march 7, 2006 astronomy 2010 1 chapter 23: black holes

March 7, 2006March 7, 2006 Astronomy 2010Astronomy 2010 11

Chapter 23: Black HolesChapter 23: Black Holes


Fact, Fiction, or UnknownFact, Fiction, or UnknownThis is a game where you (or I) make This is a game where you (or I) make

statements about black holes (or wormholes) statements about black holes (or wormholes) and then we discuss whether these are fact, and then we discuss whether these are fact, fiction, or unknown.fiction, or unknown.


General RelativityGeneral RelativityTo understand what black holes are, we begin To understand what black holes are, we begin

with an introduction to Einstein’s theory of with an introduction to Einstein’s theory of general relativitygeneral relativity.. It improves on Newton’s theory of gravity.It improves on Newton’s theory of gravity.

Newton’s gravity works well in most situations Newton’s gravity works well in most situations (planetary orbits, binary stars) but fails when:(planetary orbits, binary stars) but fails when:Gravity becomes extremely intense.Gravity becomes extremely intense.Large masses move rapidly.Large masses move rapidly.Light is effected by a large mass.Light is effected by a large mass.


The Equivalence PrincipleThe Equivalence Principle The equivalence principle The equivalence principle

says that an object will says that an object will behave the same whether behave the same whether in gravity or accelerating at in gravity or accelerating at an equivalent rate.an equivalent rate.

No experiment can No experiment can distinguish between gravity distinguish between gravity and acceleration. We must and acceleration. We must get the same result.get the same result.

Astronauts feel weightless Astronauts feel weightless in orbit because their in orbit because their acceleration cancels acceleration cancels gravity.gravity.


Here’s the RubHere’s the Rub

Aim a laser beam from the rear to front of a shuttle.Aim a laser beam from the rear to front of a shuttle. In zero gravity the laser will hit the front center of the shuttle.In zero gravity the laser will hit the front center of the shuttle. In free fall around the Earth, the laser must hit the same spot In free fall around the Earth, the laser must hit the same spot

-- but from the time the light leaves the laser until it reaches -- but from the time the light leaves the laser until it reaches the front, the shuttle has moved!the front, the shuttle has moved!

The light is bent by gravity to hit the front center! The light is bent by gravity to hit the front center!


General Relativity: Warped SpaceGeneral Relativity: Warped Space


Light “Bends”Light “Bends”


Tests of General RelativityTests of General RelativityEinstein’s theory says that the presence of Einstein’s theory says that the presence of

matter warps space and time. Gravity is matter warps space and time. Gravity is replaced by warping of space-time.replaced by warping of space-time.

Predictions:Predictions:Precession of the perihelion of MercuryPrecession of the perihelion of MercuryLight will be bent when passing near large objectsLight will be bent when passing near large objectsTime will slow down near a large massTime will slow down near a large massGravitational redshift of lightGravitational redshift of lightMassive objects will collapse to a singularity (black Massive objects will collapse to a singularity (black

hole).hole).


Deflection of LightDeflection of LightArthur Eddington mounted two expeditions in Arthur Eddington mounted two expeditions in

1919, one to Brazil and the other to West 1919, one to Brazil and the other to West Africa, to view a total eclipse and measure the Africa, to view a total eclipse and measure the deflection of starlight passing near the Sun.deflection of starlight passing near the Sun.

Both obtained measurements that agreed with Both obtained measurements that agreed with GR predictions GR predictions fame for Einstein & fame for Einstein & Eddington.Eddington.

Gravitational lensing is now a tool:Gravitational lensing is now a tool:multiple images of distant objectsmultiple images of distant objectsmicrolensing: one image but brightness changesmicrolensing: one image but brightness changes


gravitational lens -- gravity can bend light around a very heavy obstacle

possible gravitational lens observed


Lensing of Distant GalaxiesLensing of Distant Galaxies

Hubble picture of distant galaxies lensed by nearergalaxy (bright fuzzystructure). Lensed galaxies appear as arcs in the picture.Can be used to estimate the mass ofthe intermediategalaxy.


Gravity's Final VictoryGravity's Final VictoryA star more massive than about 18 MA star more massive than about 18 Msunsun leaves leaves

behind a core larger than 3 Mbehind a core larger than 3 Msunsun

Neutron degeneracy pressure fails Neutron degeneracy pressure fails Nothing can stop its gravitational collapse.Nothing can stop its gravitational collapse.Core collapses to a Core collapses to a singularitysingularity::

zero radiuszero radius infinite density infinite density

Near the singularity gravity is so strong that not Near the singularity gravity is so strong that not even light can escape.even light can escape.

