Part I: Black Holes and SpaceTimeJuly 23, 2004

July 23, 2004

Topics of the Day

• Properties of black holes– Mass– Spin– Size

• A few words from Albert Einstein• Space Time• A few words from Stephen Hawking• Hawking radiation• Frame dragging

July 23, 2004

Black Hole Board Game

• Get into groups of six for board game.

• Select a partner in this group of six. – This person is your spacecraft building

teammate. (You did this yesterday)

• You should have read the Mission Briefing and the Rules of the Game last night.

• Now, play part 2 of the game.

July 23, 2004

Engage…..

• What do we know about black holes?

• What do the students need to know about black holes?

• What are some popular misconceptions about black holes?

• What are some effective ways to teach this topic?

July 23, 2004

Black Hole Medley• Project for Prof. Cominsky’s

Cosmology class several years ago• What would happen to the Earth if the

Sun was instantaneously replaced by a BH of the same mass? (By the way, this can’t happen)

• How many misconceptions can you find??

July 23, 2004

Properties of black holes

• “Black Holes have no hair” – famous quote that alludes to the fact that (under GR), BH can be completely described by:– Charge (not expected to be seen)– Mass– Spin

July 23, 2004

Masses of Black Holes• Primordial – can be any size, including very small

(If <1014 g, they would still exist) – none seen

• “Stellar mass” black holes – must be at least 3 Mo

(~1034 g) – many examples are well studied• Intermediate black holes – range from 100 to 1000

Mo - located in normal galaxies – many seen

• Massive black holes – about 106 Mo – such as in the center of the Milky Way – many seen

• Supermassive black holes – about 109-10 Mo - located in Active Galactic Nuclei, often accompanied by jets – many seen

July 23, 2004

Black Hole Structure

• BH are infamous for not letting light escape from within a certain radius (Schwarzschild, aka event horizon)

• Using non-relativistic mechanics, how would you derive this radius? Schwarzschild BH

July 23, 2004

Black Hole Structure

• Equate kinetic energy with potential energy

• Kinetic energy of particle moving at light speed: ½ mc2

• Potential energy at distance r: GMm/r

• Rsch = 2GM/c2

July 23, 2004

Black Hole Structure

• Given: Rsch = 2GM/c2

whereG =6.6742 × 10−11

N·m2/kg2 c = 3 x 108 m/s

1 Mo = 2 x 1030 kg• What is Rsch?• How does it scale?

July 23, 2004

Stellar Mass BH

• Often stars are formed in binary systems• Since they have unequal masses, the more

massive star will evolve faster - and reach the end of its main sequence lifetime

• In some cases, the supernova of the primary star will not disrupt the binary system and a COMPACT BINARY is formed

• Mass transfer can then occur from the main sequence star onto the collapsed, compact companion star - which can be a WHITE DWARF, NEUTRON STAR or BLACK HOLE

July 23, 2004

White Dwarfs, Neutron Stars and Black Holes

• White dwarfs are the size of the Earth and about 1 Mo

• Neutron stars are 10 km in radius and about 1.4 Mo

• One teaspoon of NS material weighs 100 million tons!

• After supernova, if cores are larger than 3 Mo, a black hole will be formed

• Mass transfer from normal star to compact object creates X-rays

July 23, 2004

Blondin X-ray Binary Simulation

This simulation by John Blondin (NCSU) shows a high mass star losing material to the compact object, and then forming an “accretion disk” of swirling material

July 23, 2004

Kepler’s third law

a3 = GM(T/2)2

where T is the orbital period and a is the semi-major axis of the orbit, G is the gravitational constant and M is the mass of the central object.

So – how would you use X-ray data to figure out if a black hole existed in a binary?

July 23, 2004

The First Black Hole• Cygnus X-1 binary

system• Most likely mass is

16 (+/- 5) Mo

• Mass determined by Doppler shift measurements of optical lines

July 23, 2004

Measuring Mass

• At least 12 stellar mass BH have been well studied

• Easiest to measure Doppler shift accurately when X-rays are not heating the accretion disk

• X-ray “novae”

July 23, 2004

Intermediate mass BH

• Recent simulations of starburst galaxy M82 have shown that collisions in the early life of a star cluster near the galaxy’s center can form a BH with mass 800-3000 Mo and replicate the Chandra observations

• The BH is offset from the center of the galaxy by about 600 light years

July 23, 2004

Milky Way’s Massive BH

• Best evidence comes from measurements of star motions in infrared images of central Milky Way by Ghez et al. and Genzel et al.

