Fall 2006 ASTR 2030 Homepage
Fall 2009 ASTR 2030 Black Holes: Weekly Summaries
- What is a black hole?
- An object whose gravity is so strong that not even light can escape;
- A region of spacetime where space is falling faster than light.
- Event horizon — Schwarzschild radius.
- The place (surface) from within which light cannot escape.
- The center of the black hole, where the spacetime curvature becomes infinite;
- A place where space and time as we know them come to an end.
- Astronomical evidence exists for two kinds of black holes:
- Stellar-sized black holes, observed in X-ray binary systems;
- Supermassive black holes, observed at the centers of galaxies.
- Black hole bends light around it.
- Tidal forces tear infaller apart:
- well outside the horizon of a stellar-sized black hole;
- well inside the horizon of a supermassive black hole.
- Time dilation allows you to travel faster than light.
- Stable and unstable orbits around a black hole.
- Object falling into a black hole appears to an outside observer to redshift and freeze at the horizon.
- Nothing special appears happens as you yourself fall through the horizon.
- How a scene actually looks seen at close to the speed of light.
- Light travel time.
- When you move through a scene at near the speed of light,
what you actually see is modified by the light travel time.
You don't directly see the Lorentz contraction and time dilation
apparent on spacetime diagrams,
but rather Lorentz contraction and time dilation
modulated by light travel time delays.
- Relativistic beaming:
- Aberration: the scene is concentrated ahead, expanded behind;
- Color shifts: the scene is blueshifted ahead, redshifted behind;
- Brightness changes: the scene is brightened ahead, dimmed behind;
- Time changes: the scene is speeded up ahead, slowed down behind.
- The rules of 4-dimensional perspective (pdf)
- Twin paradox.
This was mainly a week of summary and review, in preparation for the midterm.
See Review for Th Sep 17 midterm
for questions to study.
- Quasars are unresolved (quasi-stellar),
extremely bright (as much as 1000 times as luminous as a whole galaxy)
objects seen at the centers of galaxies.
Typically they have large redshifts, indicating that they are moving rapidly away from us,
which in turn indicates that they are far away.
They are thought to be powered by supermassive black holes at the centers of galaxies.
- The quasar 3C273 and its jet
- Two indications that the jet is moving at almost the speed of light:
- The jet is superluminal &mdash blobs in the jet are observed to move several times faster than the speed of light.
- We see only one jet, the jet coming towards us, which is relativistically brightened;
there is undoubtedly a second jet going in the opposite direction, which we do not see because it is relativistically dimmed.
- Astronomical black holes — read Th Ch 8, 9
- The observational evidence for stellar-mass black holes:
- The compact object in an x-ray binary system can be no larger in size than a white dwarf;
- If the mass of the compact object is measured from the orbital dynamics to be more than 3 solar masses
(larger than the maximum possible mass of a white dwarf or neutron star),
then astronomers conclude that it must be a black hole.
- The observational evidence that the centers of galaxies contain supermassive black holes:
The most direct evidence is:
- A lot of mass (inferred from velocities of stars or gas)
- in a small space (inferred from imaging).
Supporting evidence is:
- Active Galactic Nuclei.
- X-ray binary systems
- The supermassive black hole at the center of the Milky Way
- Observations of the motions of stars, both angular motions on the sky, and radial motions from spectroscopy (redshifts and blueshifts),
indicate the presence of a 4 × 106 solar mass black hole at the center of our own Galaxy, the Milky Way.
- John Kormendy's 2001 census of Supermassive Black Holes in Galactic Nuclei
- Observations of the centers of nearby galaxies
indicate the presence of a large unseen gravitational mass in a small region
— it must be a black hole.
- Every galaxy large enough to have a bulge appears to have a central black hole.
- Black Hole masses range from millions (106) to billions (109) of solar masses.
- M87, the huge galaxy at the center of the Virgo cluster, at the center of the Local Supercluster of galaxies,
contains the most massive black hole known in the local Universe, 3 × 109 solar masses.
- Maser emission from M106 reveals a thin, warped accretion disk around a 3.9 × 107 solar mass black hole.
- Schwarzschild black hole — read Th Ch 3, and Ch 6 page 244 and following.
