Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program I. Comparison of activity indices

Aims. Other stars are known to have magnetic cycles similar to that of the Sun. The relationship between these activity variations and the observed radial-velocity is still not satisfactorily understood. In this first paper our aim is to assess the long-term activity variations in the low end of the main sequence, having in mind a planetary search perspective. Methods. We used a sample of 30 M0-M5.5 stars from the HARPS M-dwarf planet search program with a median timespan of observations of 5.2 years. We computed chromospheric activity indicators based on the Ca II H and K, H{\alpha}, He I D3, and Na I D1 and D2 lines. All data were binned in to average out undesired effects such as rotationally modulated atmospheric inhomogeneities. We searched for long-term variability of each index and determined the correlations between them. Results. While the S_CaII, H{\alpha}, and Na I indices showed significant variability for a fraction of our stellar sample (39%, 33%, and 37%, respectively), only 10% of our stars presented significant variability in the He i index. We therefore conclude that this index is a poor activity indicator at least for this type of stars. Although the H{\alpha} shows good correlation with S_Ca II for the most active stars, the correlation is lost when the activity level decreases. This result appears to indicate that the Ca II-H{\alpha} correlation is dependent on the activity level of the star. The Na I lines correlate very well with the S_Ca II index for the stars with low activity levels we used, and are thus a good chromospheric activity proxy for early-M dwarfs. We therefore strongly recommend the use of the Na I activity index because the signal-to-noise ratio in the sodium lines spectral region is always higher than for the calcium lines.