• S2, the closest star to Sgr A* (the radio source at the exact center of the Milky Way) indicates a mass of 2.6 million +/- 0.2 Mo

• S2 is at a distance of 17 light-hours from Sgr A* - whose event horizon is 26 light seconds

movie

July 23, 2004

NGC 4261 – best HST photo

• 100 million light years away

• 1.2 billion Mo black hole in a region the size of our Solar System

• Mass of disk is 100,000 Mo

• Disk is 800 light years across

July 23, 2004

Chandra finds supermassive BH everywhere!

Black holes in quasars

QSO

Galaxy

Empty

Black holes in“normal” galaxies

Black holes in empty space

Chandra deep field

July 23, 2004

Albert Einstein

• “I want to know God's thoughts...the rest are details.”

• “Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world.” • “With fame I become more

and more stupid, which of course is a very common phenomenon.”

God does not play dice with the Universe

July 23, 2004

Break: What do you know about Einstein?

• Why is 2005 the World Year of Physics?

• Can you name 3 of Einstein’s most famous contributions to physics? •Everything should be made as simple as possible, but not simpler

•Education is what remains after one has forgotten everything he learned in school

•Two things are infinite: the universe and human stupidity; and I'm not sure about the the universe."

(http://rescomp.stanford.edu/~cheshire/EinsteinQuotes.html)

July 23, 2004

Einstein and Relativity• 1905 – Theory of Special Relativity

– Applies to objects at a constant velocity– Time dilation and length contraction – Space and time are intertwined – Matter and energy are equivalent

Length contraction and time dilationmovie

July 23, 2004

Einstein and Relativity 1916 – Theory of General Relativity

Applies to objects that are accelerated

Describes the effects of gravity on spacetime

Spacetime Acceleration

July 23, 2004

Einstein’s GR equation

Gab = 8 G Tab c2

where Gab describes the geometry of

spacetime and Tab describes the flow of energy and momentum through spacetime

Gab and Tab are tensors

“Matter tells spacetime how to curve and spacetime tells matter how to move”

-- J. A. Wheeler

July 23, 2004

Solutions to GR equations

• Non-rotating, spherical black hole (Schwarzschild)

• Rotating, axisymmetric BH (Kerr)

• White holes• Wormholes

July 23, 2004

Motion in spacetime

• What is the motion of a particle in spacetime?

• Do particles follow straight lines?

July 23, 2004

Spacetime activity

• Bedsheet, small balls and heavy weight

• Try rolling the balls across the sheet with and without the weight

• Can you make a small ball curve in an orbit around the weight?

July 23, 2004

Hamilton’s black hole trajectory

• Minimum stable orbit is at 3 Schwarzschild radii or 300 km for this 30 Mo black hole

• In order to orbit any closer, you must fire thrusters to maintain forward motion

July 23, 2004

Hamilton’s orbiting a black hole

• Orbiting the black hole at close to the photon sphere. We are moving at almost the speed of light, so the relativistic beaming effects are quite strong.

July 23, 2004

Bob Nemiroff’s black hole movies

• Approaching a black hole

• Circling the black hole

July 23, 2004

Hamilton’s Wormhole

Complete Schwarzschild geometry consists of a black hole, a white hole, and two Universes connected at their horizons by a wormhole, also known as the Einstein-Rosen bridge

July 23, 2004

Measuring spin

Two views of matter spinning around BH

July 23, 2004

Active Galaxy Activity #3• Do you know how astronomers use light

to compute the size of a black hole?

•Here is a time history of flux from an active galaxy.

•What is happening here?

•What does this tell you about the size of the black hole?

July 23, 2004

Measuring size

• The size of an object is related to the light variations seen from an object bySize = c t

where c is the speed of light

and t is the timescale of the fastest variations seen from the object

• Why do we use the fastest variations?

• How does this work?

July 23, 2004

Image a Black Hole!

0.1 arc sec resolution

HST Image M87

MAXIM0.1 micro arc sec resolution

4-8 arc sec

Close to the event horizon the peak energy is emitted in X-rays

Micro-Arcsecond X-ray Imaging

Mission

July 23, 2004

Stephen Hawking

• “God not only plays dice, he also sometimes throws the dice where they cannot be seen.”

• “My goal is simple. It is complete understanding of the universe, why it is as it is and why it exists at all.”

• “It is not clear that intelligence has any long-term survival value.”