- No-hair theorem:
An isolated black hole rapidly (on few light crossing times) evolves
to a state characterized by just 3 properties:
It loses its "hair" by gravitational radiation.
- Electric charge
- Angular momentum (spin)
- A Schwarzschild black hole is the simplest kind of black hole,
one with mass, but no electric charge, and no spin.
- Falling into a Black Hole:
Journey into a Schwarzschild black hole
- What happens when you watch someone else fall into a black hole?
- What happens when you fall into a black hole?
- The Schwarzschild geometry for a non-rotating, uncharged black hole
- Intervals of spacetime can be either timelike, or lightlike, or spacelike:
- Timelike = possible worldline of a particle (traveling normally, at less than the speed of light)
- Lightlike = possible worldline of light
- Spacelike = a possible now-line: a line between two events that are simultaneous with respect to some observer (a particle would have to travel faster than light to follow such a line)
This week was about how to script a movie.
We watched excerpts from two movies, Contact, and Walt Disney's The Black Hole.
Read Thorne Ch 4 in preparation for Project 4 next week.
- A well-structured movie has 3 parts, a beginning, a middle, and an end:
- The first part of the movie should set up the "World", or genre, of the story.
The story could be a cartoon, a cowboy film, an action movie, or whatever,
but once the world has been set up, the movie should remain consistent
to that world.
While setting up the "World",
the movie should introduce the hero, the villain, and any other
The movie is often more interesting if the hero has flaws
and the villain has qualities.
- The main part of the movie should be characterized by Conflict.
The hero should encounter problems of one kind or another.
A novel can develop characters by getting inside their heads
and telling you what the characters are thinking,
but that is not possible in a movie.
Movies develop characters by facing them with problems,
and seeing how the characters respond to those problems.
The hero should overcome the problems encountered.
Often overcoming the problems generates new problems,
so that there is a cycle between encountering problems
and overcoming them.
- In its final part, the movie should build up to a Climax.
The climax should be the most exciting part of the movie.
The movie should end with closure, a resolution of some kind.
If you have a budget, spend it here.
Sometimes the movie ends with the climax;
other times there is an epilogue after the climax.
Sometimes the ending is perfect like a fairy tale,
but it can be more interesting if the ending has a twist
or is not perfect.
- What happens to cold matter when you compress it very prodigiously?
Read Thorne Ch 5.
- A solid or liquid is almost incompressible
because the atoms are tightly packed together.
In a solid, the atoms form a regular lattice,
while in a liquid the atoms are irregularly stacked.
- Atoms resist compression
because electrons satisfy an exclusion principle:
you can't pack electrons together more closely than a wavelength.
- Like any particle, an electron is both wave and particle:
For a non-relativistic electron,
momentum p equals mass times velocity,
p = m v.
- The wavelength of electrons in atoms is set by their orbital velocities.
The characteristic atomic velocity of electrons is
1/137 of the speed of light:
The (1/137) factor is the fine-structure constant,
which describes the characteristic strength of electromagnetism.
- To compress atoms requires compacting electrons
to the point where their velocities exceed the atomic velocity c/137.
This requires a pressure exceeding the pressure at the center of Jupiter.
- Thus planets of Jupiter's mass or less
are made of incompressible liquid or solid;
this is why the moons and planets in the solar system all have about
the same density,
and more massive planets have larger radii.
- At pressures higher than the pressure at the center of Jupiter,
electrons are squeezed out of atoms,
and form a compressible electron degenerate gas.
- Thus cold objects more massive than Jupiter
are held up by electron degeneracy pressure.
They are effectively cold white dwarfs.
- An electron degenerate gas is so compressible
that larger mass white dwarfs have smaller radii.
- The white dwarf sequence terminates
when the electrons have been compressed to the point that
their velocities are relativistic (almost the speed of light).
This happens at the Chandrasekhar limit of 1.4 solar masses.
- If mass is added to a white dwarf to bring it above 1.4 solar masses,
then the white dwarf will collapse.
- A white dwarf that exceeds the Chandrasekhar limit
will collapse to a neutron star.
- A neutron star is held up in part by the degeneracy pressure of neutrons,
and in part by the strong (nuclear) force.
- The neutron star sequence terminates at an upper mass limit of about 3 solar masses.
