Post on 21-Dec-2015
transcript
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 HolesBlack 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”
• Escape Velocity
• Earth:
• Jupiter:
• Sun:
• Notice the trend: the more massive the object is, the faster you have to go to escape its gravitational pull
R
GMVescape
2
km/s 2.11escapeV
km/s 618escapeVkm/s 59.6escapeV
• 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
HistoryHistory
• Proposed late 1700’s by John Michell– What if Vescape = c ?
• “Black Stars”
2
2
c
GMRs 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
RS
This book has a mass, M = 1 kg metersc
GMRS
27-2
10 x 1.482
• A star core that collapses to a black hole still has the same mass, but it’s concentrated in a vanishingly-small volume– Infinite density– “Singularity”
Cross-section of core 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, andthey watched for subtle changes in the stars’ apparent positions that indicated gravitywas 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
SunPlanetary orbits
This is the “boundary” ofthe black hole…
Inside this sphericalboundary, we know absolutely nothing
Curved Spacetime near a Black Hole
Goes all the way down(singularity of infinite density)
Event Horizon
• 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
10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000times the age of the Universe!
• Other types of radiation– Quantum mechanical– Uncertainty principle:
tE Mass-energy equivalence2c
tm
Despite rumors to the contrary, you can get something for nothing!
You can “borrow” energy from the quantum nature of spacetime to createpairs of particles
Constantly changing & dynamic…
…like the bubbles in Champagne, new onesare constantly emerging and old ones are constantly being destroyed
Introduction to Astronomy
Here, an electron andanti-electron are created from the quantum “foam”within reach of the gravitationalfield of the black hole
This just so happens tooccur near the eventhorizon.
The positron crosses theevent horizon and is lostforever.
The black hole then appearsto 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
But here, gravity is very strong
Oh no, not again.
Weaker gravity here
Stronger gravity here
Turns you intospaghetti!
Same phenomenaresponsible 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 lightfrom inside the falling elevator
Watching a beam of light fromoutside
• 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 massOf 20 5 solar masses
They orbit each other every 5½ days
• Merging Black Holes ( in galaxy cluster Abell 400 )
Composite X-Ray & Radioobservations
Jets of Radio synchrotronradiation
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 weobserve as a “Gravitational Force”
The curvature arounda fast-moving, massivebody 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
The Hanford, Washington Site
4 foot diameter, 2.5 mile longhigh-vacuum pipes
Bouncing laser beams backand forth in each arm…
A passing gravitational wavewill alter the length of the armsmaking the laser beams combineand interfere
Laser interference:One arm is longer thanthe other
No interference:Arms are equal length
LIGO is sensitive enough to detect a change of 10-13 cm
(that’s 1000 times smaller than a Hydrogen atom!)
• LISA – the search for gravitational waves
Laser InterferometerSpace Antenna
3 armed configurationseparated by 5 millionkm (3 million miles)
Each node contains a “test mass” that is isolatedfrom everything exceptgravity…
A passing gravitational wavewill alter how the masses moveand can be detected bycombining the 3 laser beams
Test mass: Each spacecraft flies in tight formation, with the entirebody controlled by micronewton thrusters to keep it centered aroundthese 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 TIMENEXT TIME
• The Milky Way Galaxy