A multi-wavelength view of the multiple activity cycles of ? Eridani

e Eridani is a highly active young K2 star with an activity cycle of about 3 yr established using Ca II H& K line index measurements (S-MWO). This relatively short cycle has been demonstrated to be consistent with X-ray and magnetic flux measurements. Recent work suggested a change in the cyclic behaviour. Here, we report new X-ray flux and S-MWO measurements and also include S-MWO measurements from the historical Mount Wilson program. This results in an observational time baseline of over 50 yr for the S-MWO data and of over 7 yr in X-rays. Moreover, we include Ca II infrared triplet (IRT) index measurements (S-Ca IRT) from 2013 to 2022 in our study. With the extended X-ray data set, we can now detect the short cycle for the first time using a periodogram analysis. Near-simultaneous S-MWO data and X-ray fluxes, which are offset by 20 days at most, are moderately strongly correlated when only the lowest activity state (concerning short-term variability) is considered in both diagnostics. In the S-MWO data, we find strong evidence for a much longer cycle of about 34 yr and an 11-yr cycle instead of the formerly proposed 12-yr cycle in addition to the known 3-yr cycle. The superposition of the three periods naturally explains the recent drop in S-MWO measurements. The two shorter cycles are also detected in the S-Ca IRT data, although the activity cycles exhibit lower amplitudes in the S-Ca IRT than in the S-MWO data. Finally, the rotation period of e Eri can be found more frequently in the S-MWO as well as in the S-Ca IRT data for times near the minimum of the long cycle. This may be explained by a scenario in which the filling factor for magnetically active regions near cycle maximum is too high to allow for notable short-term variations.