Neutron Stars and Black Holes - Kruger Physics &...
Transcript of Neutron Stars and Black Holes - Kruger Physics &...
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Neutron Stars
and
Black Holes
Chapter 11:
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Neutron Stars
Typical size: R ~ 10 km
Mass: M ~ 1.4 – 3 Msun
Density: r ~ 1014 g/cm3
→ A piece of neutron
star matter of the size
of a sugar cube has a
mass of ~ 100 million
tons!!!
A supernova
explosion of a
M > 8 Msun star
blows away its
outer layers.
The central core
will collapse into
a compact object
of ~ a few Msun.
Pressure becomes so high
that electrons and protons
combine to form stable
neutrons throughout the
object.
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Discovery of Pulsars
=> Collapsing stellar core spins up to
periods of ~ a few milliseconds.
Angular momentum conservation
=> Rapidly pulsed (optical and radio) emission from
some objects interpreted as spin period of neutron stars
Magnetic fields are amplified up to
B ~ 109 – 1015 G.
(up to 1012 times the average
magnetic field of the sun)
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The Crab Pulsar
Remnant of a supernova observed in A.D. 1054
Pulsar wind + jets
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The Crab Pulsar
Visual image X-ray image
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Light curves of the Crab Pulsar
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The Lighthouse Model of Pulsars
A Pulsar’s
magnetic field
has a dipole
structure, just
like Earth’s.
Radiation
is emitted
mostly
along the
magnetic
poles.
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Images of Pulsars and
other Neutron Stars
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The Effects of Pulsar Winds
Pulsars blow off
a constant
stream (wind)
of high-energy
particles:
Pulsar Winds
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Compact Objects with
Accretion Disks
Black holes and
neutron stars
can be part of a
binary system.
=> Strong X-ray source!
Matter gets
pulled off from
the companion
star, forming an
accretion disk.
Heats up to a
few million K
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Neutron Stars in Binary Systems:
X-ray binaries
Example: Her X-1
2 Msun (F-type) star
Neutron star
Accretion disk material heats to several million K
=> X-ray emission
Star eclipses
neutron star and
accretion disk
periodically
Orbital period = 1.7 days
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The X-Ray Burster 4U 1820-30
Optical Ultraviolet
Several bursting X-ray sources have been observed:
Rapid outburst followed by gradual decay
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Black Holes
Just like white dwarfs (Chandrasekhar
limit: 1.4 Msun), there is a mass limit for
neutron stars:
Neutron stars can not exist
with masses > 3 Msun
We know of no mechanism to halt the collapse
of a compact object with > 3 Msun.
It will collapse into a single point – a singularity:
=> A Black Hole!
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Escape Velocity
Velocity needed to
escape Earth’s gravity
from the surface:
vesc ≈ 11.6 km/s
vesc
Now, gravitational
force decreases with
distance (~ 1/d2) =>
Starting out high
above the surface =>
lower escape velocity
vesc
vesc
If you could compress
Earth to a smaller radius
=> higher escape
velocity from the surface
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The Schwarzschild Radius
=> There is a limiting radius
where the escape velocity
reaches the speed of light, c:
Vesc = c Rs = 2GM ____
c2
Rs is called the
Schwarzschild Radius.
G = Universal const. of gravity
M = Mass
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Schwarzschild Radius
and Event Horizon
No object can travel faster than the speed of light.
We have no way of
finding out what’s
happening inside the
Schwarzschild radius.
=> nothing (not even
light) can escape
from inside the
Schwarzschild radius
“Event horizon”
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The Gravitational Field
of a Black Hole
Distance from
central mass Gra
vita
tio
na
l
Po
ten
tia
l
The gravitational potential (and gravitational
attraction force) at the Schwarzschild radius of
a black hole becomes infinite.
However, at large distances, it is not different
from the gravitational potential of a normal star.
If you replaced the sun with a black
hole of the same mass, the orbits of
the planets would not change!
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General Relativity Effects
Near Black Holes
An astronaut
descending down
towards the event
horizon of the BH will
be stretched vertically
(tidal effects) and
squeezed laterally.
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General Relativity Effects
Near Black Holes
Time dilation
Event Horizon
Clocks starting at
12:00 at each point
After 3 hours (for an
observer far away
from the BH): Clocks closer to the
BH run more slowly.
Time dilation
becomes infinite at
the event horizon.
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General Relativity Effects
Near Black Holes
Gravitational Red Shift
Event Horizon
All wavelengths of emissions
from near the event horizon
are stretched (red shifted).
Frequencies are lowered
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Observing Black Holes No light can escape a black hole.
=> Black holes can not be observed directly.
If an invisible
compact object is
part of a binary, we
can estimate its
mass from the
orbital period and
radial velocity.
Mass > 3 Msun
=> Black hole!
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Compact object
with > 3 Msun must
be a black hole!
Evidence for a Black Hole:
Masses of Compact )bjects
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Evidence for a Black Hole:
The Event Horizon If compact object is a neutron star, matter falling onto it,
produces an X-ray outburst when it impacts on the surface.
This can not happen if the compact object is a black
hole: matter would just fall through the horizon and
disappear without a trace!
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Compact Objects with
Disks and Jets
Some X-ray binaries
show jets perpendicular
to the accretion disk.
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Gamma-Ray Bursts (GRBs) Short (~ a few s), bright bursts of gamma-rays
Later discovered with X-ray
and optical afterglows lasting
several hours – a few days
GRB of May 10, 1999:
1 day after the GRB 2 days after the GRB
Many have now been associated
with host galaxies at large
(cosmological) distances.
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Gamma-Ray
Bursts (GRBs)
Currently favored model for
Gamma-Ray Bursts:
The Hypernova
Probably related to the
supernova-like deaths of very
massive (> 25 Msun) stars:
Iron core collapses to form a
black hole instead of a
neutron star (as in a “normal”
supernova).