- A neutron star whose mass exceeds about 3 solar masses
will collapse to a black hole.
- At the end of the week we did Project 4,
to critique Chapter 4 of Thorne as if it were a story.
A star that for a while becomes comparable in brightness to its parent galaxy.
Thorne Ch 5 talks a bit about supernovae.
- 1054. Chinese astronomer Yang Wei-te reported a "guest star" (supernova) in constellation Taurus,
which was recorded in the
Annals of the Sung Dynasty.
- 1931. Fritz Zwicky points out that some novae (new stars)
are exceptionally bright. He calls them "supernovae".
He begins a solo campaign to discover supernovae.
- 1932. James Chadwick discovers the neutron.
- 1933. Baade & Zwicky
make their famous prediction that supernovae produce neutrons stars.
- 1940s. Baade and others
measure the expansion rate of Messier 1, the Crab nebula,
and show that it must have originated in an explosion around 1054.
They conclude that the Crab nebula is the remnant of the Supernova of 1054.
- 1967. Jocelyn Bell discovers a pulsar,
with a precise period of 1.337301 seconds,
then three more.
The first few pulsars are given the name "LGM" (Little Green Men).
Observations that pulsars pulse over a wide range of radio frequencies
ruled out the possibility of the source being intelligent life.
- 1968. American astronomers discover a 0.033 second pulsar in the Crab nebula.
The period is too short and too regular to be anything other than a rotating neutron star.
- Today. More than 1300 pulsars are now known in our Galaxy, with periods ranging from 0.00156 to several seconds.
A pulsar is a rotating, magnetized neutron star.
There are two kinds of supernova:
Core collapse supernova
Core collapse supernova
Show H lines
Show no H lines
In star-forming regions, spiral arms
Anywhere in a galaxy
Young, massive star (> 8 solar masses)
Old white dwarf
- Most stars spend most of their lives fusing Hydrogen (H) to Helium (He) at their centers.
These are main sequence stars.
The Sun is a main sequence star.
- When stars exhaust H at their center,
the He core contracts, H burns in a shell around the core,
the envelope expands, and the star becomes a Red Giant.
In the Red Giant phase, the star develops a strong wind.
- For stars less massive than about 8 suns,
the wind eventually drives off the entire envelope.
For a while, the star is seen as a
Planetary Nebula (nothing to do with planets),
containing a small hot star inside a glowing gaseous nebula.
The central star cools to become a White Dwarf.
- For stars more massive than about 8 suns,
the He core burns to heavier elements.
The core develops a complicated multi-layered structure.
At the center is iron (Fe), which contains no more nuclear fuel
— Fe is the most tightly bound of all nuclei.
- The inert Fe core is held up by electron degeneracy pressure.
When its mass has increased to 1.4 solar masses, the Chandrasekhar limit,
the core collapses to a neutron star.
Electrons and protons are pressed together into neutrons,
releasing an explosion of neutrinos:
The collapsing envelope of the star bounces off the neutron star core,
producing a Supernova.
- A core-collapse supernovae is powered by the gravitational energy
released by the collapse of the core.
- Computer simulation by Adam Burrows.
- For stars more massive than about 25 or 30 suns,
material falling back on to the newly formed neutron star
takes the neutron star over its 3 solar mass limit, causing it to collapse to a black hole.
- A carbon-oxygen white dwarf accretes from a companion star.
- When its mass has increased to 1.4 solar masses, the Chandrasekhar limit,
the white dwarf starts to collapse.
- Carbon ignites at the center.
- Because the pressure is electron degeneracy pressure,
the increase in temperature does not initially change the pressure.
The temperature skyrockets, causing the nuclear burning to be explosive.
- The white dwarf incinerates and explodes,
producing a thermonuclear supernova that leaves nothing behind.
Mitch Begelman lectured on:
Active Galactic Nuclei — a generic term for a variety of phenomena seen at the centers of galaxies
Quasars are the most extreme (luminous) form of Active Galactic Nuclei
- Variable — on timescales of days to years.
- Non-stellar spectrum — radio, x-rays, gamma-rays; optical emission lines.
- Jets, often relativistic — superluminal motion, one-sided.
