What is the ultimate fate of a star that becomes a black dwarf?

The ultimate fate of a star that becomes a black dwarf involves ceasing to emit detectable light. A black dwarf represents a theoretical stage in the life cycle of a star, specifically a white dwarf that has cooled down significantly over an extended period—many billions of years—after the star has exhausted its nuclear fuel.

In this cooling process, the white dwarf originally emits light due to residual heat but eventually loses that energy. As it cools, it no longer produces light through nuclear fusion, which has already ceased to occur. The star's temperature falls to a point where it transitions into a black dwarf, effectively becoming an inert remnant that fails to emit electromagnetic radiation that can be detected by our instruments.

As for the other choices, nuclear fusion does not occur in black dwarfs, as this phase is characterized by the lack of fusion processes. A black dwarf does not remain luminous due to its low temperature, and the collapse into a neutron star is a condition that arises from more massive stars ending their lives, not from the process leading to a black dwarf. Thus, the correct understanding of a black dwarf is strictly tied to its inability to produce light, marking its fate as an object that ceases to emit detectable energy.