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How do luminosity classes in the MK system improve spectroscopic parallax estimates?

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Diagram illustrating how astronomers calculate the distance to a star using parallax: Earth is shown in two positions on opposite sides of its orbit around the Sun, with lines extending to a nearby star X and further to distant background stars. The apparent shift in star X's position, measured as angle A, is used to determine its distance, with the baseline labeled as 186,000,000 miles. — Parallax Calculating stellar distances.

In the context of spectroscopic parallax, the MK system improves distance estimates by providing a two-dimensional classification that accounts for both a star's temperature and its intrinsic luminosity.12

While the traditional Henry Draper spectral classification is based primarily on surface temperature, it does not distinguish between stars of different sizes that share the same temperature—such as a small dwarf star and a massive supergiant. The MK system addresses this by assigning one of five luminosity classes (represented by Roman numerals I to V) based on spectral lines that are sensitive to the star's atmospheric pressure and intrinsic brightness.312

By identifying the luminosity class, astronomers can accurately estimate the star's absolute magnitude. Once the absolute magnitude is known, it can be compared with the star's observed apparent magnitude to calculate the distance using the inverse square law. This refinement significantly increases the precision of distance measurements compared to methods relying on spectral type alone.145