EI Eridani: A star under the influence The effect of magnetic activity in the short and long term

Context. Homogeneous photometric time series spanning decades provide a unique opportunity to study the long-term cyclic behavior of active spotted stars such as our target EI Eridani. In addition, with ultraprecise space photometry data, it is possible to investigate the accompanying flare activity in detail. However, the rotation period of approximate to 2 days for EI Eri makes it impossible to achieve time-resolved surface images from a single ground-based observing site. Therefore, for this purpose, spectroscopic data from a multi-site observing campaign are needed. Aims. We use our photometric time series of more than 40 yr to analyze the long-term behavior of EI Eri. We investigate flare activity using photometric data obtained with the Transiting Exoplanet Survey Satellite (TESS). The MUlti-SIte COntinuous Spectroscopy (MUSICOS) campaign in 1998 was designed to achieve high-resolution, multi-wavelength spectroscopic observations from many sites around the globe, which meant that uninterrupted phase coverage of EI Eri became available. We use these data to reconstruct successive surface-temperature maps of the star in order to study the changes of starspots on a very short timescale. Methods. We used long-term seasonal period analysis of our photometric time series to study changes in the rotational period. We also applied short-term Fourier-transform to look for activity cycle-like changes. We also studied the phase and frequency distribution of hand-selected flares. We applied our multi-line Doppler imaging code to reconstruct four consecutive Doppler images. These images were also used to measure surface differential rotation with our cross-correlation technique. In addition, we carried out tests to demonstrate how Doppler imaging is affected by the fact that the data came from several different instruments with different spectral resolutions. Results. Seasonal period analysis of the light curve reveals a smooth, significant change in period, possibly indicating the evolution of active latitudes. Temperature curves from B - V and V - I show slight differences, indicating the activity of EI Eri is spot dominated. Short-term Fourier transform reveals smoothly changing cycles of between 4.5 and 5.5 yr and of between 8.9 and 11.6 yr. The time-resolved spotted surface of EI Eri from Doppler imaging enabled us to follow the evolution of the different surface features. Cross-correlating the consecutive Doppler maps reveals surface shear of alpha = 0.036 +/- 0.007. Our tests validate our approach and show that the surface-temperature distribution is adequately reconstructed by our method. The tests also indicate how accurately the cross-correlation method can reproduce the surface shear as a function of the spectral resolution.