Black Holes

1
Black Holes

• Astronomy 315
• Professor Lee Carkner
• Lecture 16

2
Relativity

• Relativity asks the question
• How do physical phenomena depend on the
  observers 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.

3
Special Relativity

• Two postulates
• The speed of light is the same for everyone
• c 3X108 m/s
• This is the fastest anything can travel

4
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
5
Moving Clock

• Someone standing outside the train would see the
  mirror and detector moving
• Since the moving laser beam has farther to travel
  (d gt d0)
• so the time seen outside the train is
• Compared to a clock at rest
• t0 2d0/c
• t gt t0

d
6
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

7
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!

8
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

9
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

10
Graviatational Red Shift

• The ball slows down and loses energy
• The frequency of light changes as it moves near a
  mass

11
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

12
Black Hole

• Mass
• Size singularity
• Density
• Supported by unsupported
• Progenitor
• Example high mass X-ray binaries

13
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

14
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

15
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 (c3X108 m/s), the light
  cannot escape and the object is a black hole
• If light cant escape, nothing can
• Light is gravitationally red shifted to zero

16
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

17
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

18
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

19
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

20
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

21
Deneb
Vega
Cygnus X-1
Altair
22
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

23
Next Time

• Read Chapter 23.1-23.7
• Observing List 2 due Monday
• Test 2 on Wednesday