Magnetic field and rotation in lower main-sequence stars: An empirical time-dependent magnetic Bode's relation?

We find a significant correlation between the magnetic and rotational moments for a sample of 112 lower main-sequence stars. The rotational moment is calculated from measurements of the rotation period in most of the stars (not from the projected rotational velocity inferred from Doppler broadening). The magnetic moment is computed from a database of homogeneous measurements of the mean level of Ca II H and K emission fluxes sampled for most of the stars over an interval of 25 yr. The slope connecting the logarithm of the magnetic moment and the logarithm of the rotational moment is about + 0.5-0.6, with a Pearson correlation coefficient of about + 0.9. The scatter of points from the mean relation has a component that is natural and caused by decade-long surface variability.