• Proved that if GR is true and the universe is expanding, then a singularity existed at the birth of the universe

July 23, 2004

Hawking Radiation• Hawking radiation results from the formation of

virtual particle pairs near the black hole’s event horizon. The total energy of the pair, E1 + E2 =0.

• According to quantum mechanics, virtual pairs of particles are always being created from the vacuum – they usually annihilate, disappearing back into the vacuum

• However, if the pair is formed near a black hole, one particle can become real (E1>0) and escape, while the other falls into the black hole

• The escaping particle makes Hawking radiation, while to conserve energy, the particle that falls in has to have E2<0, which lowers the energy of the black hole, and eventually causes it to evaporate.

July 23, 2004

Hawking Radiation

• Bigger black holes are colder and fainter

• Hawking radiation will eventually lead to the death of all BHs at the end of time

Hawking radiation from a very small black hole

Evaporation of mini-black hole in a gamma-ray burst

July 23, 2004

Information escapes a BH?

• Hawking radiation produces a paradox:– He previously claimed that no information

can escape from a BH– Yet, the escaping particle carries away the

information about its partner – as charge, etc. must be conserved in pair production

• He has now (as of last week) concluded that information can escape from a BH

• Details were released yesterday (7/21)

July 23, 2004

Frame dragging activity

• Paper plate, honey, peppercorns, food dye, superball

• What happens when the ball spins?movie

July 23, 2004

Frame Dragging• Predicted by Einstein’s theory

of General Relativity• Rotating bodies drag space

and time around themselves as they rotate – like a spinning object stuck in molasses

• It may have been observed by RXTE in neutron star and black hole binaries in oscillations caused by matter in precessing accretion disks

Precessing top

July 23, 2004

Frame Dragging• Gravity Probe B –now launched!• Will test 2 predictions of GR using 4 extremely

accurate gyroscopes– Measure space-time reference frame of Earth –

gyroscopes will move 6.6 arcseconds per year– Measure frame dragging of Earth – gyroscopes

will move by 42 milliarcseconds per year

These two effects are at right angles to

each other

July 23, 2004

Reflection and Debrief

July 23, 2004

Reflection and Debrief(Evaluate)

• Now what do we know?

• What are the big ideas here?

• What do our students need to know?

• Is there anything else we need to know?

• Misconceptions

(take notes)

July 23, 2004

Common Misconceptions

• Black holes are black because they don’t emit any light or suck up all light

• BH are emitting gravity or are the definition of gravity

• BH travel through space acting like cosmic vacuum cleaners

• BH are wormholes = time travel machines• If we had a BH at the location of the Sun, it

would suck in the Earth

July 23, 2004

Reflection and Debrief (Evaluate)

• What are some of the effective ways to teach these topics?

• Standards???

(take notes)

July 23, 2004

Web Resources

• Astronomy picture of the Day http://antwrp.gsfc.nasa.gov/apod/astropix.html

• Imagine the Universe http://imagine.gsfc.nasa.gov

• Relativity animations http://www.pbs.org/wgbh/nova/einstein/relativity/index.html

• NCSA’s Unveiling the Hidden Universe http://www.ncsa.uiuc.edu/Cyberia/Bima/BimaHome.html#Unveiling

• Jim Brau at the U of Oregon Astro 122 notes http://blueox.uoregon.edu/~jimbrau/astr122

• Intermediate mass black hole http://chandra.harvard.edu/press/04_releases/press_041004.html

July 23, 2004

Web Resources

• Pictures from the Hubble Space Telescope http://oposite.stsci.edu/pubinfo/pictures.html

• Chris Hillman’s Relativity Page http://www.math.washington.edu/~hillman/relativity.html

• Andrew Hamilton’s Black Hole Flight Simulator http://casa.colorado.edu/~ajsh/bhfs/screenshots/

• Stephen Hawking’s Home page http://www.hawking.org.uk/

• Genzel Group Milky Way BH video http://www.eso.org/outreach/press-rel/pr-2002/pr-17-02.html#vid-02-02

July 23, 2004

Web Resources

• Rossi X-ray Timing Explorer http://oposite.stsci.edu/pubinfo/pictures.html

• Gravity Probe B http://einstein.stanford.edu

• Micro-Arcsecond X-ray Imaging Mission http://maxim.gsfc.nasa.gov

• Laser Interferometric Space Array http://lisa.nasa.gov

• Bob Nemiroff’s black hole movies http://antwrp.gsfc.nasa.gov/htmltest/rjn_bht.html

• ROSAT X-ray images http://wave.xray.mpe.mpg.de/rosat/calendar/2000/oct