|Let's use these expressions for pressure to figure
out the size of white dwarfs.
We had two expressions: one from hydrostatic equilibrium, and one from degeneracy pressure. If the WD is to be in equilibrium, these pressures must balance.
In this case we derive the mass-radius relationship for white dwarfs:
But as we look at more and more massive white dwarfs, they will have higher and higher densities. The electrons will be found in higher and higher energy states, so their speed will approach the speed of light. What happens if we do the same calculation with relativistic degeneracy?
We get a strange result: for relativistic degeneracy, you tend to a constant mass. But this can't really happen: if you add more mass, you need faster-than-light electrons to support the WD, which is impossible. If there is too much mass, the WD will collapse.
This means the "constant mass" is actually a maximum mass that can be supported by degeneracy. This maximum mass is known as the Chandraskhar Limit, and is
Mch = 1.44 Msun
So we can plot the Mass-Radius relationship for white dwarfs: