of the best black hole candidates Deneb Vega Cygnus X-1 Altair X-ray Binaries Compact objects in binary systems can exhibit many properties due to mass transfer from the normal star to the compact object: Cataclysimic variable: X-ray Burster: irregular outbursts of fusion from hydrogen building up on a neutron star High mass X-ray Binary: Next Time Read Chapter 23.1-23.7 Observing List #2 due Monday Test 2 on Wednesday