Download Black holes

Black Holes
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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
For photons emitted at event horizon, gravitational redshift is
infinite. The observed frequency is zero, i.e. the photons are
never observed.
RS
2GM
   1 

1

2
Rc
R
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?
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
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.
2.
3.
4.
blue light
blue light at first, then turning red
blue light, then red, then nothing
nothing
Black holes evaporate
Seeing Black Holes
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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 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)
Luminosity
• Gravitational energy is converted to kinetic
energy as particles fall towards BH
• Efficiency of generators:
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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 

LEdd  30,000L 
 M 
Black holes shine brightest in X-rays
Why?
Luminosity of a ‘Black Body’ Radiator
For the spherical object, the total power radiated
= the total luminosity is:
L=
4
2
4R T
T = temperature
 = Stephan-Boltzman constant
= 5.6710-8 W/m2 ·K4
R = radius
Luminosity Law
LA  R A 

 
LB  RB 
2
 TA 
 
 TB 
4
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.
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
TA  R A 
  
TB  RB 
1 / 2
1/ 4
 LA 
 
 LB 
TA
1 / 2
1/ 4
2
30,000  6000

1 1 / 200,000
TB
TA = 6000  5700 K = 30,000,000 K
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?