Astronomy 102. October 6, 2005.

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Astronomy 102.October 6, 2005.
M2-9 Wings of a Butterfly Nebula,Credit B.
Balick (U. Washington) et al., WFPC2, HST, NASA
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Solar Structure.
Schematic view of the inner structure of the Sun,
Image courtesy of NASA
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Energy generation in the sun.
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Stellar Structure.

• The main energy source that powers most stars is
  the fusion of hydrogen into helium.
• The energy generated heats up the stellar
  interior and increases the thermal pressure
  inside the star.
• The thermal pressure generated by the hot fusion
  products, which tries to increase the size of the
  star, is balanced by the gravitational force that
  tries to compress the stellar matter.

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Next stage red giants.
The red giant star Betelgeuse the red giants are
stars that exhausted their Hydrogen fuel and are
burning Helium and heavier elements. Image
courtesy of NASA, Hubble Space Telescope Institute
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Throwing away the outer shellplanetary nebula.

• An erupting, massive star in the Milky Way.
  NASA's Hubble Space Telescope has identified one
  of the most massive stars known, emitting as much
  as 10 million times the power of our Sun and with
  a radius larger than the distance between the Sun
  and the Earth.
• Image courtesy of NASA.

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Almost out of fuel white dwarfs.
The planetary nebula NGC 2440 contains one of the
hottest white dwarf stars known. The white dwarf
can be seen as the bright dot near the picture's
center. Image courtesy of H. Bond (STSci), R.
Ciardullo (PSU), WFPC2, HST, NASA.
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The death of a very massive star supernova.Our
life is possible because of supernovas!
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What really happens when stars collapse?Confineme
nt of elementary particles.

• Electrons, protons, and neutrons can be confined
  to small spaces by surrounding them with of
  particles of the same type.
• The space occupied by the elementary particles is
  reduced when their number increases.
• The distance between the elementary particles
  becomes small enough, their wave-like properties
  become important.
• At small inter-particle distances, the particles
  not only experience electric repulsion, but also
  quantum-mechanical repulsion.

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Degeneracy pressure.

• When the quantum repulsion dominates, the
  electrons are said to be degenerate (this quantum
  repulsion is also known as the Pauli exclusion
  principle).
• Protons can confine each other in a similar
  fashion so can neutrons. Because electrons are
  less massive, though, they become degenerate with
  less confinement (a space roughly 1800 times
  larger compared to protons and neutrons).
• The Pauli exclusion principle does not apply to
  light.

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Degeneracy pressure.

• If one confines an electron wave to a smaller
  space, its wavelength is made shorter.
• Just as is the case for light, a shorter
  wavelength means a larger energy for each
  confined electron.
• With this increase in energy, each electron
  exerts itself harder on the walls of its cell
  this is the same as an increase in pressure.
• This extra pressure from the increase in wave
  energy under very tight confinement is degeneracy
  pressure (Fowler, 1926).

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Degeneracy pressure.

• Another, equivalent, way to view the
  wave-particle duality-induced extra resistance to
  compression is to invoke the Heisenberg
  uncertainty principle
• The more precisely the position of an elementary
  particle is determined along some dimension, the
  less precisely its momentum (mass times velocity)
  along that same direction is determined.
• In other words confining a bunch of elementary
  particles each to a very small distance (thus
  determining each position precisely) leads to a
  very large variation in their momenta and speeds.
• Confine to smaller space increase speed of
  particles on average increase the force they
  exert on their cell walls (degeneracy pressure).

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Mid-lecture break.

• Midterm exam 1 will be held on Tuesday October 11
  during the regular class time.
• The material covered on this exam includes all
  material covered up to and including lecture 10
  (Tuesday October 4).
• Homework set 3 is due tomorrow, Friday 10/7, at
  8.30 am.

The central star in this planetary nebula, NGC
6543, is well on its way to becoming a white
dwarf. (Hubble Space Telescope and Chandra X-ray
Observatory/ NASA, STScI, CfA)
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Degeneracy pressure and white dwarfs.

• Most stable stars are stable because their weight
  is held up by gas pressure.
• White dwarfs are stars which are stable, but
  their weight is held up by the electron
  degeneracy pressure.
• White dwarfs are created from normal stars at the
  end of their life, when they have run out of
  fuel, cant generate sufficient thermal pressure,
  and collapse under their own weight.
• The electron degeneracy pressure can prevent
  stars from from collapsing so far that they
  acquire horizons and become black holes.

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White dwarfs.

• White dwarfs are stars similar in mass and
  temperature to normal stars, but are much fainter
  and much smaller - the size of planets.
  Discovered in 1862, they were a hot topic in
  astronomy in the 1920s. Thousands are known
  today.
• Sirius, the brightest star in the sky, has a
  companion star which is a white dwarf. The
  contrast between these stars is huge at visible
  wavelengths, but much smaller for X-rays.

