The Stellar Graveyard Key Ideas:

White Dwarfs:

• Remnant of a low-mass star (less than 4 solar masses)
• Supported by Electron Degeneracy
• Maximum mass in this state of matter is 1.4 solar masses

Neutron Stars:

• Remnants of a massive star (post supernova core)
• Supported by Neutron Degeneracy
• Maximum mass is 3 solar masses.
• Very rapid rotation.

Black holes

• If the mass of the remnant core is greater than 3 solar masses, there is no known source against further collapse.

  So, what happens to the cores of dead stars? They continue to collapse until either:

  • new pressure law takes hold to halt further collapse & they settle into a new equilibrium

  • If too massive they collapse to zero radius and become a Black Hole

Degenerate Gas Law

At high density, a new gas law takes over:

• Pack many electrons into a tiny volume
• These electrons fill all low-energy states
• Only high-energy = high-pressure states left

Result is a "Degenerate Gas":

• Pressure is independent of Temperature.
• Compression does not lead to heating.

White dwarfs are supported by electron degeneracy which occurs at a density of matter that is 10⁷ grams per cubic centimeter. (10 tons per cubic centimeter).

If the mass of the core exceeds 1.4 solar masses, electron degeneracy breaks and the core would collapse until its supported by neutron degeneracy which occurs at nuclear densities of 10¹⁴ grams per cubic centimeter (100 million tons per cubic centimeter).

If the mass of the core exceeds 3 solar masses, then even neutron degeneracy breaks and the core collapses down to zero radius and infinite density opps ...

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White Dwarfs

These are the remnant cores of stars with M_* < 4 M_sun.

They are held up against gravity by Electron Degeneracy Pressure.

Properties:

• Mass < 1.4 M_sun
• Radius ~ R_earth (<0.02 R_sun)
• Density ~ 10^6-7 g/cc
• No nuclear fusion or gravitational contraction

Evolution of White Dwarfs

White dwarfs shine by leftover heat.

• No energy source (no fusion, nothing)
• Cools off and fades away slowly.

Ultimate State: A "Black Dwarf":

• Old, cold white dwarf
• Takes ~10 Tyr to cool off
• Galaxy is not old enough for there to be any Black Dwarfs yet.

Note: Be careful not to confuse Black Dwarfs (old, cold remnant cores of low-mass stars) with "Black Holes" (the extremely collapsed cores of very massive stars).

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Neutron Stars

Remnant cores of massive stars:

• 4 < M* < 18 M_sun (??)
• Leftover core of a core-bounce supernova

Held up by Neutron Degeneracy Pressure:

• Mass ~1.2 - 2 M_sun (???)
• Radius ~10 km
• Density ~10¹⁴ g/cc

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Structure of a Neutron Star

At densities > 2x10¹⁴ g/cc:

• nuclei melt into a sea of subatomic particles.
• protons & electrons combine into neutrons.

Surface is cooler, forming a solid crystalline crust!

Inside is exotic matter: superfluid neutrons, superconducting protons, and stranger subatomic particle matter:

And now, all about black holes.

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Key Ideas:

Black Holes are totally collapsed objects

• gravity so strong not even light can escape
• predicted by General Relativity

Schwarzschild Radius & Event Horizon

Find them by their Gravity

• X-ray Binary Stars

Black Hole Evaporation

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Gravity's Final Victory

A star more massive than about 18 M_sun would leave behind a cores larger than 2-3 M_sun:

Neutron degeneracy pressure would fail and nothing can stop its gravitational collapse.

Core would collapse into a singularity, and object with

• zero radius
• infinite density

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Black Hole

Close to the singularity:

• Gravity is so strong that nothing, not even light, can escape.
• Infalling matter is shredded by powerful tides and crushed to infinite density.

Becomes a Black Hole:

• "Black" because they neither emit nor reflect light.
• "Hole" because nothing entering can ever escape.

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Einstein's Outrageous Legacy:

Laplace (1795) described "corps obscurs"

• objects with an escape velocity of the speed of light
• used Newtonian Gravity to compute its size

A proper treatment such an extreme gravitational field requires General Relativity:

• Einstein's theory of gravitation (1915)
• First solutions by Karl Schwarzschild (1916)
• Not taken seriously until the 1960s.

This description forms the basis of our modern picture of Black Holes.

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Schwarzschild Radius

Light cannot escape from a Black Hole if it comes from a radius closer than the Schwarzschild Radius, R_S:

Where M = Mass of the Black Hole

A black hole with a mass of 1 M_sun would have a Schwarzschild Radius of R_S=3 km.

