White Dwarfs & the Chandrasekhar Limit (OCR A Level Physics): Revision Note

White Dwarf's & the Chandrasekhar Limit

• A white dwarf is the remnant of a low mass star

• At the end of the star’s life, the outer layers of the star have been ejected, leaving a core which is:

  • Very hot

  • Dense

  • Solid

• Nuclear fusion no longer takes place and the heavier elements (usually carbon and oxygen) remain

  • Instead, it radiates energy in the form of photons from previous fusion reactions

Electron Degeneracy Pressure

• Matter is compressed into a very small volume when the core of a star collapses

• The electrons in the atoms are no longer free to move between  energy levels

• Electrons are forced to fill the available energy levels

  • Electrons fill the lowest available energy levels first

  • Usually, only excited electrons will fill the higher energy levels

  • Compression of the matter in a collapsing core forces electrons into higher energy levels, not because they are in a higher energy state, but because there is nowhere else to go

  • This rush of electrons to find an available space creates a pressure called electron degeneracy pressure, resulting in an outward acting force

• For a low-mass star, the outward electron degeneracy pressure balances the inward gravitational force, preventing further collapse and resulting in a stable white dwarf star

Car Park Analogy for Electron Degeneracy Pressure

The Chandrasekhar Limit

• The Chandrasekhar limit is the maximum mass of a stable white dwarf star

• This is when the mass of a core is up to 1.4 times the mass of the Sun

  The Chandrasekhar limit of a white dwarf is 1.4 M_Sun

• If a white dwarf exceeds the Chandrasekhar limit:

  • Electron degeneracy pressure no longer can prevent the collapse of the core

  • Protons and electrons combine to become neutrons - this is how a neutron star forms

• A low-mass star will:

  • Become a red giant and then a white dwarf

  • If the core's mass is less than 1.4 M_Sun 

• A high-mass star will:

  • Become a red supergiant and then a neutron star or a black hole

  • If the core's mass is greater than 1.4 M_Sun