What specific duration does the cooling rate of a white dwarf directly measure?

The time elapsed since the white dwarf formed.

The method utilizing white dwarf cooling rates functions as a chronological clock based on thermal decay, rather than tracking the total stellar life cycle. A white dwarf is the dense, hot stellar remnant left after a Sun-like star sheds its outer layers, having ceased fusion processes. Once established, the white dwarf no longer generates internal energy; instead, it radiates away its immense, stored thermal energy through cooling. This cooling process follows a highly predictable physical law. Therefore, measuring the current temperature of a white dwarf allows astronomers to calculate exactly how long this cooling process has been underway, providing a measurement of the time elapsed since the star became a white dwarf. It is important to remember that this measured cooling time must be supplemented by an estimate of the progenitor star's initial evolutionary time to determine the star's total age.