How does the mass of a white dwarf relate to its radius?

The relationship between the mass of a white dwarf and its radius is an important concept in astrophysics, primarily described by the principles of electron degeneracy pressure and the effects of gravity. A white dwarf is the remnant core of a star that has exhausted its nuclear fuel, and as it cools down, it is supported against gravitational collapse by electron degeneracy pressure.

As the mass of a white dwarf increases, its gravitational force also increases. However, because of the principles governing electron degeneracy pressure, the increased mass leads to compression of the star, making the white dwarf denser and ultimately smaller in size. This is contrary to what one might intuitively expect, where a more massive object is often assumed to be larger. In this case, due to the balance of forces at play, a more massive white dwarf will actually have a smaller radius.

This phenomenon is encapsulated in the concept of the Chandrasekhar limit, which is roughly 1.4 solar masses. Above this limit, the electron degeneracy pressure cannot support the increased gravitational force, leading to the potential collapse of the white dwarf into a neutron star or black hole. Thus, the correct answer highlights the inverse relationship between the mass and radius of white dwarfs, emphasizing that