- Some AGN, known as blazars (after the prototype, BL Lac),
have featureless spectra variable down to hour timescales
interpreted as we are looking down the maw of a relativistic jet which is pointed directly at us,
and therefore brightened, blueshifted, and speeded up.
MAXIM (MicroArcsecond X-Ray Imaging Mission).
- 3C273, the nearest bright quasar, the first quasar discovered, by Maarten Schmidt in 1963.
- Name quasar shortened from quasi-stellar-object
— an unresolved, star-like source with a non-stellar spectrum and a large redshift.
- Large redshift, from the expansion of the Universe, indicates that quasars are at cosmological distances.
- Quasars were most abundant at a redshift of 2, when the Universe was younger.
- Intensely luminous, as much as 1000 times the brightness of their parent galaxy.
- Typically variable, on timescales of days; this indicates that they are less than lightdays in size.
Phew we needed that.
- See Hawking radiation.
Read Thorne Ch 12.
- The 2nd law of thermodynamics asserts that entropy always increases in time.
Entropy is a quantitative measure of disorder.
The 2nd law is thought to be one of the most fundamental laws of physics.
- As of 1970, it appeared that black holes violated the 2nd law,
because stuff that fell through the horizon, carrying entropy with it, simply disappeared.
- Hawking (1970) showed that when two black holes merge,
the area of the horizon must increase:
the merged black hole's horizon area must exceed the sum
of the two original black holes' horizon areas.
- Jacob Bekenstein (1972) noticed a formal analogy between the equations of the thermodynamics
and those of black holes,
with entropy being proportional to the area of the black hole's horizon.
- Stephen Hawking (1974) made his famous breakthrough,
the theoretical discovery of the Hawking effect.
Using sophisticated ideas of quantum field theory in curved spacetime,
he showed that black holes have a finite temperature, and they radiate.
The analogy with thermodynamics was real, not a coincidence.
The entropy of a black hole equals 1/4 of its horizon area in Planck units
(c = G = ħ = 1).
- How is Hawking radiation produced?
Quantum mechanically, virtual pairs of particles can pop out of the vacuum.
The black hole swallows one of the particles (which effectively carrys negative energy),
leaving the other particle (carrying positive energy) to go off to the outside world.
- Hawking radiation has a black body spectrum.
- The characteristic wavelength of Hawking radiation is roughly equal to
the diameter of the black hole.
Thus if you could see a black hole by its Hawking radiation,
it would look fuzzy, a quantum mechanical object.
- The Hawking temperature and luminosity of astronomical black holes is tiny.
The radiation observed from near astronomical black holes is emitted
by hot gas from an accretion disk, not Hawking radiation.
- The Hawking temperature and luminosity of so-called mini-black holes
is much larger.
Stephen Hawking hypothesized that mini-black holes might be created in the Big Bang,
but there is no observational evidence for their existence.
- A mini-black hole with mass less than the mass of a mountain
can evaporate in the age of the Universe.
A mini-black hole of 1000 tons will evaporate in 1 second,
in a burst of gamma rays and high energy particles.
From a human point of view this is a large explosion,
but astronomically it is a tiny explosion,
far less energetic than a nova, supernova, or gamma-ray burst.
- Thorne Ch 10.
- General relativity predicts that masses that accelerate non-uniformly
will produced gravitational waves, which propagate at the speed of light.
- Werner Benger's video of two black holes merging,
producing gravitational waves.
- A passing gravitational wave produces an oscillating tidal force,
which could be detected by an oscillation in the distance between freely-falling masses.
- To date no gravitational waves have been detected directly.
(Laser Interferometer Gravitational-wave Observatory)
has two detectors, one in Washington State, the other in Louisiana.
Ligo is as yet too insensitive to detect gravitational waves,
but a future upgrade,
may permit the first detection of gravitational waves.
- NASA's ambitious possible future mission
(Laser Interferometer Space Antenna),
three spacecraft in a triangle a million kilometers on a side,
should easily dectect gravitational waves from merging black holes
and other objects.
- The gradual decrease in the orbital period of the
Hulse-Taylor binary pulsar
is consistent with the loss of energy by gravitational waves predicted by
Fall 2009 ASTR 2030 Homepage
Updated 2009 Dec 10