Simple scaling laws for the thickness and mean electron density of stellar chromospheres as functions of surface gravity and chromospheric heating are proposed. These scaling laws are shown to be a consequence of hydrostatic equilibrium, the influence of gas ionization on plasma cooling functions, and the assumption that chromospheric heating is relatively constant with height. It is argued that line width-luminosity correlations similar to those observed in the Ca II K and Mg II k resonance lines are implied by the chromospheric scaling laws if the outer edges of the K and k emission cores are formed in the Lorentzian wings of the absorption profile. The results are compared with the Wilson-Bappu effect, empirical width-luminosity correlations for Ca II K1 minimum features, and solar-plage profiles of the Ca II K and Mg II k resonance lines.
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T. R. Ayres (1979) studied this question.