Transcript 11 Stellar Remnants - Journigan-wiki

Stellar Remnants
White Dwarfs, Neutron Stars and Black
Holes
Warm Up-12/11/12
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When a white dwarf forms, is the former star
always at the end of its life cycle? What can
happen to it?
Does degeneracy still exist in stellar
remnants?
What is the Chandrasekhar number and what
does it mean?
What is the exclusion principle?
Warm Up
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What is the exclusion principle?
How does a low-mass star become a
high-mass stellar remnant?
What is gravitational red-shift?
What happens to a white dwarf as mass
is added to it?
If you pack electrons too closely, they
remain in what state?
Warm Up
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What is a nova and how do they occur?
What is a Roche Lobe?
What is a LaGrange Point?
What is a mass transfer stream?
What is an accretion disk?
What is a neutron star?
Warm Up
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What was the mission objective for Apollo 13?
Where was Apollo supposed to land?
Who was the mission commander?
Who was the mission pilot?
What mishap occurred on board that
threatened the mission?
What additional problems (2) did the crew
encounter?
What were the solutions to those problems?
Warm Up
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What is electron degeneracy and which stellar remnant
is it associated with?
What is neutron degeneracy and which stellar remnant
is it associated with?
What two forces provide equilibrium to white dwarfs?
What two forces provide equilibrium to neutron stars?
Why can nothing escape from inside the event horizon
of a black hole?
What happens to white dwarfs that exceed the
Chandrasekhar limit?
Contrast Type I supernovae with Type II supernovae.
Word Wall Elements
Example/Characteristic
Example/Characteristic
Example/Characteristic
Definition
WORD
WORD
Used correctly in a sentence
Simile
Simile
Simile
Vocabulary for Word Wall Elements
Type I Supernova
Type II Supernova
Roche Lobe/LaGrange Point
White Dwarf/Nova
Neutron Star/Pulsar
Black Hole/Schwarzschild Radius/Event Horizon
Event Horizon/Escape Velocity
White Dwarfs and Light
As light loses energy its wavelengths begin
to increase and they are stretched toward
the red end of the spectrum. This
phenomenon is called gravitational
redshift. The amount of shift depends on
the star’s mass.
Warm Up
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What is a gravitational red shift?
When a star reaches the end of its
evolutionary cycle, is it necessarily the
end of its life?
Is light a particle or a wave? Why?
Stellar Remnants
All stars must eventually die. Space is
littered with their bodies. Because they
have exhausted their fuel, they no longer
shine. The environment in which they
were created made them quite exotic.
Stellar forces have crushed white dwarfs to
the point that a piece the size of an ice
cube would weigh around 16 tons.
Stellar Remnants
Neutron stars have been crushed to the
point that their electrons and protons have
been merged. In the most massive stars,
the stars have collapsed so completely that
their immense gravity warps space to the
extent that no light escapes from them.
Dead Doesn’t Mean Inconspicuous
While these remnants are dead as far as
stellar evolution is concerned, many still
effect those things around them. Some
steal matter from there companions until
they explode while some collapse even
more until they reach an explosive end.
White Dwarfs
White dwarfs, the
remnants of small
mass stars, have a
diameter about the
size of the Earth.
While they do not
shine, they do radiate
heat. The average
surface temperature
of a white dwarf is
about 10,000 K.
White Dwarfs
The composition of the star is mainly
carbon and oxygen with a thin surface
layer of hydrogen and helium. There is far
too little gas to ever combust, however.
White dwarfs simply continue to cool and
reach a core temperature of around
20,000 K.
White Dwarfs
It would take longer than the Universe has
existed for one to cool to the extent it
would no longer be detected. These
remnants are called black dwarfs.
The Structure of a White Dwarf
There density and lack of fuel make white
dwarfs different from ordinary stars,
although they are at hydrostatic
equilibrium. External pressure is supplied
by an interaction between its electrons
that limit how many can occupy a given
volume. This gives the remnant a peculiar
property, added mass will make the white
dwarf shrink.
The Structure of a White Dwarf
Even more crucial, the mass of the
remnant must be below critical level or
they will collapse more. Also, because they
are so dense ( 1 ton/cm3) the star’s atoms
are packed very tightly, this compresses
the orbits of the electrons circling their
nuclei. The electrons are packed so tightly
that many of them cannot relax from an
excited state into a ground state.
The Structure of a White Dwarf
This leads to degeneracy pressure (as you
know). The physical law called the
exclusion principle limits the number of
electrons that can be squeezed into a
volume. When a gas is squeezed to this
extent it heats up but does not create a
corresponding increase in the star’s
pressure.
Degeneracy Pressure and the
Chandrasekhar Limit
Added mass makes the dwarf shrink
despite degeneracy. The additional
gravitational forces created by this
additional mass squeezes the star even
more. The remnant creates enough
degeneracy pressure to overcome these
additional forces until its mass reaches the
Chadrasakher Limit, about 1.4 solar
masses.
