1. Incredible
Shrinking
Stars
The End States of Stars

2. White Dwarfs

3. Earth
White Dwarf
White Dwarf Facts
* Composition: carbon, oxygen
* Mass limit < 1.4 M (Chandrasekhar Limit)
* Avg mass  0.5 M
Mass, radii  density  1 ton/cm3

4. Sirius B (white dwarf)
Sirius
Ultimate fate:
continuous cooling . . .

5. Neutron Stars

6. Neutron Star: Final state of stellar core in some
supernova explosions.
Composition: neutrons
Mass: 1 – 2 M
Density ~ 108 ton/cm3
~ 10 km

7. Living on a Neutron Star
1. Your weight is enormous
m = your mass
M = neutron star mass
R = neutrons star radius
150 lbs on Earth  ~ 1013 lbs on a neutron star

8. 2. Marshmallows become dangerously explosive
Energy released equivalent to
detonating ~ 10 tons of TNT.
1 meter
Splat!
Drop marshmallow on
neutron star.

9. (large diameter, slow spin)
* Neutron stars should be rapidly spinning . . .
Neutron Star
(small diameter,
rapid spin)
Core, before collapse
(large diameter, slow spin)

10. Slow
Fast

11. * Neutron stars should have strong magnetic fields . . .
Field lines become concentrated.

12. Finding neutron stars
1. They should be hot: T  106 K
L = surface area  T4
small
tiny
very
high

14. Conversion of energy of rotation into
em radiation
* Rotating magnetic
field creates electric
field.
* Electric field drives
electrons along lines
of magnetic field.
* Electrons radiate –
mainly where magnetic field strong.

15. Rotating neutron star: Pulsar

16. Crab Nebula Pulsar

17. Crab pulses
X-ray
Period =
33 milliseconds
(~ 30 rotations per
second)
Visual
Radio

18. Pulsar Sounds
Vela Pulsar: pulses/second
PSR : 640 pulses/second

19. Black Holes

20. Mass Limits
* White Dwarf: M  1.4 M
* Neutron Star: M  M
If stellar core should become iron with
mass  M . . .
Black Hole results!

21. What is Gravity?
Newton
Einstein
Equivalence Principle

22. Space is curved – Gravity is a result of geometry!
[2-dimensional analog]

23. Light is affected by gravity . . .
Light from distant star follows
curvature of space near Sun.

24. Gravity causes time to slow down . . .
Observes
ground-floor
clock to be
slow.
Photon loses energy
as it moves upward –
gravitational redshift.

25. Top of tower
Bottom of tower
e.g.,
2 cycles/sec
(a) 1 cycle/sec
more ticks of clock
(a) fewer ticks of clock

26. Black hole: infinitely deep ‘puncture’ in space-time.

27. Schwarzchild Black Hole
Singularity: zero volume,
infinite density!
Schwarzchild Radius (RS)
At RS, escape velocity =
speed of light
Event Horizon

28. RS (km) = 3M M = mass in units of Sun’s mass
e.g., M = 1 M  RS = 3  1 = 3 km
6 km
The Sun as a black hole

29. Escape velocity
(mi/sec) 7
300
3000
100,000
From surface of:
Earth
Sun
white dwarf
neutron star

30. Falling into a Black Hole
1. Stretching
Less gravity
2. Squeezing
Tide
More gravity
Result: Heating
B. H.

31. As seen by outside observer,
time runs slower & slower
as person approaches B.H.
B. H.

32. * By their effects on other objects.
Detecting Black Holes
* By their effects on other objects.
Strong x-ray source
Only one star detected
Motion of that star  unseen star is very
massive