I have been reading about white dwarfs, whose radius-mass relation is: $$R \sim M^{-1/3}$$ because of the degeneracy pressure. Could anyone provide me with a qualitative explanation of this relation? I am not capable of understanding how radius decreases as mass increases. Thanks.

• By what mechanism can the radius increase? Assume the added material is cold and has no kinetic energy. – ProfRob Feb 26 '20 at 20:52

The effect is not limited to degenerate matter. Gas giant planets behave the same at mass about Jupiter and above.

Adding mass, you get two effects: you increase gravity that compresses the matter and you increase the amount of matter that piles up. Both effects are profoundly non-linear and interdependent. In some mass intervals increasing gravity overcomes the increased "piling up".