Black Holes

Astronomy 315Professor Lee

CarknerLecture 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/ct > 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

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 23.1-23.7 Observing List #2 due Monday Test 2 on Wednesday