Incredible Shrinking Stars The End States of Stars

White Dwarfs

Earth 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 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/cm 3 ~ 10 km

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

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 T 4 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) = 3 M 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.

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