Black Holes and Quasars
Black holes represent the final victory of gravity
over all other forces. Small ones are formed when massive stars
collapse; big ones lurk in the centers of galaxies. They are almost
invisible when isolated, but some of the most violent events in the
universe involve matter falling into black holes.
Topics
- Properties
- Detection
- Activity
Reading
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14.1 |
The Formation of a Stellar-Mass Black Hole |
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p. 325-326 |
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14.2 |
The Photon Sphere |
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p. 326 |
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14.3 |
The Event Horizon |
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p. 327-328 |
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14.7 |
Detecting a Black Hole |
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p. 330-334 |
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14.8 |
Supermassive Black Holes |
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p. 335-336 |
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17.1 |
Active Galactic Nuclei |
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p. 339-402 |
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17.3 |
How Are Quasars Powered? |
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p. 406-409 |
Properties
A black hole forms when an object's gravitational
field is too powerful for light to escape. Once this happens, many
details about the object -- its composition, for example -- become
irrelevant. The simplest kind of black hole does not rotate, and
all its properties are determined by just one thing: its
mass.
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A simple black hole of mass M has a radius
RS ∝ M
known as the Schwarzschild radius or the
horizon radius. A ray of light launched upward
from this radius can just barely escape the gravity of the
black hole. Nothing inside this radius can get out; this
region cannot influence the rest of the universe in any way.
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At the center of a non-rotating black hole is a
singularity -- a point where gravity becomes
infinitely strong. Everything within the Schwarzschild radius is
pulled into the singularity and destroyed.
Critical Orbits
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The smallest possible circular orbit around a black hole has a
radius of 1.5 RS. Light
is the only thing fast enough to actually travel in this
orbit, so this radius is called the photon
sphere. Anything which comes within photon sphere
will eventually fall into the hole unless it uses
rocket power to escape.
The smallest orbit which is stable, meaning that
small departures from a perfect circle are allowed, has a
radius of 3 RS.
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Schwarzschild Radius: A Newtonian Derivation
In Newtonian physics, the velocity needed to escape
an object of mass M and radius R is √2 times the
velocity of a circular orbit at that radius, or
ve =
&radic(2 G M ⁄ R)
where G is Newton's gravitational constant.
Setting ve =
c, the speed of light, and solving for R yields the
Schwarzschild radius:
For an object with mass
M = 1 MSun,
the Schwarzschild radius is
RS = 2.96 km.
In other words, the Sun would have to contract to a radius of
2.96 km to become a black hole.
Note that
RS ∝ M, so
the Schwarzschild radius for any other mass is easily computed:
multiply the mass in units of the Sun's mass by 2.96 km.
Rotating Black Holes
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Most black holes probably rotate. A rotating black hole has a
flattened region, the ergosphere, in which
nothing can remain at rest; the hole's rotation drags space
with it. The event horizon nests within the ergosphere.
Objects which fall into the ergosphere can extract energy
from the black hole's rotation.
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Rotating black hole [Wikipedia]
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In a rotating black hole the singularity is a ring
instead of a point. Theoretically, it's possible to fall through
this ring and avoid being shredded by infinite gravitational forces.
We're not sure what happens next...
Detection
A black hole which is sitting quietly by itself is
hard to detect. It has, of course, a strong gravitational field,
but far away from the hole the field is no stronger than it would be
for any other object of the same mass.
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In theory, one way to detect a black hole is by its effect on
light; light rays passing near the hole are deflected by its
gravity. Here's what a
10 MSun back hole would
look like from a distance of 600 km. Of course,
anbody so close to a black hole of this size would be torn
apart by the hole's gravitational field!
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Black hole [Wikipedia]
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A more practical way to detect a black hole is to
study the orbits of stars and/or gas orbiting around it.
The Black Hole in the Center of the Milky Way
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Tracking individual stars in the center of the Milky Way shows
that they move in elliptical orbits about an object with a
mass of
MBH = 3.7×106 MSun .
This is too large a mass to be hidden in any star or star
cluster! Some very contrived alternatives to a black hole
exist, but most of these would naturally become black holes
anyway. The most logical conclusion is that our galaxy has a
large black hole at its center.
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Stellar Orbits in the Central Parsec [UCLA]
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Note: these orbits obey Kepler's laws, but because
they are tilted, their foci don't always correspond to the position
of the black hole.
Black Hole in Giant Elliptical Galaxy M87
Spectra show that one side of this disk is red shifted
(receding) while the other is blue shifted (approaching).
This implies the disk is rotating with a speed of about
550 km ⁄ sec.
The mass at the center of the disk is roughly
MBH = 3×109 MSun .
This is almost 1000 times the mass of the black hole at the
center of the Milky Way!
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Hubble Confirms Existence of Massive Black Hole [STScI]
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Black Holes in other Galaxies
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Studies of many galaxies have now turned up similar evidence.
It appears that the black holes at the centers of galaxies are
usually about 0.1% of the stellar mass of the bulge (counting
elliptical galaxies as all bulge).
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Activity
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A black hole which is actively capturing matter is much easier
to detect; the gas spiraling in toward the hole heats up and
emits intense light, while high-speed jets may extend along
the axis of a rotating hole.
These jets appear to be produced when a rotating black hole
encounters a magnetic field. The black hole acts like a
electrical generator, and the voltage accelerates charged
particles.
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Black hole [Wikipedia]
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Jet in M87
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Jets are also seen escaping the centers of galaxies. Here's the
jet associated with the black hole in M87.
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A Cosmic Searchlight [StScI]
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Double Jets in Merging Galaxies
In this composite X-ray (blue) + radio (pink) image, a pair of
galaxies spiral toward a merger, with their respective jets
tracing their gyrations. The optical image below shows the
two galaxies; they're tiny compared to the jets
they produce!
3C 75 in Abell 400 [Harvard]
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3C 75 in Abell 400 [Harvard]
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Quasars
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Quasars are extremely luminous objects found in the centers of
galaxies. They can outshine their hosts by factors of 100 or
more. They may vary erratically, dimming or brightening by a
factor of two in a few weeks.
These properties strongly support the idea that
quasars are powered by matter falling into black holes.
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HST Images of Quasars [IAS]
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Rapid Variations
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The rapid variations in brightness tell us that quasars must
be extremely small. An energy source one light year in radius
can't turn on or off in less than one year; for example, even
if the entire surface goes dark at the same instant, light
from the edge is still arriving a year after the light from
the center stops.
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To change brightness in just a few weeks, the
central engines of quasars can be no more than a few light-weeks in
radius.
Extreme Luminosity
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The high luminosities of quasars require more energy
than ordinary stars can possibly provide. At best, nuclear fusion
converts about 1% of the available mass into energy, and in most
stars the fraction converted is more like 0.1%. Matter swirling
into a black hole can convert 10% to 30% of its mass into energy
before it finally falls in.
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Astronomy Picture of the Day [NASA]
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Quasar and Black Hole Demographics
If quasars are powered by matter falling into black
holes, the amount of quasar light seen in the universe should be
related to the amount of matter now locked up in black holes.
Although the details are still sketchy, this
prediction seems to be correct. We now know that most galaxies of
any size have central supermassive black holes. The quasar activity
we observe can be produced when black holes like these form and
grow. The surprising conclusion is that most galaxies are
sleeping quasars; ready to reawaken whenever more matter
falls into their central black holes.
