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 = 3X10 8 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 d 0, the time from laser firing to detection can be found  velocity = distance /time t 0 = 2d 0 /v  This is for a clock at rest d0d0

Moving Clock   Someone standing outside the train would see the mirror and detector moving   Since the moving laser beam has farther to travel (d > d 0 )   so the time seen outside the train is  Compared to a clock at rest t 0 = 2d 0 /c t > t 0 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 = ½mv 2 ), 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=3X10 8 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: R S = (2GM/c 2 )   This is the definition of a black hole

Tidal Force  F = GMm/r 2   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 M sun   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

Cygnus X-1 Vega Altair Deneb

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  Observing List #2 due Monday  Test 2 on Wednesday