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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/cm 3. Sirius B (white dwarf). Sirius.

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Incredible

Shrinking

Stars

The End States of Stars



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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


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Sirius B (white dwarf)

Sirius

Ultimate fate:

continuous cooling . . .



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~ 10 km

Neutron Star: Final state of stellar core in some

supernova explosions.

  • Composition: neutrons

  • Mass: 1 – 2 M

Density ~ 108 ton/cm3


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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


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1 meter

Splat!

2. Marshmallows become dangerously explosive

Energy released equivalent to

detonating ~ 10 tons of TNT.

Drop marshmallow on

neutron star.


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* Neutron stars should be rapidly spinning . . .

Neutron Star

(small diameter,

rapid spin)

Core, before collapse

(large diameter, slow spin)


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Slow

Fast



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very

high

small

tiny

Finding neutron stars

1. They should be hot: T  106 K

L = surface area  T4


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* Rotating magnetic

field creates electric

field.

* Electric field drives

electrons along lines

of magnetic field.

* Electrons radiate –

mainly where magnetic field strong.




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Crab pulses

X-ray

Period =

33 milliseconds

(~ 30 rotations per

second)

Visual

Radio


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Vela Pulsar: 11.2 pulses/second

PSR 1937+21: 640 pulses/second

Pulsar Sounds



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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!


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What is Gravity?

Einstein

Newton

Equivalence Principle


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Space is curved – Gravity is a result of geometry!

[2-dimensional analog]


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Light is affected by gravity . . .

Light from distant star follows

curvature of space near Sun.


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Gravity causes time to slow down . . .

Observes

ground-floor

clock to be

slow.

Photon loses energy

as it moves upward –

gravitational redshift.


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Top of tower

Bottom of tower

  • e.g.,

  • 2 cycles/sec

  • (a) 1 cycle/sec

  • more ticks of clock

  • (a) fewer ticks of clock


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


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Singularity: zero volume,

infinite density!

Schwarzchild Radius (RS)

Event Horizon

Schwarzchild Black Hole

At RS, escape velocity =

speed of light


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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


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Escape velocity

(mi/sec)

7

300

3000

100,000

From surface of:

Earth

Sun

white dwarf

neutron star


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Tide

B. H.

Falling into a Black Hole

1. Stretching

Less gravity

2. Squeezing

More gravity

Result: Heating


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B. H.

As seen by outside observer,

time runs slower & slower

as person approaches B.H.


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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


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