Degeneracy Pressure and the
Chandrasekhar Limit
Physicists believe
that when the
Chadrasekher Limit is
reached that the white
dwarf may attain
densities necessary to
develop high mass
star formations such
as neutron stars and
black holes.
White Dwarfs and Light
As light escapes from a body it has to work
against that body’s gravity, like a ball
rolling up hill. Light, however, cannot
slow down, but it can lose energy. Light’s
energy determines its frequency.
White Dwarfs in Binary Systems
Isolated dwarfs cool off and eventually
disappear, but in a binary systems this is
not necessarily true. Some dwarfs capture
gas from their neighboring companion.
The gas is rich in hydrogen. This gas
builds until it reaches the point of ignition.
White Dwarfs in Binary Systems
But, as we have seen, nuclear burning in a
degenerate gas can get explosive. This
detonating gas is expelled into space where it
forms an expanding sphere of hot gas. When
this phenomenon was first witnessed by ancient
astronomers it was called “nova stella”, for new
star. We use the shortened form today, nova.
Mass Transfer in Binary Systems
Both the dwarf and the companion are
surrounded by a region in which all
material is gravitationally attached to that
body. This region is known as a Roche
Lobe. It is a teardrop-shaped boundary,
that should the star expand beyond it, the
material outside it will fall into the other
star.
Mass Transfer in Binary Systems
The actual matter is passed through a mass
transfer stream. Where this stream passes from
the meeting Roche Lobes is called the LaGrange
Point. The LaGrange Point is a point of
gravitational neutrality where the influence of
each star counteracts the gravitational force of
its companion. To pass the LaGrange point is to
put yourself under the gravitational influence of
one member of the binary pair.
Binary Pair Diagram
The Type I Supernova
The nova process can repeat itself over and over
again given that the dwarf does not accumulate
too much material. If enough gas gathers to
push the dwarf over the Chandrasekhar Limit,
the star will collapse unto a Type I supernova.
This rapid collapse will eventually cause the
remnant to reignite and blow itself apart.
The Type I Supernova
The Type I
supernova leaves
behind no
remnant, but
completely
destroys itself. The
iron that is in your
blood was probably
made this way.
Neutron Stars
In the 1930’s, astrophysicists Walter Baade (like
the thing that washes your butt) and Fritz
Zwicky (great American name) proposed the
Type II (or high mass stellar collapse)
supernova. Almost as an afterthought, they
further proposed that the core remnant of such
an explosion would result in a neutron stars.
Neutron Stars
While the neutron star looked good on paper, no
one actually started looking for one for some
time because astronomers believed them to be
too small to observe. Theoretically, neutron
stars would be tiny even compared to the small
white dwarf.
Neutron Stars
According to Baade and Zwicky’s
calculations the neutron stars should have
a radius of about 10 kilometers and a mass
of several times that of the Sun. They also
predicted that neutron stars have a
maximum possible mass (like the white
dwarf does) of 2 to 3 solar masses.
Pulsars and the Discovery of the
Neutron Star
Due to a lack pf observational evidence, the
scientists’ ideas lay dormant for 3 decades until
1967. In that year British scientists observed
fluctuating radio signals from strange, distant
galaxies. A graduate student, Jocelyn Bell,
noticed an odd radio signal with a very precise
repetitive cycle (1.33 seconds). The signal was
dubbed “LGM-1” for little green men 1.
Pulsars
Over the next few weeks, the group found
several more pulsating radio sources that
they began to call “pulsars”. They knew
that the pulsating rates were likely related
to the densities of the objects, so they
realized that the sources were extremely
dense. Calculated densities made it very
unlikely that the sources were white
dwarfs.
Warm Up
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What is a pulsar?
Why do they rotate so rapidly?
What do we actually hear coming from a
pulsar?
Pulsars
In searching for an explanation,
astronomers began to take a new look at
Fritz and Zwicky’s 30 year old ideas about
neutron stars. It was Italian astronomer
Franco Pacini that linked the super dense
neutron star idea with the rapidly
pulsating radio signals by proposing that
the stars didn’t actually pulse, but rather
rotate rapidly. Some rotate as fast as 30
times per second.
Pulsars
So, how can a stellar core spin so rapidly?
The answer is simple. It is the
conservation of angular momentum. Like
an ice skater bringing in her arm to spin
more rapidly, when a star collapses its
radius is slashed.
Conservation of Angular
Momentum
The law of conservation of angular
momentum states that:
L = MVR where L is angular momentum
M is mass of the object
V is rotational velocity of an object
And
R is the object’s radius.
Conservation of Angular
Momentum
Angular momentum must be
conserved, therefore according to L =
MVR, if radius decreases then velocity
must increase to keep L constant.
Emissions from Neutron Stars
Like big motors, by varying their magnetic
fields, neutron stars create an electric
field. This electric field strips charged
particles off the surface of the remnant
and hurls them at nearly the speed of light
out into space.
