Download Lecture 18

ASTR 1200
Announcements
Problem sets 5 and 6 due this week.
Third exam November 20
(next week)
Website
http://casa.colorado.edu/~wcash/APS1200/APS1200.html
A Newtonian Black Hole
Energy Falling To Surface
Kinetic Energy
GMm 1 2
 mv
R
2
OR
2GM
R 2
c
if v=c
Schwarzschild Radius
2GM
R 2
c
Two errors cancel.
This is the radius of the “Event Horizon”
The event horizon is a true singularity in space-time.
It is a place where time and space cease to exist.
Curved Space
Rubber Sheet Analogy
Properties - Basic
1. Mass (Schwarzschild Black Hole)
2. Electric Charge (doesn’t happen)
3. Angular Momentum (Kerr Black Hole)
No “Surface” Features
No Magnetic Fields
No Pulsing
“No Hair”
Time Dilation
t 
t
RS
1
r
As r approaches Rs t gets longer and longer.
When r reaches the event horizon, time stops.
We know how to make a time machine with a forward switch only!
Just fly to a black hole and orbit above the surface.
But you can fall in really fast as viewed from outside.
http://www.space.com/27701-interstellar-movie-science-black-holes.html
Hawking Radiation
The vacuum makes pairs of
electrons and positrons that pop
into existence and then annihilate
without any net effect.
Above a black hole, one can get
sucked in. The other annihilates
above the surface to cause
radiation.
Since its close to the surface, the
light gets redshifted escaping,
but it carries energy with it!
Temperature
hc 3
108
T

K
2
16 kGM
M
Hawking derived that the temperature of a black hole is thermal.
Energy for the radiation comes from the mass of the hole.
The black hole shrinks with time.
  M x7 x10 years
3
67
That’s a really long time unless the black hole is tiny.
A 1kg black hole would last only 10-16s.
Artist’s impression of Cyg X-1 (NASA)
6M0 BH orbiting an O9 star.
2000pc away in Cygnus
The Milky Way
Stars Beyond Counting
100 Billion Stars
Orbital Period
R3
(10000 x3x1016 )3
15
8
P  2
 6.28 x

3
x
10
s

10
years
11
12
30
GM
6.7 x10 x10 x 2 x10
Takes the Sun 200million years to orbit Milky Way.
Sun is 4600 million years old.
The Sun is 23 Galactic Years Old.
A Spiral Galaxy Like Milky Way
Milky Way – Edge-On
The Milky Way
Formation of Milky Way
• Analogous to formation of the Sun
• Start with big blob of gas
• Let it collapse
Disk Stability Again
Globular Clusters
Gas has friction and collapses to disk.
Stars have huge momentum with small cross section.
When a star forms it remains frozen in its initial orbit forever.
Little knots of high density
are first to form into stars.
These are the globular clusters.
They each contain a million stars.
There are about 100 orbiting the
Milky Way.
The Globular Cluster – M80