Wilson-Bappu effect

The Wilson-Bappu effect is a relation discovered in the 1950s between the luminosity of G-type stars, K-type stars and M-type stars (both their main-sequence and giant variants) and the width (line broadening) of a particular emission line: the Ca II K line (ionized calcium, 393.366 nm, a Fraunhofer line), a width is referred to as W₀. The relation provides a means of stellar distance determination, especially useful for groups of stars, in which case the effects of some variance can be reduced.

The relationship seems odd to me, that the luminosity of the entire star somehow correlates to the broadening of an emission line despite the fact that this luminosity reflects a combination of surface temperature and radius, and a single relation holds for stars of such varying radii. The line is produced in the chromosphere and the effect is potentially a clue to the chromosphere of "stars in general" as opposed to specifically that of the Sun. An obvious candidate-mechanism is Doppler broadening from chromosphere turbulence, but this passes on the mystery to how such chromosphere turbulence could be affected by the total luminosity in such manner.