A study of the magnetic activity and variability of GJ 436

We present a magnetic activity study of GJ 436 using spectroscopic data from HARPS, spanning over 14 yr, and additional data from NARVAL, falling within the HARPS observations. We study the Ca II H&K, He I D3, Na I doublet, H α, and Ca II IRT triplets lines and explore linear correlations between them. Using the full HARPS data set, we found indices H α versus Ca II H&K & H α versus He I to correlate positively. From the NARVAL data set, covering one observing epoch, we found Ca II IRT₃ versus Ca II IRT₂ & Ca II IRT₃ versus H α index to correlate negatively. We investigate long and short-term periodicity in these index variations, using the Generalized Lomb-Scargle periodogram. For Ca II H&K, Na I and H α indices, we detect long-term periods of 2470.7 d (∼ 6.8 yr), 1861.6 d (∼ 5.1 yr), and 2160.9 d (∼ 5.9 yr) respectively, consistent with GJ 436's photometric cycle of ∼ 7.4 yr. Applying the 'Pooled Variance' technique to H α & Na I indices, we found ∼ 2500 d to be the period of an activity cycle mechanism, in good agreement with the detected 2470.7 d period. For Ca II H&K and H α indices, we detect short-term periods of 39.47^+0.11_−0.15 d and 40.46^+0.44_−0.52 d, respectively, identified as the stellar rotation period. The stellar rotation is detected after pre-whitening the long-term periodicity. It is detected as well in the analysis of individual observing epochs.