Compare this with a typical 0.6 M_sun White Dwarf, which would have a radius of about 1 R_earth (6370km), and a 1.4 M_sun neutron star, which would have a radius of about 10km.

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Event Horizon

R_S defines the "Event Horizon" surrounding the black hole's singularity:

• Events occurring inside R_S are invisible to the outside universe.
• Anything closer to the singularity than R_S can never leave the black hole
• The Event Horizon hides the singularity from the outside universe.

The Event Horizon marks the "Point of No Return" for objects falling into a Black Hole.

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Gravity around Black Holes

Far away from a black hole:

• Gravity is the same as a star of the same mass.
• If the Sun became a Black Hole, the planets would all orbit the same as before.

Close to a black hole:

• R < 3 R_S, there are no stable orbits - all matter gets sucked in.
• At R = 1.5 R_S, photons would orbit in a circle!

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Journey to a Black Hole: A Thought Experiment

Two observers: Jack & Jill

Jack, in a spacesuit, is falling into a black hole. He is carrying a low-power laser beacon that flashes a beam of blue light once a second.

Jill is orbiting the black hole in a starship at a safe distance away in a stable circular orbit. She watches Jack fall in by monitoring the incoming flashes from his laser beacon.

He Said, She Said...

From Jack's point of view:

• He sees the ship getting further away.
• He flashes his blue laser at Jill once a second by his watch.

From Jill's point of view:

• Each laser flash take longer to arrive than the last
• Each laser flash become redder and fainter than the one before it.

Near the Event Horizon...

Jack Sees:

• His blue laser flash every second by his watch
• The outside world looks oddly distorted (positions of stars have changed since he started).

Jill Sees:

• Jack's laser flashing about once every hour.
• The laser flashes are now shifted to radio wavelengths, and
• the flashes are getting fainter with each flash.

Down the hole...

Jill Sees:

• One last flash from Jack's laser after a long delay (months?)
• The last flash is very faint and at very long radio wavelengths.
• She never sees another flash from Jack...

Jack Sees:

• The universe appear to vanish as he crosses the event horizon
• He gets shredded by strong tides near the singularity and crushed to infinite density.

Moral:

The powerful gravity of a black hole warps space and time around it:

• Time appears to stand still at the event horizon as seen by a distant observer.
• Time flows as it always does as seen by an infalling astronaut.
• Light emerging from near the black hole is Gravitationally Redshifted to longer (red) wavelengths.

Take a Virtual Trip to a Black Hole or Neutron Star. Pictures & movies by relativist Robert Nemiroff at the Michigan Technical University.

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Seeing what can't be seen.

Question:

If no light gets out of a black hole, how can we ever hope to find one?

Answer:

Look for the effects of their gravity on their surroundings.

For example, search for stellar-mass black holes in binary star systems by looking for:

• A star orbiting around an unseen massive companion.
• X-rays emitted by gas heated to extreme temperatures as it falls into the black hole.

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X-Ray Binaries

Bright, variable X-ray sources identified by X-ray observatory satellites:

• Spectroscopic binary with only one set of spectral lines - the second object is invisible.
• Gas from the visible star is dumped on the companion, heats up, and emits X-rays.
• Estimate the mass of the unseen companion from the parameters of its orbit.

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Black Hole Candidates

A number of X-ray binaries have been found with unseen companions with Masses > 3 M_sun, too big for a Neutron Star.

Some Candidates:

Cygnus X-1: M = 6-10 M_sun

V404 Cygni: M > 6 M_sun

LMC X-3: M = 7-10 M_sun

None are as yet iron-clad cases, but in general things are looking pretty good.

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Black Holes are not totally Black!

"Classical" General Relativity says:

• Black Holes are totally black
• Can only grow in mass and size
• Last forever (nothing gets out once inside)

But, General Relativity does not include the effects of Quantum Mechanics.

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Hawking Radiation

Stephen Hawking looked at the problem by considering quantum effects occurring near the event horizon of a Black Hole.

He showed that:

• Black holes slowly "leak" particles with a blackbody spectrum.
• Each particle carries off a little of the black hole's mass
• The smaller the mass of the black hole, the faster it leaks.

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Evaporating Black Holes

Black Holes evaporate slowly by emitting subatomic particles and photons via "Hawking Radiation".

The Smaller the mass, the faster the evaporation.

For black holes in the real universe, the evaporation rate is VERY slow:

• A 3 M_sun black hole would require about 10⁶³ years to completely evaporate.
• This is about 10⁵³ times the present age of the Universe.

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