The Chandrasekhar mass

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The Chandrasekhar mass

• Relativistic degeneracy pressure
• The maximum mass of a white dwarf
• The fate of a white dwarf pushed over the limit

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I.5 Relativistic effects on degeneracy pressure

• Consider degenerate cold gas.
• Maximum momentum of particle is
• Assume non-relativistic physics maximum velocity
  given by
• So, particles have to be moving at relativistic
  speeds when density satisfies

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• Onset of relativistic effects makes degeneracy
  pressure less effective than it would otherwise
  be
• WHY??

Rel.
log(P)
Non-rel
log(?)
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Back to white dwarfs

• Look at effect of relativistic electron
  degeneracy in White Dwarfs

Pressure gradient weight
gravity
ED pressure
with
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• For relativistic degeneracy, the mass is
  determined
• Complete calculation gives
• This is called the Chandrasekhar mass it is the
  maximum possible mass of a White Dwarf.

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Subrahmanyan Chandrasekhar
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I.6 Pushing a white dwarf over the edge

• Some white dwarfs are in a binary system and
  accrete matter from a companion star

M.A.Garlick 1998
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so a white dwarf may grow to the Chandrasekhar
mass!
M.A.Garlick 1998
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• Accretion
• Mass approaches Chandrasekhar mass
• Central density and temperature increases
• Then, suddenly
• He or C/O in white dwarf core starts to undergo
  nuclear fusion
• Energy release leads to rapid rise in temperature
• Rise in temperature makes fusion occur faster
• Get a thermonuclear runaway whole star is
  incinerated to iron/nickel in few seconds
• Energy release blows the star apart
• TYPE-1A Supernova

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Some numbers

• Fractional change in mass during fusion
• Energy released
• Velocity induced in debris
• Escape velocity

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Nuclear mass per particle
Iron-56
Nuclear mass / nucleon
Atomic number
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Binding energy
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HST
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Website of K.Krisciunas (Notre Dame)
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Chandra observation of Tycho supernova remnant
(exploded 1572)