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

# Lecture 20: Black Holes

Readings: Ch 24, sections 24-3, 5, 6, 7 & 8

## Key Ideas

Black Holes are totally collapsed objects
gravity so strong not even light can escape
predicted by General Relativity

Find them by their Gravity
X-ray Binary Stars

Black Hole Evaporation

## Gravity's Final Victory

A star more massive than about 18 Msun would leave behind a post-supernova core this is larger than 2-3 Msun:

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

Core would collapse into a singularity, and object with

• infinite density

## Black Hole

The Ultimate Extreme Object
• 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.

Light cannot escape from a Black Hole if it comes from a radius closer than the Schwarzschild Radius, RS to the singularity:
Where M = Mass of the Black Hole

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

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

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

RS 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

RS defines the "Event Horizon" surrounding the black hole's singularity:
• Events occurring inside RS are invisible to the outside universe.
• Anything closer to the singularity than RS 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

Far away from a black hole:
• Gravity is the same as that of star of the same mass.

Close to a black hole:

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

## 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.

## Seeing what cannot be seen...

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

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

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.

• A black hole candidate, conservatively, would be a system in which the mass of the unseen companion was larger than 3 Msun, the more massive the better.

## Black Hole Candidates

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

Currently 20 confirmed black hole candidates in our Galaxy:

First was Cygnus X-1: M = 7-13 Msun
Largest is GRS1915+105: M = 10-18 Msun
Most are in the range 4-10 Msun

Estimated to be as many as 1 Billion stellar-mass black holes in our Galaxy, which points out how very hard it is to find something that does not emit any radiation of its own.

## 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.

## Evaporating Black Holes

Black Holes evaporate slowly by emitting subatomic particles and photons via "Hawking Radiation":
• Very cold thermal radiation (Temperatures of ~10 nanoKelvin)
• Bigger Black holes are colder
The smaller the mass, the hotter the black hole, and so the faster the evaporation.

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

• A 3 Msun black hole would require about 1063 years to completely evaporate.
• This is about 1053 times the present age of the Universe.
Probably unimportant today, but it could be an important process in the distant future of the Universe.

## A Final Word

Physicist John Archibald Wheeler (b. 1911), who coined the term "black hole", has been one of the most innovative thinkers on space and time. The singularity at the center of the black hole, which we passed over quickly, is not a simple beast. Its existance, at least in the classical theory of relativity, is a real problem that is telling us about the limits of our ideas. Prof. Wheeler has put it this way:

[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."
from "Geons, Black Holes, & Quantum Foams: A Life in Physics" by Wheeler and Ford (1998, AIP Press)
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Updated: 2007 August 3