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

Author

Katie M

Expertise

Physics

## 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.

 A 2.5 × 1030 kg B 3.0 × 1030 kg C 2.0 × 1031 kg D 2.8 × 1031 kg

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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