Astronomy 162: Introduction to Stars, Galaxies, & the Universe Prof. Richard Pogge, MTWThF 9:30

Lecture 20: Black Holes

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

Emit "Hawking Radiation"

Gravity's Final Victory

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

Black Hole

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

Becomes a Black Hole:

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

Schwarzschild Radius

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.

Comparison of a 1.5 M_sun Black Hole and Neutron Star with Island of Manhattan for scale.

R_S is named for German physicist Karl Schwarzschild who in 1916 was one of the first people to explore the implications of Einstein's then-new General Theory of Relativity, the modern theory of Gravity.

The Event Horizon

• 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.

Gravity around Black Holes

• Gravity is the same as that of star of the same mass.

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!

Journey to a Black Hole: A Thought Experiment

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.

Seeing what cannot be seen...

Question:

If black holes are black, how can we hope to see them?

Answer:

Look for the effects of their gravity on their surroundings.

• Look for stars orbiting around an unseen massive object
• Look for X-rays emitted by gas that is superheated as it falls into a black hole.

X-Ray Binaries

• 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.

• A black hole candidate, conservatively, would be a system in which the mass of the unseen companion was larger than 4 M_sun, the more massive the better.

Black Hole Candidates

Examples:

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. Most of the current work is going into refining the mass estimates, and looking for other evidence that we are really dealing with a black hole.

Black Holes are not totally Black!

• 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.

Evaporating Black Holes

• Very cold thermal radiation (Temperatures of ~10 nanoKelvin)
• Bigger Black holes are colder

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.

A Final Word

[The black hole] "teaches us that space can be crumpled like a piece of paper into an infinitesimal dot, that time can be extinguished like a blown-out flame, and that the laws of physics that we regard as 'sacred', as immutable, are anything but."