Magnetic structure in cool stars. XIII - Appropriate units for the rotation-activity relation

The paper compares relations between coronal and chromospheric emissions, and between activity and stellar rotation, in which the radiative emissions that measure the magnetic activity of cool stars are expressed in different units. The surface flux density appears to be the most suitable unit in which to express the radiative emission measuring stellar magnetic activity: the luminosity introduces an extra dependence on stellar radius, whereas the flux density normalized by the bolometric flux density introduces a dependence on color. The dependence on color in the relation between rotation period and radiative flux density cannot be repaired by a simple color-dependent scaling of the rotation period. For example, dividing the rotation period by the turnover time of convective eddies cannot yield a single, color-independent relation between rotation and activity, and this scaling disrupts the similarity in behavior of dwarfs and giants in the rotation-activity relation.