# If the sun and stars are supported by gas pressure, what supports a white dwarf?

Feb 17, 2016

White Dwarfs are supported by electron degeneracy pressure .

#### Explanation:

The degeneracy pressure is a kind of pressure that appears as a result of Pauli Exclusion Principle, a purely quantum mechanical effect.

I can try explaining what this degeneracy pressure is. But understanding this requires some basic ideas from quantum mechanics.

You can see a white dwarf as a gravitational potential well, confining free electrons - which are fermions. So the system can be modelled as fermionic particles in a box. Particles like electrons cannot have arbitrary energy. Energy is quantised in quantum mechanics and the allowed discrete values of energies are arranged into energy states. Fermions are subject to the Pauli Exclusion Principle, according to which there can be no more than two electrons in a energy state (corresponding to two different spin states).

So electrons cannot all go into lower energy state. If we try to pack electrons into lower energy state the quantum law that excludes two fermions from occupying the same quantum state would manifest as a pressure called the degeneracy pressure which prevents any further gravitational compaction. So the electron degeneracy pressure supports a white dwarf against gravitational collapse.

Subrahmanyam Chandrasekhar found that there is a maximum limit for the mass of a star that can be supported against gravitational collapse by electron degeneracy pressure. This mass limit is called the Chandrashekhar Limit and has a value of about $1.4 {M}_{s u n}$. A White Dwarf that exceeds this value has no choice but to collapse further to become a Neutron Star or a Black Hole.