Escape Velocity: Rocket AnalogyEscape Velocity: Rocket Analogy

light: 299,792 km/s


Black Holes: Key ConceptsBlack Holes: Key ConceptsBlack Holes are totally collapsed objectsBlack Holes are totally collapsed objects

gravity so strong not even light can escapegravity so strong not even light can escapepredicted by General Relativity predicted by General Relativity

Find them by their Gravity – Binary stars Find them by their Gravity – Binary stars Orbit of visible partnerOrbit of visible partnerAccretion disk – matter sucked in from partnerAccretion disk – matter sucked in from partnerX-ray BinariesX-ray Binaries

Gravitational microlensingGravitational microlensing


Black Hole FormationBlack Hole FormationSupernovae explosionSupernovae explosion

collapsing core passes through a neutron star stagecollapsing core passes through a neutron star stageneutron star not stableneutron star not stabledegeneracy pressure insufficientdegeneracy pressure insufficient

Core becomes a Black Hole:Core becomes a Black Hole:"Black" because it neither emits nor reflects light."Black" because it neither emits nor reflects light."Hole" because nothing entering can ever escape. "Hole" because nothing entering can ever escape.

Only its enormous mass remainsOnly its enormous mass remains


Near the SingularityNear the Singularity

Gravity is so strong Gravity is so strong that nothing, not that nothing, not even light, can even light, can escape.escape.

Infalling matter is Infalling matter is shredded by shredded by powerful powerful tidestides and and crushed to infinite crushed to infinite density. density.


Schwarzschild RadiusSchwarzschild Radius Light cannot escape from a Black Hole if it comes from Light cannot escape from a Black Hole if it comes from

a radius closer than the Schwarzschild radiiusa radius closer than the Schwarzschild radiius

M = Mass of the Black Hole, c = speed of light, G = newton’s M = Mass of the Black Hole, c = speed of light, G = newton’s constantconstant

At this distance: escape velocity = speed of lightAt this distance: escape velocity = speed of light Light speed is the fastest possible speed!Light speed is the fastest possible speed! mass of 1 Mmass of 1 Msunsun a Schwarzschild Radius of 3 km. a Schwarzschild Radius of 3 km.


Event HorizonEvent HorizonSchwarzschild radius marks the Schwarzschild radius marks the Event HorizonEvent Horizon

surrounding the black hole's singularity:surrounding the black hole's singularity:Events occurring inside are invisible to the outside Events occurring inside are invisible to the outside

universe.universe.Anything closer to the singularity can never leave Anything closer to the singularity can never leave

the black holethe black holeThe Event Horizon hides the singularity from The Event Horizon hides the singularity from

the outside universe.the outside universe. ““Point of No Return” for objects falling into a Point of No Return” for objects falling into a

black hole. black hole.


Gravity Around Black HolesGravity Around Black HolesFar away from a black hole:Far away from a black hole:

Gravity is the same as for a star of the same mass.Gravity is the same as for a star of the same mass.

If the Sun became a Black Hole, all the planets If the Sun became a Black Hole, all the planets would continue in the same orbits. would continue in the same orbits.

Close to a black hole:Close to a black hole:

R < 3 RR < 3 RSS, there are no stable orbits - all matter , there are no stable orbits - all matter eventually gets sucked in.eventually gets sucked in.

Simulated Views of a Black Hole Simulated Views of a Black Hole

far away up close


Falling into a Black HoleFalling into a Black Hole Falling toward a black hole wouldn’t be a pleasant experience…Falling toward a black hole wouldn’t be a pleasant experience… Falling feet-first, your body would be scrunched sideways and Falling feet-first, your body would be scrunched sideways and

stretched along the length of your body by the tidal forces of the stretched along the length of your body by the tidal forces of the black hole. Your body would look like a spaghetti noodle!black hole. Your body would look like a spaghetti noodle!

Stretching happens because your feet would be pulled much Stretching happens because your feet would be pulled much more strongly than your head. more strongly than your head.

Sideways scrunching happens because all points of your body Sideways scrunching happens because all points of your body would be pulled toward the center of the black hole. would be pulled toward the center of the black hole.

Your shoulders would be squeezed closer together as you fell Your shoulders would be squeezed closer together as you fell closer to the center of the black hole. closer to the center of the black hole.

Tidal stretching/squeezing of anything falling into a B.H. is Tidal stretching/squeezing of anything falling into a B.H. is conveniently forgotten in Hollywood movies.conveniently forgotten in Hollywood movies.


Falling into a Black HoleFalling into a Black HoleA friend watching you as you enter a B.H., A friend watching you as you enter a B.H.,

would see your clock run slower and slower would see your clock run slower and slower (than his) as you approached the event horizon. (than his) as you approached the event horizon.

This is the effect of "time dilation".This is the effect of "time dilation".Your friend would see you take an infinite Your friend would see you take an infinite

amount of time to cross the event horizonamount of time to cross the event horizon time would appear to stand still. time would appear to stand still.

However, in your reference frame your clock However, in your reference frame your clock would run forward normally and you would would run forward normally and you would reach the center very soon. reach the center very soon.


Gravitational RedshiftGravitational RedshiftIf you beamed back the progress of your If you beamed back the progress of your

journey into a black hole, your friend journey into a black hole, your friend would have to tune to progressively longer would have to tune to progressively longer wavelengths (lower frequencies) as you wavelengths (lower frequencies) as you approached the event horizon.approached the event horizon.

This is the effect of This is the effect of gravitational redshiftgravitational redshift..Eventually, the photons would be Eventually, the photons would be

stretched to infinitely long wavelengths. stretched to infinitely long wavelengths.


Seeing the Invisible Seeing the Invisible QuestionQuestion: : If no light gets out of a black hole, how can we ever If no light gets out of a black hole, how can we ever

hope to find one? hope to find one? AnswerAnswer: : Look for the effects of their Look for the effects of their gravitygravity on nearby objects. on nearby objects.

For example, search for black holes in binary star For example, search for black holes in binary star systems: systems:

A star orbiting around an unseen massive companion. A star orbiting around an unseen massive companion. X-rays emitted by gas heated to extreme temperatures as it X-rays emitted by gas heated to extreme temperatures as it

falls into the black hole. falls into the black hole.


orbit depends mass of two objects

black hole and visible star orbit around a center of black hole and visible star orbit around a center of mass mass

motion of visible companion betrays black hole motion of visible companion betrays black hole Kepler's 3rd law Kepler's 3rd law total mass of the system. total mass of the system. If the mass of the unseen object is too big for a neutron If the mass of the unseen object is too big for a neutron

star or a white dwarf, then it is very likely a black hole! star or a white dwarf, then it is very likely a black hole!

What if a Binary Partner is a What if a Binary Partner is a Black Black Hole?Hole?

AccretionAccretion from Binary Partner from Binary Partner

Motion of Motion of Accretion Accretion Disk from Disk from Doppler Doppler ShiftShift

Measure Measure Black Black Hole Hole mass mass


X-Ray Binaries X-Ray Binaries Bright, variable X-ray sources identified by X-Bright, variable X-ray sources identified by X-

ray observatory satellites: ray observatory satellites:

Spectroscopic binary with only one set of spectral Spectroscopic binary with only one set of spectral lines - the second object is invisible. lines - the second object is invisible.

Gas from the visible star is dumped on the Gas from the visible star is dumped on the companion, heats up, and emits X-rays. companion, heats up, and emits X-rays.

Estimate the mass of the unseen companion from Estimate the mass of the unseen companion from the parameters of its orbit. the parameters of its orbit.

X-Ray EmissionX-Ray EmissionVisible Star

Gas pulled off

black hole

accretion disk

Gas temperature increases

closer to BH. Gas near BH emits x-rays.


Chandra X-ray ObservatoryChandra X-ray ObservatoryDetects/images X-ray sources Detects/images X-ray sources that are billions of LY away. that are billions of LY away.

Chandra’s mirrors are the Chandra’s mirrors are the largest, most precisely shaped largest, most precisely shaped and aligned, and smoothest and aligned, and smoothest mirrors ever constructed. mirrors ever constructed.

Images 25 times sharper than Images 25 times sharper than the best previous X-ray the best previous X-ray telescope. telescope. This focusing power is equivalent This focusing power is equivalent

to the ability to read a newspaper to the ability to read a newspaper at a distance of half a mile. at a distance of half a mile.

Chandra's improved sensitivity is Chandra's improved sensitivity is making possible more detailed making possible more detailed studies of black holes, studies of black holes, supernovae, and dark matter. supernovae, and dark matter.

Launched by Space Shuttle Launched by Space Shuttle Columbia on July 23, 1999. Columbia on July 23, 1999.One of NASA's Great Observatories.One of NASA's Great Observatories.


X-Ray EmissionX-Ray EmissionVisible star close loses some of its gas to the Visible star close loses some of its gas to the

black holeblack holeGas material forms an Gas material forms an accretion diskaccretion disk as it as it

spirals onto the black holespirals onto the black holegas particles in the disk rub against each and gas particles in the disk rub against each and

heat up from friction heat up from friction friction increases inward causing increasing friction increases inward causing increasing

temperature closer to the event horizontemperature closer to the event horizonnear event horizon, the disk is hot enough to near event horizon, the disk is hot enough to

emit X-rays. emit X-rays.


