Magnetic activity in the HARPS M-dwarf sample. The rotation-activity relationship for very low-mass stars through R'HK

Atmospheric magnetic fields in stars with convective envelopes heat stellar chromospheres. Starting with the historical Mount Wilson monitoring program, CaH&K lines have been widely used to trace stellar magnetic activity, and as a proxy for rotation period and consequently for stellar age. Monitoring stellar activity has also become essential in filtering out false-positives due to magnetic activity in extra-solar planet surveys. The Ca H&Kemission is traditionally quantified through the R'HK-index, which compares the chromospheric flux in the doublet to the overall bolometric flux of the star. Much work has been done to characterize this index for FGK-dwarfs, but M-dwarfs were left out of these analyses and no calibration of their Ca ii H&K emission to an R'HK exists to date. We set out to characterize the magnetic activity of the low and very low-mass stars by providing a calibration of the R'HK-index that extends to the realm of M-dwarfs, and by evaluating the relation between R'HK and the rotation period. We calibrated the bolometric and photospheric factors for M-dwarfs to properly transform the S-index into the R'HK. We monitored magnetic activity through the Ca ii H&K emission lines in the HARPS M-dwarf sample. The R'HK index, like the fractional X-ray luminosity L_X/Lbol, shows a saturated correlation with rotation, with saturation setting in around a ten days rotation period. Above that period, slower rotators show weaker Ca ii activity, as expected. Under that period, the R'HK index saturates to ~10^-4. Stellar mass modulates the Ca ii activity, with R'HK showing a constant basal activity above 0.6Msun and then decreasing with mass between 0.6Msun and the fully-convective limit of 0.35Msun. Short-term variability of the activity correlates with its mean level, stars with higher R'HK index show larger R'HK variability, as previously observed for earlier spectral types.