Black Holes

• Escape velocity

• Event horizon

• Black hole parameters

• Falling into a black hole

Massive bodies and escape speed

Gravity bends the path of light

A nonrotating black hole has only a “center” and a “surface”

• The black hole is surrounded by an event horizon which is the sphere from which light cannot escape

• The distance between the black hole and its event horizon is the Schwarzschild radius (RSch= 2GM/c2)

• The center of the black hole is a point of infinite density and zero volume, called a singularity

Event horizon

Gravitational Redshift

R

R

Rc

GM S 12

12

For photons emitted at event horizon, gravitational redshift is infinite. The observed frequency is zero, i.e. the photons are never observed.

Event Horizon

• How large is the event horizon for a one solar mass black hole?

• RS = 2GM/c2 = 2.95 km

• How about a ten solar mass black hole?

• Mass– As measured by the

black hole’s effect on orbiting bodies, such as another star

• Total electric charge– As measured by the

strength of the electric force

• Spin = angular momentum– How fast the black hole

is spinning

Three parameters completely describe the structure of a black hole

Most properties of matter vanish when matter enters a black hole, such as chemical composition, texture, color, shape, size, distinctions between protons and electrons, etc

Rotating black holes

• A rotating black hole (one with angular momentum) has an ergosphere around the outside of the event horizon

• In the ergosphere, space and time themselves are dragged along with the rotation of the black hole

As you fall into to a black hole, you shine a blue flashlight at a friend exterior to the

hole, she sees

1. blue light

2. blue light at first, then turning red

3. blue light, then red, then nothing

4. nothing

Black holes evaporate

Seeing Black Holes

• Observed properties of black holes

• Gravitational energy

• Rotating black holes

• Eddington luminosity

• Accretion disks

• Jets

Accretion disk

Accretion disks

• Disks form because infalling matter has angular momentum.

• Accretion leads to release of gravitational energy.

• Inner regions of disks rotate very rapidly – near the speed of light.

• The luminosity of a black hole is limited by its mass.

Seeing black holes

Observed properties of black holes

Luminosity

Orientation

Jets

Gravitational energy

Black holes generate energy from matter falling into them.

Rotating black holesFor non-rotating black holes:

- event horizon is at the Schwarzschild radius

- inner edge of the disk is at 3 Schwarzschild radii

For maximally rotating black holes:

- event horizon is at ½ Schwarzschild radius

- inner edge of the disk is at ½ Schwarzschild radius

Schwarzschild radius = 3 km (M/MSun)

Luminosity• Gravitational energy is converted to kinetic

energy as particles fall towards BH

• Efficiency of generators:– Chemical burning < 0.000001%– Nuclear burning < 1%– Non-rotating black hole = 6%– Rotating black hole = 42%

Eddington Luminosity

Limit on the brightness of a black hole

Eddington Luminosity

M

MLL 000,30Edd

Black holes shine brightest in X-rays

Why?

For the spherical object, the total power radiated = the total luminosity is:

L = 4R2T4

T = temperature = Stephan-Boltzman constant = 5.6710-8 W/m2 ·K4

R = radius

Luminosity of a ‘Black Body’ Radiator

Luminosity Law

1 2

If star A is 2 times as hot as star B, and the same radius, then it will be 24 = 16 times as luminous.

42

B

A

B

A

B

A

T

T

R

R

L

L

Black holes shine brightest in X-rays

• Take BH of one solar mass

• Event horizon is 3 km or 1/200,000 of Sun’s radius

• Luminosity can be 30,000 time the Sun’s luminosity

Black holes shine brightest in X-rays

1 2

TA = 6000 5700 K = 30,000,000 K

4/12/1

B

A

B

A

B

A

L

L

R

R

T

T

6000000,30000,200/1 4/12/1

B

A

T

T

A object’s color depends on its surface temperature

• Wavelength of peak radiation:Wien Law max = 2.9 x 106 / T(K) [nm]

Electromagnetic spectrum

Black holes are so hot that they mainly produce X-rays

Review Questions• What are the two facts which caused Einstein to

invent the special theory of relativity?

• What are two key consequences of special relativity for how we observe moving objects?

• What effect does gravity have on spacetime?

• How do astronomers search for black holes?

• How are black holes actually simpler than any other objects in astronomy?

Review Questions

• What are fundamental versus observed properties of black holes?

• What is the efficiency of a BH for conversion of matter to energy?

• What is the maximum luminosity for a BH of a given mass?

• At what wavelength range do stellar mass black holes produce most of their radiation?