5.10.4 White Dwarfs & 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

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

Worked Example

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