A detailed understanding of the rotation-activity relationship using the 300 Myr old open cluster NGC 3532

The coeval stars of young open clusters provide insights into the formation of the rotation-activity relationship that elude studies of multi-age field populations. We measure the chromospheric activity of cool stars in the 300 Myr old open cluster NGC 3532 in concert with their rotation periods to study the mass-dependent morphology of activity for this transitional coeval population. Using multi-object spectra of the Ca ii infrared triplet region obtained with the AAOmega spectrograph at the Anglo- Australian Telescope, we measure the chromospheric emission ratios for 454 FGKM cluster members of NGC 3532. The morphology of activity against colour appears to be a near-mirror image of the cluster's rotational behaviour. In particular, we identify a group of 'desaturated transitional rotators' that branches off from the main group of unsaturated FGK slow rotators, and from which it is separated by an 'activity gap'. The few desaturated gap stars are identical to the ones in the rotational gap. Nevertheless, the rotation-activity diagram is completely normal. In fact, the relationship is so tight that it allows us to predict rotation periods for many additional stars. We then precisely determine these periods from our photometric light curves. Our activity measurements show that all fast rotators of near-solar mass have evolved to become slow rotators, demonstrating that the absence of fast rotators in a colour-period diagram is not a detection issue but an astrophysical fact. We also identify a new population of low-activity stars among the early M dwarfs, enabling us to populate the extended slow rotator sequence in the colour-period diagram. The joint analysis of chromospheric activity and photometric time series data thus enables comprehensive insights into the evolution of the rotation and activity of stars during the transitional phase between the Pleiades and Hyades age. (Abridged)