What specific measure of intrinsic brightness corresponds to the vertical axis of the H-R diagram?

Absolute magnitude

The vertical axis on the Hertzsprung-Russell diagram measures a star's luminosity, which is defined as its true, intrinsic energy output, independent of its distance from an observer. The standard way astronomers quantify this intrinsic brightness on the diagram is by using absolute magnitude. It is vital to distinguish this from apparent brightness, which describes how bright a star seems from Earth but is dependent on distance. On the absolute magnitude scale used here, lower or even negative numbers signify much brighter stars, placing them higher on the vertical scale. Conversely, dim stars correspond to higher positive magnitude numbers, situated lower down the diagram. This logarithmic scale allows the comparison of actual power output across vast cosmic distances.