Abstract
<jats:p>M dwarfs are prime targets for exoplanet searches due to their low masses and radii, which enable the detection of small planets in their habitable zones (HZs). However, the magnetic activity of M dwarfs can introduce signals in radial velocity measurements that may be mistaken for planetary signatures, making the understanding of stellar activity cycles crucial for accurate planet detection and characterisation. We aim to identify and characterise long-term magnetic activity cycles in M dwarfs using a homogeneous and extensive spectroscopic dataset in order to better understand their magnetic variability and its implications for exoplanet detection. We analysed 13 years of high-resolution spectra obtained with the SOPHIE spectrograph for two early M dwarfs known to host exoplanets. We simultaneously monitored chromospheric activity using two indicators, the Hα index and the Mount Wilson S-index. Long-term trends were modelled using both sinusoidal and low-order polynomial fits to robustly identify stellar activity cycles. As a complement, we used TESS photometric data to assess the short-term variability of both targets. We detected long-term variability consistent with stellar magnetic cycles in both targets. For GJ 617A, we report a cycle of approximately 4.8 years, while for GJ 411, we find several characteristic timescales of variability of about 4.9 years. In addition, TESS photometric data reveal signs of short-term variability in GJ617A. The periods of the long-term variability detected for GJ 617A and GJ 411 do not coincide with any of the planetary signals previously reported, which reinforces the hypothesis that they are of magnetic origin. If indeed the variability is due to activity, the cycles detected would not be driven by the same mechanism: The cycle in GJ 617A is consistent with a solar-like dynamo, while the rotation seems to play a different role in the long-term cycles detected in GJ 411.</jats:p>