White dwarfs like Procyon B have low luminosities because they are extremely small and have exhausted most of their nuclear fuel. These stars are the remnants of low to medium-mass stars, which have exhausted their nuclear fuel and have collapsed under their own gravity. During this process, the outer layers of the star are ejected into space, leaving behind a dense core of electron-degenerate matter. This core is composed mostly of carbon and oxygen nuclei and is held up by electron degeneracy pressure, which is a result of the Pauli exclusion principle. The core is very hot initially and radiates its energy away, causing the white dwarf to glow brightly for a short period of time. However, since white dwarfs have small masses and radii, they have low surface areas and thus emit very little radiation. This, in turn, results in low luminosities.