Chandrasekhar Limit

Chandrasekhar worked out how big a star could be and still separate itself against its own gravity after it had used still s up all its fuel.

The idea was this : When the star becomes small, the matter particles gets very near each other . But the Pauli exclusion principle says that two matter particles cannot have both the same position and same velocity .

The matter particles must therefore have different velocities.

This makes them move away from each other, and so tends to make the star expand. A star can therefore maintain itself at constant radius by a balance between the attraction of gravity and the repulsion that arises from the exclusion principle, just as earlier in its life the gravity was balanced by the heat.

Chandrasekhar realized , however , that there is a limit to the repulsion that the exclusion principle can provide.

The theory of relativity limits the maximum difference in the velocities of the matter particles in the star to the speed of light.

This means that when the star got sufficiently dense, the repulsion caused by the exclusion principle would be less than the attraction of gravity.

Chandrasekhar calculated that a cold star of more than about one and half times the mass of the sun would not be able to support itself against its own gravity. This mass is now known as the Chandrasekhar limit.

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