Main-sequence companions to white dwarfs - II. The age-activity-rotation relation from a sample of Gaia common proper motion pairs

Magnetic activity and rotation are related to the age of low-mass main-sequence stars. To further constrain these relations, we study a sample of 574 main-sequence stars members of common proper motion pairs with white dwarfs, identified thanks to Gaia astrometry. We use the white dwarfs as age indicators, while the activity indexes and rotational velocities are obtained from the main-sequence companions using standard procedures. We find that stars older than 5 Gyr do not display H alpha nor Ca II H&K emission unless they are fast rotators due to tidal locking from the presence of unseen companions and that the rotational velocities tend to decrease over time, thus supporting the so-called gyrochronology. However, we also find moderately old stars (similar or equal to 2-6 Gyr) that are active presumably because they rotate faster than they should for their given ages. This indicates that they may be suffering from weakened magnetic braking or that they possibly evolved through wind accretion processes in the past. The activity fractions that we measure for all stars younger than 5 Gyr range between similar or equal to 10 and 40 per cent. This is line with the expectations, since our sample is composed of F, G, K, and early M stars, which are thought to have short (<2 Gyr) activity lifetimes. Finally, we observe that the H alpha fractional luminosities and the R '(HK) indexes for our sample of (slowly rotating) stars show a spread (-4 >log(L-H alpha/L-bol); log(R '(HK)) > -5) typically found in inactive M stars or weakly active/inactive F, G, K stars.