Transcript Incredible10 - courses.psu.edu

Incredible
Shrinking
Stars
The End States of Stars
White Dwarfs
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
Sirius B (white dwarf)
Sirius
Ultimate fate:
continuous cooling . . .
Neutron Stars
Neutron Star: Final state of stellar core in some
supernova explosions.
• Composition: neutrons
• Mass: 1 – 2 M
Density ~ 108 ton/cm3
~ 10 km
Living on a Neutron Star
1. Your weight is enormous
GmM
W 
2
R
m = your mass
M = neutron star mass
R = neutrons star radius
150 lbs on Earth  ~ 1013 lbs on a neutron star
2. Marshmallows become dangerously explosive
Energy released equivalent to
detonating ~ 10 tons of TNT.
1 meter
Drop marshmallow on
neutron star.
Splat!
* Neutron stars should be rapidly spinning . . .
Neutron Star
(small diameter,
rapid spin)
Core, before collapse
(large diameter, slow spin)
Slow
Fast
* Neutron stars should have strong magnetic fields . . .
Field lines become concentrated.
Finding neutron stars
1. They should be hot: T  106 K
L =
small
surface area
tiny

T4
very
high
2. 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.
Rotating neutron star: Pulsar
Crab Nebula Pulsar
Crab pulses
X-ray
Visual
Radio
Period =
33 milliseconds
(~ 30 rotations per
second)
Pulsar Sounds
Vela Pulsar: 11.2 pulses/second
PSR 1937+21: 640 pulses/second
Black Holes
Mass Limits
* White Dwarf: M  1.4 M
* Neutron Star: M  2 - 3 M
If stellar core should become iron with
mass  2 - 3 M . . .
Black Hole results!
What is Gravity?
Newton
Einstein
Equivalence Principle
Space is curved – Gravity is a result of geometry!
[2-dimensional analog]
Light is affected by gravity . . .
Light from distant star follows
curvature of space near Sun.
Gravity causes time to slow down . . .
Observes
ground-floor
clock to be
slow.
Photon loses energy
as it moves upward –
gravitational redshift.
Top of tower
Bottom of tower
e.g.,
(b) 2 cycles/sec
(a) 1 cycle/sec
(b) more ticks of clock
(a) fewer ticks of clock
Black hole: infinitely deep ‘puncture’ in space-time.
Schwarzchild Black Hole
Singularity: zero volume,
infinite density!
Schwarzchild Radius (RS)
Event Horizon
At RS, escape velocity =
speed of light
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
From surface of:
Earth
Sun
Escape velocity
(mi/sec)
7
300
white dwarf
3000
neutron star
100,000
Falling into a Black Hole
1. Stretching
Less gravity
2. Squeezing
Tide
More gravity
Result: Heating
B. H.
As seen by outside observer,
time runs slower & slower
as person approaches B.H.
B. H.
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