Emissions from Neutron Stars
As these particles ride the neutron star’s electric
field away from the star they produce radiation,
much like a radio transmitter does. This
radiation, called non-thermal radiation is
funneled through the poles and emitted in the
shape of a tight cone.
The Pulsar
As these dense bodies rotate at astounding speeds, they
radiate outward from their magnetic poles. The
magnetic and rotational poles do not coincide and the
radiation beams obliquely to the axis of rotation. Like a
giant lighthouse, only if the Earth lies in the path of the
radiation, is it seen.
The Pulsar
Emitting this tremendous radiation field
does have its drawbacks, however. Like
dragging an anchor, the field slowly
decreases the rotational rate on the pulsar.
Eventually, the neutron star/pulsar will
cease to rotate and it will then become
“invisible” to us.
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What did Fritz and Zwicky propose?
What is the estimated mass of a neutron star?
What was the name of the first pulsar, discovered by
Jocelyn Bell?
Why do pulsars spin so quickly?
What does the law of conservation of angular
momentum state?
If a star collapses and its radius is reduced, what
happens to its rotational velocity?
The energy released from a neutron star is in the form
of what?
What happens to pulsars over time? Why?
Are pulsars frequently detected in binary pairs?
Neutron Stars in Binary Systems
Because neutron stars come from
supernovae, they rarely exist in binary
pairs. The explosive forces that create
neutron stars often destroy or dislodge
their companion.
Black Holes
When stars that are more massive than 10
solar masses reach the end of their lives,
they can compress their cores with so
much pressure that they rift the fabric of
space-time. To understand black holes
you have to understand escape velocity!
Escape Velocity
Escape velocity is the
speed an object must
attain to prevent
being drawn back into
another body’s
gravity. The shuttle
has to go about 7
miles per second to
escape Earth’s
gravity.
Escape Velocity
Mathematically, escape velocity is defined
as :
V = (2GM/R)1/2 where:
V = Escape velocity
G = Gravitational constant (6.8 10-11 m/s)
M= Mass (kg)
R = Radius of object (m)
Practical Application
For example, which has the higher escape
velocity, our Sun or a white dwarf with one
solar mass?
The white dwarf, because its radius is 100
times less has an escape velocity (1001/2)
or 10 times greater than our Sun. That's
about 6,000 km/sec.
See?
Practical Application
What about a neutron star whose radius is
105 times smaller than the Sun? Its escape
velocity jumps to 180,000 m/s or about
half the speed of light. Further compact a
neutron star till its radius is four times
smaller still and its escape velocity exceeds
the speed of light and a black hole is
created.
Early Supporters
The idea of an object
whose escape
velocity exceeded the
speed of light was
proposed in 1780’s by
English cleric, John
Mitchell. Slightly
more than a decade
later, French
mathematician Pierre
Simon Laplace
entertained the same
idea.
Go Figure
Following their logic and
using an improved escape
velocity, you can calculate
radii needed to become a
black hole. The formula:
R = 2GM/c2 where:
G = Gravitational constant (6.8
x 10-11 m/s)
M= Mass (kg)
c = speed of light
Go Figure
How small would you have to shrink our
Sun for it to become a black hole? You
would have to shrink it to about 3
kilometers across or 1.9 miles.
Why Space is Like a Water Bed
Imagine taking a
baseball and placing it
in the middle of water
bed. The ball makes a
small depression in
the mattress. You
roll a marble past the
depression and the
marble it trapped in
the curvature of the
mattress and comes
to rest beside the
baseball.
Why Space is Like a Water Bed
Now, imagine placing a bowling ball in the
center of the bed. The depression is ever
deeper, the curvature more exaggerated.
The marble now rolls in father and hits the
bottom harder.
The Formation of Black Holes
We infer from this analogy that strength of
attraction between bodies depends on the
amount the surface into which it is
embedded is curved. Gravity works like
this according to general relativity.
The Formation of Black Holes
Now replace the bowling ball with the a
safe and it will tear through the fabric of
the mattress. So too, a black hole is a tear
in the fabric of space time.
The Formation of Black Holes
A German astrophysicist Karl
Schwarzschild pioneered the calculations
describing the structure of black holes.
The distance across a black hole is called
the Schwarzschild radius in his honor.
Black Holes
If you look at general relativity to find out
the size of black holes you get the same
answer we got before: R = 2GM/c2 .
The Curvature of Space
General relativity (Einstein) predicted
these curves in space and they have been
proven to exist experimentally. The effect
of this curvature can be measured when
looking at radio or light waves and it
exactly coincides with predictions.
Black Holes
Where this exaggerated curvature prevents
even light from escaping is call the event
horizon and it coincides with the point
where escape velocity is greater than the
speed of light. This marks the point where
nothing can escape from the black holes
gravitational attraction.