Electron degeneracy pressure and white dwarfs

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Electron degeneracy pressure and white dwarfs

• Quantum mechanics of cold particles in a box
• Electron degeneracy pressure
• Structure of white dwarfs

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I.3 Cold particle in a box

• Consider three electrons in a box. Suppose they
  are as cold as you can make them they are in
  their quantum ground state.

Length L
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• For a given particle, its kinetic energy is
• So total kinetic energy is

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• What happens if we squeeze the box?
• Particle energies go up as L is decreased. We
  must be doing work on the box. We are doing work
  against degeneracy pressure.

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• Detailed calculation shows that (provided it is
  not too dense) the electron degeneracy pressure
  of a cold gas is
• The maximum electron momentum is

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A connection to something familiar

• Whats the typical distance between electrons?
• Whats typical momentum of electron?
• So for two neighboring electrons

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Discussion point

• Is the metal frame of your chair degenerate?
• You will need to know

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Discussion point

• Is the professor degenerate?

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I.4 Electron degeneracy pressure and White Dwarfs

• Electron degeneracy is responsible for balancing
  gravity in White Dwarfs

Pressure gradient weight
gravity
ED pressure
with
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• So, an approximate expression for radius of white
  dwarf is
• Exact calculation gives

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Discussion point

• Remind each other how White Dwarfs fit into the
  general picture of stellar evolution. Given
  this, why have I chosen to scale the white dwarf
  mass-radius relation to ?2 ?

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