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