Sirius B
Sirius A
Chandra X-ray Observatory image (NASA/CfA)
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White dwarfs.
X-Ray Image
Optical Image
The central star in this planetary nebula, NGC
6543, is well on its way to becoming a white
dwarf. (Hubble Space Telescope and Chandra X-ray
Observatory/ NASA, STScI, CfA)
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White dwarfs Sirius B.

• From its measured distance from Sirius A and
  their orbital period (plus Newtons laws), we
  know that the mass of Sirius B is 1 Msun.
• From its observed color (blue-white), we know
  that its temperature is rather high 29,200K,
  compared to 5,500K for the Sun and 10,000K for
  Sirius A.
• Its luminosity is only 0.003 Lsun, much less than
  that of Sirius A (13 Lsun).
• From all of this information, astronomers can
  determine the diameter of Sirius B. The result
  is 9.8 x 103 km, slightly smaller than that of
  the Earth (1.3 x 104 km).
• Thus, Sirius B has the mass of a star, but the
  size of a planet.

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White dwarfs.

• What did we conclude so far about white dwarfs
• Electron degeneracy generates the pressure that
  prevents the star from collapsing.
• A white dwarf has the mass of a star, but the
  size of a planet.
• Eventually, the white dwarf will cool down and
  become a brown dwarf.

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The theory of white dwarfs.

• Chandrasekhar developed the theory of white
  dwarfs, by combining the theory of degeneracy
  pressure with the standard theory of stellar
  structure.
• The theory predicted a size close to that
  observed for Sirius B.
• The theory also predicted that higher-mass white
  dwarfs are smaller in size. This makes sense
  since the gravitational force increases with
  increasing mass, and an increase in degeneracy
  pressure requires a smaller star.

Chandrasekhar (19101995)
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Chandrasekhars first theory of white dwarfs.
Circumference (cm)
Earths Circumference
Mass (Msun)
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Chandrasekhars theory of white dwarfs.

• For stars heavier than about a solar mass,
  Chandrasekhar found that the confinement imparted
  so much energy to the electrons in the center of
  the star that the electron speeds are close to
  the speed of light.
• Fowlers theory of degenerate matter did not take
  Einsteins special theory of relativity into
  account. Chandrasekhar had to start over, and
  combine relativity and quantum mechanics into a
  new theory of relativistic degeneracy pressure.

Chandrasekhar (19101995)
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Chandrasekhars theory of white dwarfs.

• The more massive the degenerate star, the closer
  the electron speeds get to the speed of light.
• The closer the speed of the electrons get to the
  speed of light, the harder it is to accelerate
  the electrons further.
• Thus, the electron degeneracy pressure doesnt
  keep increasing as much with tighter confinement
  the electrons reach a point where they cannot
  move any faster. There is a maximum to the
  electron degeneracy pressure, and a corresponding
  maximum weight that degeneracy pressure can
  support.
• If the weight cannot be supported by electron
  degeneracy pressure, the degenerate star will
  collapse to smaller sizes.

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Chandrasekhars relativistic theory of white
dwarfs.
Circumference (cm)
Earths Circumference
Mass (Msun)
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Chandrasekhars relativistic theory of white
dwarfs.

• Important result of the theory there is a
  maximum mass for white dwarfs, which turns out to
  be 1.4 Msun. Electron degeneracy pressure cannot
  hold up a heavier mass.
• Implication for stars with core mass less than
  1.4 Msun, core collapse is stopped by electron
  degeneracy pressure before the horizon size is
  reached.
• However, for stars with cores more massive than
  1.4 Msun, the weight of the star overwhelms
  electron degeneracy pressure, and the collapse
  can keep going.
• What can stop heavier stars from collapsing all
  the way to become black holes after they burn out?

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Chandrasekhars relativistic theory of white
dwarfs.
The Sun and smaller stars will become white
dwarfs after they burn out and, lacking the gas
pressure generated by their nuclear heat source,
collapse under their weight. What about Sirius
A, which weighs a good deal more than the limit?
Sun, if it does not loose any mass
Sirius A
Small star
Circumference (cm)
??
Mass (Msun)
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Chandrasekhars relativistic theory of white
dwarfs.
Seven white dwarfs
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Chandrasekhars relativistic theory of white
dwarfs.

• Today, thousands of white dwarf stars are known.
  All stellar masses under 1.4 Msun are
  represented, but no white dwarf heavier than 1.4
  Msun has ever been found.
• For this work, Chandrasekhar was awarded the 1983
  Nobel Prize in Physics.
• The NASA Chandra X-ray Observatory (CXO) is named
  in his honor.

Chandrasekhar (19101995)
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NASA's Chandra X-ray Observatory.

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Enough for today.Good luck studying for exam 1.
IC 1396 H-Alpha Close-Up Credit Nick Wright
(University College London), IPHAS Collaboration