Black Holes

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Black Holes
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A stellar mass black hole accreting material from
a companion star
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Black Holes and General Relativity
General Relativity Einstein's description of
gravity (extension of Newton's). Published in
1915. It begins with
1. The Equivalence Principle In an elevator
with no windows, there is no way to distinguish
effects of gravity from the effects of the
elevator being accelerated
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2. Gravitational Redshift
light received when elevator receding at some
speed.
later, speed gt 0
Consider accelerating elevator in free space (no
gravity).
time zero, speed0
light emitted when elevator at rest.
Received light has longer wavelength (or shorter
frequency) because of Doppler Shift ("redshift").
Gravity must have same effect! Verified in
Pound-Rebka experiment.
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3. Gravitational Time Dilation A photon moving
upwards in gravity is redshifted. Since
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the photon's period gets longer. Observer 1
will measure a longer period than Observer 2.
So they disagree on time intervals. Observer 1
would say that Observer 2's clock runs slow!
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All these effects are unnoticeable in our daily
experience! They are tiny in Earths gravity, but
large in a black holes.
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Escape Velocity
Velocity needed to escape the gravitational pull
of an object.
2GM R
vesc
Escape velocity from Earth's surface is 11 km/sec.
If Earth were crushed down to 1 cm size, escape
velocity would be speed of light. Then nothing,
including light, could escape Earth. This
special radius, for a particular object, is
called the Schwarzschild Radius, RS. RS a
M.
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Black Holes
If core with about 3 MSun or more collapses, not
even neutron pressure can stop it (total mass of
star about 25 MSun). Core collapses to a point,
a "singularity".
Gravity is so strong that nothing can escape, not
even light gt black hole. Schwarzschild radius
for Earth is 1 cm. For a 3 MSun object, its 9
km.
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Event horizon imaginary sphere around object
with radius equal to Schwarzschild radius.
Event horizon
Schwarzschild Radius
Anything crossing over to inside the event
horizon, including light, is trapped. We can
know nothing more about it after it does so.
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Black hole achieves this by severely curving
space. According to Einstein's General
Relativity, all masses curve space. Gravity and
space curvature are equivalent.
Like a rubber sheet, but in three dimensions,
curvature dictates how all objects, including
light, move when close to a mass.
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Curvature at event horizon is so great that space
"folds in on itself", i.e. anything crossing it
is trapped.
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Approaching a Black Hole
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Circling a Black Hole at the Photon Sphere
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Effects around Black Holes
1) Enormous tidal forces. 2) Gravitational
redshift. Example, blue light emitted just
outside event horizon may appear red to distant
observer. 3) Time dilation. Clock just
outside event horizon appears to run slow to a
distant observer. At event horizon, clock
appears to stop.
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Black Holes have no Hair
Properties of a black hole - Mass - Spin
(angular momentum) - Charge (tends to be zero)
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Black Holes can have impact on their environments
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Do Black Holes Really Exist? Good Candidate
Cygnus X-1
- Binary system 30 MSun star with unseen
companion. - Binary orbit gt companion gt 7
MSun. - X-rays gt million degree gas falling
into black hole.
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Supermassive (3 million solar mass) Black Hole at
the Galactic Center
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The Milky Way Galaxy
c
b
a
d
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Take a Giant Step Outside the Milky Way
Artist's Conception
Example (not to scale)
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Take a Giant Step Outside the Milky Way
Artist's Conception
Example (not to scale)
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from above ("face-on") see disk and bulge
Perseus arm
Orion arm
Sun
Cygnus arm
Carina arm
from the side ("edge-on")
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Another galaxy NGC 4414. The Milky Way roughly
resembles it.
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M31
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The Three Main Structural Components of the Milky
Way
1. Disk
- 30,000 pc diameter (or 30 kpc) - contains
young and old stars, gas, dust. Has spiral
structure - vertical thickness roughly 100 pc
- 2 kpc (depending on component. Most gas and
dust in thinner layer, most stars in thicker
layer)
2. Halo
- at least 30 kpc across - contains globular
clusters, old stars, little gas and dust, much
"dark matter" - roughly spherical
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3. Bulge
- About 4 kpc across - old stars, some gas,
dust - central black hole of 3 x 106 solar
masses - spherical
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Shapley (1917) found that Sun was not at center
of Milky Way
Shapley used distances to variable RR Lyrae
stars (a kind of Horizontal Branch star) in
Globular Clusters to determine that Sun was 16
kpc from center of Milky Way. Modern value 8
kpc.
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Stellar Orbits
Halo stars and globular clusters swarm around
center of Milky Way. Very elliptical orbits with
random orientations. They also cross the disk.
Bulge similar to halo.
Disk rotates.
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Precise Distance to Galactic Center
Distance 7.94 /- 0.42 kpc
SgrA
Eisenhauer et al. 2003
Orbital motion 6.37 mas/yr
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Rotation of the Disk
Sun moves at 225 km/sec around center. An orbit
takes 240 million years. Stars closer to center
take less time to orbit. Stars further from
center take longer.
gt rotation not rigid like a phonograph record or
a merry-go-round. Rather, "differential
rotation". Over most of disk, rotation velocity
is roughly constant.
The "rotation curve" of the Milky Way
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Spiral Structure of Disk
Spiral arms best traced by Young stars and
clusters Emission Nebulae HI Molecular
Clouds (old stars to a lesser extent) Disk not
empty between arms, just less material there.
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Problem How do spiral arms survive? Given
differential rotation, arms should be stretched
and smeared out after a few revolutions (Sun has
made 20 already)
The Winding Dilemma
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The spiral should end up like this
Real structure of Milky Way (and other spiral
galaxies) is more loosely wrapped.
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Proposed solution Arms are not material
moving together, but mark peak of a compressional
wave circling the disk
A Spiral Density Wave
Traffic-jam analogy
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Now replace cars by stars and gas clouds. The
traffic jams are actually due to the stars'
collective gravity. The higher gravity of the
jams keeps stars in them for longer.
Calculations and computer simulations show this
situation can be maintained for a long time.
Traffic jam on a loop caused by merging
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Molecular gas clouds pushed together in arms too
gt high density of clouds gt high concentration
of dust gt dust lanes.
Also, squeezing of clouds initiates collapse
within them gt star formation. Bright young
massive stars live and die in spiral arms.
Emission nebulae mostly in spiral arms.
So arms always contain same types of objects, but
individual objects come and go.
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90 of Matter in Milky Way is Dark Matter
Gives off no detectable radiation. Evidence is
from rotation curve
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Solar System Rotation Curve when almost all mass
at center, velocity decreases with radius
("Keplerian")
Rotation Velocity (AU/yr)
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R (AU)
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Not enough radiating matter at large R to explain
rotation curve gt "dark" matter! Dark matter
must be about 90 of the mass!
Composition unknown. Probably mostly exotic
particles that don't interact with ordinary
matter at all (except gravity). Some may be
brown dwarfs, dead white dwarfs Most likely
it's a dark halo surrounding the Milky Way.
Mass of Milky Way
6 x 1011 solar masses within 40 kpc of center.
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Seeing into the center of the Milky Way
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Seeing into the center of the Milky Way