Stellar Remnants

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Stellar Remnants

• White Dwarfs, Neutron Stars and Black Holes

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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.

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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.

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Dead Doesnt 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.

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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.

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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.

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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.

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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.

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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 stars 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.

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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 stars pressure.

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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.

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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.

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White Dwarfs and Light

• As light escapes from a body it has to work
  against that bodys gravity, like a ball rolling
  up hill. Light, however, cannot slow down, but
  it can lose energy. Lights energy determines
  its frequency.

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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 stars mass.

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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.

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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.

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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.

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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.

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Binary Pair Diagram
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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.

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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.

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Neutron Stars

• In the 1930s, 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.

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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.

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Neutron Stars

• According to Baade and Zwickys 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.

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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.

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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.

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Pulsars

• In searching for an explanation, astronomers
  began to take a new look at Fritz and Zwickys 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 didnt actually pulse, but rather rotate
  rapidly. Some rotate as fast as 30 times per
  second.

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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.

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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 objects radius.

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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.

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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.

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Emissions from Neutron Stars

• As these particles ride the neutron stars
  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.

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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.

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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?

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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.

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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!

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Escape Velocity

• Escape velocity is the speed an object must
  attain to prevent being drawn back into another
  bodys gravity. The shuttle has to go about 7
  miles per second to escape Earths gravity.

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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)

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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?

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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.

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Early Supporters

• The idea of an object whose escape velocity
  exceeded the speed of light was proposed in
  1780s by English cleric, John Mitchell.
  Slightly more than a decade later, French
  mathematician Pierre Simon Laplace entertained
  the same idea.

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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

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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.

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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.

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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.

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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.

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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.

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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.

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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 .

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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.

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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.