Transcript Lec10

Pulsars
• A pulsar is a
neutron star that
beams radiation
along a magnetic
axis that is not
aligned with the
rotation axis
Pulsars
• The radiation beams
sweep through
space like
lighthouse beams as
the neutron star
rotates
Why Pulsars must be Neutron Stars
Circumference of NS = 2π (radius) ~ 60 km
Spin Rate of Fast Pulsars ~ 1000 cycles per second
Surface Rotation Velocity ~ 60,000 km/s
~ 20% speed of light
~ escape velocity from NS
Anything else would be torn to pieces!
What can happen to a neutron
star in a close binary system?
Matter falling toward a neutron star forms an
accretion disk, just as in a white-dwarf binary
Accreting matter
adds angular
momentum to a
neutron star,
increasing its
spin
Episodes of
fusion on the
surface lead to
X-ray bursts
A black hole is an object whose gravity is so
powerful that not even light can escape it.
Supernovae/Supernova Remnants
• Massive stars fuse heavier elements, up to
Iron (Fe)
• Core is billions of Kelvin and greater than
Chandrasekhar Limit (1.4 Msun)
• Rapid collapse to neutron star
• Rebound of core results in expulsion of
outer layers  Supernova Remnant
Before/After!
Tycho SNR (1572)
Supernova 1987A (light took
170,000 years to get here!)
Black Holes
The Science Behind The Science Fiction
A black hole is an object whose gravity is so
powerful that not even light can escape it.
Thought Question
What happens to the escape velocity from an object if
you shrink it?
A. It increases
B. It decreases
C. It stays the same
Hint:
Escape Velocity
Initial Kinetic
Energy
=
Final Gravitational
Potential Energy
(escape velocity)2
G x (mass)
=
2
(radius)
Eluding Gravity’s Grasp
Escape Velocity
2GM
Vesc 
R
Escape Velocity
Speed Needed To
Escape An Object’s
Gravitational Pull
Mass M
Radius R
Earth: Vesc = 27,000 miles/hour (11 km/s)
Sun: Vesc = 1.4 million miles/hour (600 km/s)
“Dark Stars”
Rev. John Michell (1783) & Pierre-Simon Laplace (1796)
Speed of light  1 billion miles/hour (3x105 km/s)
What if a star were so small,
escape speed > speed of light?
A star we couldn’t see!
Vesc = speed
of light 
Earth mass:
Solar mass:
R  1 inch
R  2 miles
“Surface” of a Black Hole
• The “surface” of a black hole is the radius at which
the escape velocity equals the speed of light.
• This spherical surface is known as the event horizon.
• The radius of the event horizon is known as the
Schwarzschild radius.
Neutron star
3 MSun
Black
Hole
The event horizon of a 3 MSun black hole is also about
as big as a small city
No Escape
• Nothing can escape from within the event
horizon because nothing can go faster than light.
• No escape means there is no more contact with
something that falls in.
Mass versus
radius for a
neutron star
Objects too heavy
to be neutron stars
collapse to black
holes
Neutron Star Limit
• Neutron pressure can no longer support a neutron
star against gravity if its mass exceeds about 3
Msun
• Some massive star supernovae can make black
hole if enough mass falls onto core
Singularity
• Beyond the neutron star limit, no known force can
resist the crush of gravity.
• As far as we know, gravity crushes all the matter into
a single point known as a singularity.
Singularity
• The shrunken star too
small to be measured
but with indefinite
density
If the Sun shrank
into a black hole, its
gravity would be
different only near
the event horizon
Black holes don’t suck!
Einstein’s theory of gravity is built
on the principle that
1. The speed of light is constant.
2. As an object speeds up its clock runs faster.
3. The effects of gravity cannot be distinguished
from the effects of acceleration.
4. Motion is a relative state.
How about if there is wind?
Speed of light is constant
Our conceptions of space and time has to
be changed.
• Facts:
• Regardless of speed or direction, observers always
measure the speed of light to be the same value.
• Speed of light is maximum possible speed.
• Consequences:
– The length of an object decreases as its speed increases
– Clocks passing by you run more slowly than do clocks
at rest (example: solar wind particles)
Time dilation
Special Relativity: Length Contraction
Equivalence principle
Gravitational redshift
Gravity deforms space-time
Precession of Mercury’s orbit
Gravity bends the path of light
Geodesics in curved spacetime
Gravity bends the path of light
Light waves are stretched out leading to a gravitational
redshift
Tidal forces near the
event horizon of a
3 MSun black hole
would be lethal to
humans
Tidal forces would be
gentler near a
supermassive black
hole because its radius
is much bigger
Falling into a black hole
Falling into a black hole gravitational tidal forces pull
spacetime in such a way that time becomes infinitely long
(as viewed by distant observer).
The falling observer sees ordinary free fall in a finite time.
Falling into a black holes
•
•
•
With a sufficiently large black hole, a freely falling observer
would pass right through the event horizon in a finite time,
would be not feel the event horizon.
A distant observer watching the freely falling observer would
never see her fall through the event horizon (takes an infinite
time).
Falling into smaller black hole, the freely falling observer
would be ripped apart by tidal effects.
Falling into a black hole
• Signals sent from the freely falling observer would be time
dilated and redshifted.
• Once inside the event horizon, no communication with the
universe outside the event horizon is possible.
• But incoming signals from external world can enter.
• Time travel and other fairy tales…
Seeing black holes
Seeing black holes
How do we know it’s a BH?
• Nature is tricky: couldn’t it be another “small
like a neutron star or a white dwarf?
star”
• Measure mass of “X-ray star” by motion of its companion (a
star like the sun)
Mass > 3 solar
masses  BH!
Chandrasekhar
• Roughly a dozen BHs found this way (tip of the iceberg)
Black Hole Verification
•
•
Need to measure mass
— Use orbital properties of companion
— Measure velocity and distance of orbiting gas
It’s a black hole if it’s not a star and its mass
exceeds the neutron star limit (~3 MSun)
One famous X-ray binary with a likely black hole is in
the constellation Cygnus
Gamma-Ray Bursts
• Brief bursts of
gamma-rays
coming from space
were first detected
in the 1960s
•
•
Observations in the 1990s showed that many gammaray bursts were coming from very distant galaxies
They must be among the most powerful explosions in
the universe—could be the formation of a black hole
Supernovae and Gamma-Ray
Bursts
• Observations show that at least some gamma-ray bursts
may be produced by supernova explosions
• Some others may come from collisions between
neutron stars
Quasars
• Small, powerful source
of energy thought to be
cores of distant spiral
galaxies
Quasars and Active Galaxies
• Active galaxies are galaxies with exceptionally bright and
compact nuclear regions, called Active Galactic
Nuclei (AGN).
• The energy source of AGN is ultimately gravity, in
the form of accretion of gas onto a supermassive black hole, one the most efficient engines
in the Universe.
THE AGN ZOO: jet-powered radio lobes
What is the energy source of AGN?
The one characteristic that all AGN share is fast variability, from
which astronomers infer the size of the ‘central engine’.
A Unified Model for AGN
Are the different classes of AGN truly different ‘beasts’?
In the Unified Model for AGN, the apparent differences
are mainly due to inclination effects.
The ingredients are: the hole, the disk, the jet, some
orbiting clouds of gas, plus a dusty torus that surrounds
the inner disk.
A Unified Model for AGN
A Unified Model for AGN: observational
confirmations