Download Black Holes - Department of Physics, USU

Introduction to Astronomy
• Announcements
– No class on Thursday 24 Jul 2008
– Homework #7 due on Monday
Review
• Stellar Birth
• Stellar Life (a.k.a. the main sequence)
• Stellar Death (no more Hydrogen)
– Low mass stars
• White dwarfs, surrounded by planetary nebula
– High mass stars
• Neutron stars
• Black Holes
We pick up here
Black Holes
(Cue sinister music)
• The ultimate fate of high-mass stars
– About 10 solar masses
• Higher mass = more gravitational
compression when fuel runs out
– Core squeezed harder than that which
produces white dwarfs and neutron stars
– Degenerate neutron pressure cannot stop
collapse
– Gravity > Strong nuclear force
• Ball of neutrons already at nuclear density is
squashed into an even smaller volume
• “infinite density”
2
GM
• Escape Velocity Vescape 
R
• Earth: Vescape  11.2 km/s
• Jupiter: Vescape  59.6 km/s
• Sun: Vescape  618 km/s
• Notice the trend: the more massive the
object is, the faster you have to go to
escape its gravitational pull
• What if gravity is so strong that the escape
velocity is > speed of light?!
– NOTHING would be able to escape…
• No apples, astronauts, radio waves, visible
light…absolutely nothing
History
• Proposed late 1700’s by John Michell
– What if Vescape = c
2GM
Rs  2
c
• “Black Stars”
?
Now known as the
“Schwartzschild Radius”
• ANY object can be turned into a black
hole!
• If Sun collapsed into a black hole (which it
won’t), would only be 1.9 miles in diameter
– How would Solar System be affected?
• NOT AT ALL!
• It’s gravity would be exactly the same as the Sun’s
• Only when you get near Rs (the “event horizon”),
do you feel strong pull of infinite gravity
This book has a mass, M = 1 kg
2GM
RS  2  1.48 x 10-27 meters
c
RS
• A star core that collapses to a black hole
still has the same mass, but it’s
concentrated in a vanishingly-small
volume
Cross-section of core
– Infinite density
– “Singularity”
time
• This all has to do with gravity, so let’s talk
a little about that.
Gravity
• Instead of “spooky action at a distance”, Einstein
thought there was something more elegant
about gravity
• Einstein’s General Theory of Relativity
– Matter tells spacetime how to curve
– Spacetime tells matter how to move
• Black holes tell space to get bent.
This effect was confirmed in early 1900s during a solar eclipse
The eclipse allowed astronomers to measure stars that appear close to the Sun, and
they watched for subtle changes in the stars’ apparent positions that indicated gravity
was pulling on their light … GRAVITATIONAL LENSING
• The predictions of general relativity have
been experimentally verified
– In fact, every experiment ever devised has
produced results that are exactly in
agreement with general relativity!
• Mercury’s perihelion shift
• Viking lander radio transmissions
Curved Spacetime
Planetary
orbits
Sun
This is the “boundary” of
the black hole…
Inside this spherical
boundary, we know
absolutely nothing
Curved Spacetime near a Black Hole
Goes all the way down
(singularity of infinite density)
• Conservation of Angular Momentum
– As star collapses to a black hole, rotation
speed increases
– Recall the ice-skater effect
– So event horizon actually flattens out a little
• Not a spherical horizon, oblate spheroid
• In fact, some theories predict “ring singularities” in
which the rotation speeds up enough to stop the
collapse (centripetal force), and the black hole’s
mass is concentrated in an infinitely thin ring
Static Limit: the material within this limit must be rotating
Result: You cannot fall “straight in” to a black hole. You can only circle the drain.
How do we know?
• If no light can escape, how do we even
know they exist, if we can’t see them?
• How do you know the wind exists?
– E.g. you can’t see with your eyes that the
wind is blowing. You can only see what the
wind is blowing.
– INDIRECT OBSERVATION
• We can’t directly see the black hole, but we can
observe its effects on nearby stuff
Indirect Observation of Black
Holes
• Accretion
– A black hole may pull (accrete) matter into a
fast-spinning disk around its equator
• Near the event horizon, infalling matter is speeding
around at near the speed of light!!!
• This causes extreme frictional heating in the gas,
making it emit X-rays and gamma-rays
– 10’s of millions of degrees Kelvin
Center depression and equatorial bulge from rotational dynamics
(STATIC LIMIT)
• Binary Systems
– Just like normal binary systems, black holes can exist
in binary pairs with other stars
• If we see X-ray emitting gas orbiting a region of space in
which we cannot directly see an object, probably a black hole
with a companion star
• As long as M > 5-10 MSun
– Using Kepler’s Laws, can determine mass of black
hole
Supermassive Black Holes
• Millions of times the mass of our Sun!
• Thought to lurk at the center of every
galaxy
– If actively consuming matter, called Active
Galactic Nucleus
– If not, just a gigantic black hole sitting quietly
• in fact, just waiting to wake up and feed again
(dust, gas, stars, galactic collisions)
By watching many stars
silently orbit a strangely
invisible object at the
exact center of our galaxy,
Astronomers have deduced
the existence of a huge
black hole with a mass
equal to many millions of
Suns!!!
• “Black Holes ain’t so black.”
