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

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Katie M


Katie M



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 MSun

  • 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 MSun 
  • 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 MSun

Worked example

Once fusion has been exhausted in some red giant stars, it will begin to expel its outer layers until a white dwarf remains.

Which of the following could be the mass of a white dwarf?

You may take the mass of the Sun to be 2.0 × 1030 kg.



   2.5 × 1030 kg



   3.0 × 1030 kg



   2.0 × 1031 kg



   2.8 × 1031 kg

The correct answer is: A

Step 1: List the known quantities

    • Solar mass = 2.0 × 1030 kg

Step 2: Calculate the mass of a white dwarf at the Chandrasekhar limit

    • The Chandrasekar Limit is 1.4 solar masses
    • Multiply the solar mass by the Chandrasekhar limit

1.4 × (2.0 × 1030 kg) = 2.8 × 1030 kg

Step 3: Identify the mass given in the question that is below 2.8 × 1030 kg

    • Masses below 2.8 × 1030 kg will form stable white dwarf stars
    • Masses above 2.8 × 1030 kg will not form stable white dwarf stars
    • Therefore, the only mass that fits this criterion is 2.5 × 1030 kg

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Katie M

Author: Katie M

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

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