Long-term stellar activity variations of stars from the HARPS M-dwarf sample: Comparison between activity indices

We used four known chromospheric activity indicators to measure long-term activity variations in a sample of 23 M-dwarf stars from the HARPS planet search program. We compared the indices using weighted Pearson correlation coefficients and found that in general (i) the correlation between $S_{CaII}$ and \ion{Na}{i} is very strong and does not depend on the activity level of the stars, (ii) the correlation between our $S_{CaII}$ and H$\alpha$ seems to depend on the activity level of the stars, and (iii) there is no strong correlation between $S_{CaII}$ and \ion{He}{i} for these type of stars.