– Stephen Hawking
• They can actually be assigned a “temperature”
– Strictly speaking, assigned Entropy (a thermodynamic
quantity related to the “disorder” in a system)
– Entropy depends on surface area of event horizon
– An entropy can be loosely interpreted in terms of a
temperature
– For Mbh = MSun, T ~ 10-8 K
• Temperature is small, but not zero
– Therefore it radiates some energy
• Because it radiates, it’s losing energy
(equivalent to mass, recall E = mc2)
• So black holes actually evaporate away!
– Very slowly though, lifetime ~ 1067 years
10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
times the age of the Universe!
• Other types of radiation
– Quantum mechanical
– Uncertainty principle:
Et  
Mass-energy equivalence

m t  2
c
Despite rumors to the contrary, you can get something for nothing!
You can “borrow” energy from the quantum nature of spacetime to create
pairs of particles
Constantly changing & dynamic…
…like the bubbles in Champagne, new ones
are constantly emerging and old ones are
constantly being destroyed
Introduction to Astronomy
Here, an electron and
anti-electron are created
from the quantum “foam”
within reach of the
gravitational
field of the black hole
This just so happens to
occur near the event
horizon.
The positron crosses the
event horizon and is lost
forever.
The black hole then appears
to radiate the electron!
• The Casimir Effect
– Two small neutral conducting plates placed ~
1 micrometer apart in a vacuum exert an
attractive force between them
• “virtual photons”
• ~10-7 N (1 kg = 10 N)
• Small, but measureable
• One of the rare situations where quantum effects
have large-scale observable consequences
What happens if you get too
close to a black hole?
Out here, very small curvature, so normal gravity
Oh no, not again.
But here, gravity is very strong
Weaker gravity here
Turns you into
spaghetti!
Stronger gravity here
Same phenomena
responsible for
Saturn’s rings…
• Other strange properties
– Time actually slows down near the event
horizon (time dilation)
– Time slows down near any massive body
• So your buddy watching you fall into a black hole
would actually see you frozen in time the instant
you crossed the event horizon
• In fact, time actually stops at the event horizon…
Watching a beam of light
from inside the falling elevator
Watching a beam of light from
outside
• What you would see if you looked up out
of the black hole as you fell in…
– As you cross the event horizon, your time
slows down infinitely according to an outside
observer
– On the other hand, this means that for every
nanosecond that passes for you, many
billions/trillions of years pass outside
• Result: the light from many trillions of years of the
Universe’s evolution pours in behind you!
Extreme Black Hole Theories
Einstein-Rosen Bridge
Perhaps a pathway to spatially-distant parts of the Universe?
• White Holes
– Counterpart to black holes
– Just as nothing can leave a black hole,
nothing can enter a white hole
– Incredibly theoretical
– But think about it…the water going down your
drain has to go somewhere, right?
Observations of Black Holes
• Cygnus X-1 ( ~ 7000 ly distant)
• HDE 226868
Blue supergiant
Source of mysterious X-rays…
Stellar wobble indicates a mass
Of 20  5 solar masses
They orbit each other every 5½
days
• Merging Black Holes ( in galaxy cluster
Abell 400 )
Composite
X-Ray & Radio
observations
Jets of
Radio synchrotron
radiation
Gravitational Waves
• Relatively new science (last 2 decades)
– But predicted by Einstein in 1920s
• Like dropping a pebble in a puddle creates
ripples that spread out, so too do massive
bodies create “gravitational ripples” under
the right circumstances
– Particularly, high masses and high
accelerations
General Relativity:
Spacetime is curved,
the result of which we
observe as a
“Gravitational Force”
The curvature around
a fast-moving, massive
body changes rapidly,
giving rise to “Waves”
In the fabric of spacetime
• Strange waves
– Compress in one direction, expand in another
– Gravitational wave moving into the screen
• LIGO – the search for gravitational waves
Laser Interferometry
Gravitational Observatory
4 foot diameter, 2.5 mile long
high-vacuum pipes
Bouncing laser beams back
and forth in each arm…
A passing gravitational wave
will alter the length of the arms
making the laser beams combine
and interfere
The Hanford, Washington Site
LIGO is sensitive enough to detect a change of 10-13 cm
(that’s 1000 times smaller than a Hydrogen atom!)
No interference:
Arms are equal length
Laser interference:
One arm is longer than
the other
• LISA – the search for gravitational waves
Laser Interferometer
Space Antenna
3 armed configuration
separated by 5 million
km (3 million miles)
Each node contains a
“test mass” that is isolated
from everything except
gravity…
A passing gravitational wave
will alter how the masses move
and can be detected by
combining the 3 laser beams
Test mass: Each spacecraft flies in tight formation, with the entire
body controlled by micronewton thrusters to keep it centered around
these tiny, free-floating metal cubes
Black Holes in Science Fiction
• The Hitchhiker’s Guide to the Galaxy
– The citizens of planet Magrathea use the
material spit out of a white hole to build new
planets from scratch
– The most complicated game in the Universe
is Brockian Ultra Cricket. The only time a full
set of rules were ever compiled into a single
rulebook, it was so massive it underwent
gravitational collapse and became a black
hole
• Schwartzschild Radius
– A WWII story loosely based on some real
experiences of Karl Schwartzschild
– The main character is a radio operator whose
radio is damaged and tries to get vital
information back from the front lines (the
singularity) to his commander (outside the
“event horizon”)
• Actually, the story is told from the perspective of
another soldier watching the radio operator (the
stationary observer)
NEXT TIME
• The Milky
Way Galaxy