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

Abstract: 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.