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Atmospheric magnetic fields in stars with convective envelopes heat stellarchromospheres. Starting with the historical Mount Wilson monitoring program,CaH&K lines have been widely used to trace stellar magnetic activity, and as aproxy for rotation period and consequently for stellar age. Monitoring stellaractivity has also become essential in filtering out false-positives due tomagnetic activity in extra-solar planet surveys. The Ca H&Kemission istraditionally quantified through the R'HK-index, which compares thechromospheric 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-dwarfswere left out of these analyses and no calibration of their Ca ii H&K emissionto an R'HK exists to date. We set out to characterize the magnetic activity ofthe low and very low-mass stars by providing a calibration of the R'HK-indexthat extends to the realm of M-dwarfs, and by evaluating the relation betweenR'HK and the rotation period. We calibrated the bolometric and photosphericfactors for M-dwarfs to properly transform the S-index into the R'HK. Wemonitored magnetic activity through the Ca ii H&K emission lines in the HARPSM-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 arounda ten days rotation period. Above that period, slower rotators show weaker Caii 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 constantbasal activity above 0.6Msun and then decreasing with mass between 0.6Msun andthe fully-convective limit of 0.35Msun. Short-term variability of the activitycorrelates with its mean level, stars with higher R'HK index show larger R'HKvariability, as previously observed for earlier spectral types.

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