Black Hole Candidates Black Hole Candidates A number of X-ray binaries have been found A number of X-ray binaries have been found

with unseen companions with masses > 3 Mwith unseen companions with masses > 3 Msunsun, ,

too big for a neutron star. too big for a neutron star. Some CandidatesSome Candidates: :

Cygnus X-1: M = 6-10 Msun Cygnus X-1: M = 6-10 Msun V404 Cygni: M > 6 Msun V404 Cygni: M > 6 Msun LMC X-3: M = 7-10 Msun LMC X-3: M = 7-10 Msun

NoneNone are as yet iron-clad cases, but in general are as yet iron-clad cases, but in general things are looking pretty good. things are looking pretty good.


Black Hole TheoryBlack Hole TheoryModern physics has two basic sets of laws for Modern physics has two basic sets of laws for

the universe:the universe:General relativity -- macro-scaleGeneral relativity -- macro-scaleQuantum field theory -- micro-scaleQuantum field theory -- micro-scale

The two are The two are notnot compatible! compatible!Most problems fall into one category only.Most problems fall into one category only.Black holes need both.Black holes need both.

micro-size and macro-massmicro-size and macro-massThe study of black holes (on paper) helps The study of black holes (on paper) helps

understand how to combine the two theories.understand how to combine the two theories.


Black Hole Theory (cont’d)Black Hole Theory (cont’d)Black holes are “simple” objects described by Black holes are “simple” objects described by

their mass, spin, and electric charge.their mass, spin, and electric charge.Black holes have Black holes have no hairno hair..

All event horizons are spherical, no matter what the All event horizons are spherical, no matter what the mass looked like before collapse.mass looked like before collapse.

Black holes have no magnetic field (internal).Black holes have no magnetic field (internal).Black holes have entropy (a measure of Black holes have entropy (a measure of

disorder) that is proportional to the size of the disorder) that is proportional to the size of the event horizon.event horizon.

Black holes have a temperature Black holes have a temperature black body black body

Stephen HawkingStephen Hawking

Stephen W. Hawking (b1942)

Black holes slowly "leak" Black holes slowly "leak" particles – Hawking radiationparticles – Hawking radiation quantum mechanics near the quantum mechanics near the

event horizon of a black hole. event horizon of a black hole.

Each particle carries off a little Each particle carries off a little of the black hole's mass of the black hole's mass

The smaller the mass of the The smaller the mass of the black hole, the faster it leaks. black hole, the faster it leaks.

Hawking radiation is equivalent Hawking radiation is equivalent to black body radiation.to black body radiation.


Evaporating Black Holes Evaporating Black Holes Black Holes evaporate slowly by emitting Black Holes evaporate slowly by emitting

“Hawking radiation”“Hawking radiation”Black Holes will eventually vanishBlack Holes will eventually vanishThe The smallersmaller the mass, the the mass, the fasterfaster the evaporation the evaporation

Questions Remain about Black Holes:Questions Remain about Black Holes: Is the information that falls into a Black Hole lost Is the information that falls into a Black Hole lost

forever?forever?What is inside a black hole? What is inside a black hole? Can Can wormholeswormholes be produced to travel in time and/or be produced to travel in time and/or

space?space?


Super Massive Black HolesSuper Massive Black HolesObservation of so-called active galaxies Observation of so-called active galaxies

provides strong evidence for the existence of provides strong evidence for the existence of super massive black holes which provide a super massive black holes which provide a simple explanation for the extremely energetic simple explanation for the extremely energetic nuclei.nuclei.

See Chapter 26.See Chapter 26.


Discussion QuestionDiscussion QuestionDiscuss the following question with a classmate Discuss the following question with a classmate

then write down your short answer:then write down your short answer:What would happen to the Earth’s What would happen to the Earth’s orbitorbit if the if the

Sun were suddenly replaced by a black hole Sun were suddenly replaced by a black hole with the same mass as the Sun?with the same mass as the Sun?Of course the Earth would become dark and cold. I Of course the Earth would become dark and cold. I

want you to discuss what would happen to the want you to discuss what would happen to the Earth’s Earth’s orbitorbit..


Hollywood and RealityHollywood and Reality Black holes are portrayed as cosmic vacuum cleaners Black holes are portrayed as cosmic vacuum cleaners

in TV and films, sucking up everything around them. in TV and films, sucking up everything around them. Black holes are dangerous only if something gets too Black holes are dangerous only if something gets too

close to them. close to them. Because all of their mass is compressed to a point, it is Because all of their mass is compressed to a point, it is

possible to get very close where the gravity gets very large. possible to get very close where the gravity gets very large. Objects far enough away will not sense anything Objects far enough away will not sense anything

unusual. unusual. If the Sun were replaced by a black hole of the If the Sun were replaced by a black hole of the samesame mass, mass,

the orbits of the planets would remain unchangedthe orbits of the planets would remain unchanged It would however be darker and colder. It would however be darker and colder.

march 7, 2006 astronomy 2010 1 chapter 23: black holes

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