Question

1. A white dwarf has a greater mass than either a red dwarf or a brown dwarf. Yet a white dwarf has a smaller radius than either a red dwarf or a brown dwarf. Explain why, in terms of the types of pressure that keep the different kinds of dwarfs from collapsing under their own gravity.

Answer 1

The masses of red dwarf and brown dwarf are less than the mass of a typical white dwarf which weighs around 1.2 solar masses. But it's radius is only a few kilometres. This is simply because of the absence of any pressure to counteract the gravitational collapse. In normal stars on the main sequence,there is always a battle between the outward pressure of fusion (which wants to expand the star) and inward pressure due to the gravitation(which wants to compress the star). As long as the star remains on the main sequence, there's an equilibrium between these two pressures.

Red dwarfs are supported by the fusion pressure and however, brown dwarfs are not massive enough to trigger hydrogen fusion, they are massive enough to generate enough heat in the core by fusing deuterium, to maintain their size.  But as soon as the star runs out of hydrogen to burn,the outward fusion pressure weakens and gravity starts to compress the star's core. In more massive stars, this compression heats up the core and helium fusion begins, making the star stable once again. But this helium fusion does not take place in stars which have masses smaller than 1.44Mo. for such stars,the compression continues until the gasses in the star become degenerate. Again,these stars are not massive enough to cause neutron degeneracy,so they give rise to electron degeneracy. Electron degeneracy is basically a stellar application of Pauli's exclusion principle. According to this principle,it is impossible to force two electrons to occupy the same Quantum state, even under the force of a collapsing star. So basically we can say that the star has been compressed so much,that it's electrons simply cannot get any closer to each other and this gives rise to the degeneracy pressure. This pressure halts the compression and star stops contracting,but only after it has shrunken to a radius of a few kilometres. Unlike red dwarfs and brown dwarfs,the mechanism that halts the contraction of the star,is triggered too late to maintain a large radius. Therefore white dwarfs have a smaller radius than red dwarfs and brown dwarfs.