1. Black Holes Escape velocity Event horizon Black hole parameters
Falling into a black hole

2. Massive bodies and escape speed

3. Gravity bends the path of light

5. 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

6. Event horizon

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

8. 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?

9. Three parameters completely describe the structure of a 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
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

10. 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

11. As you fall into to a black hole, you shine a blue flashlight at a friend exterior to the hole, she sees
blue light
blue light at first, then turning red
blue light, then red, then nothing
nothing

12. Black holes evaporate

13. Seeing Black Holes Observed properties of black holes
Gravitational energy
Rotating black holes
Eddington luminosity
Accretion disks
Jets

14. Accretion disk

15. 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.

16. Seeing black holes

17. Observed properties of black holes
Luminosity
Orientation
Jets

18. Gravitational energy
Black holes generate energy from matter falling into them.

20. Rotating black holes For 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)

21. Luminosity
Gravitational energy is converted to kinetic energy as particles fall towards BH
Efficiency of generators:
Chemical burning < %
Nuclear burning < 1%
Non-rotating black hole = 6%
Rotating black hole = 42%

22. Eddington Luminosity
Limit on the brightness of a black hole

23. Eddington Luminosity

24. Black holes shine brightest in X-rays
Why?

25. Luminosity of a ‘Black Body’ Radiator
For the spherical object, the total power radiated = the total luminosity is:
L = 4R2T4
T = temperature
 = Stephan-Boltzman constant
= 5.6710-8 W/m2 ·K4
R = radius

26. Luminosity Law 2 1
If star A is 2 times as hot as star B, and the same radius, then it will be 24 = 16 times as luminous.

27. 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

28. Black holes shine brightest in X-rays2 1
TA = 6000  5700 K = 30,000,000 K

29. A object’s color depends on its surface temperature
Wavelength of peak radiation:
Wien Law max = 2.9 x 106 / T(K) [nm]

30. Electromagnetic spectrum
Black holes are so hot that they mainly produce X-rays

31. 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?

32. 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?