Chromospheric Ca II activity cycles are frequently found in late-type stars, but no systematic programs have been created to search for their coronal X-ray counterparts. The typical time scale of Ca II activity cycles ranges from years to decades. Therefore, long-lasting missions are needed to detect the coronal counterparts. The XMM-Newton satellite has so far detected X-ray cycles in five stars. A particularly intriguing question is at what age (and at what activity level) X-ray cycles set in. To this end, in 2015 we started the X-ray monitoring of the young solar-like star ɛ Eridani, previously observed on two occasions: in 2003 and in early 2015, both by XMM-Newton. With an age of 440 Myr, it is one of the youngest solar-like stars with a known chromospheric Ca II cycle. We collected the most recent Mount Wilson S-index data available for ɛ Eridani, starting from 2002, including previously unpublished data. We found that the Ca II cycle lasts 2.92 ± 0.02 yr, in agreement with past results. From the long-term XMM-Newton lightcurve, we find clear and systematic X-ray variability of our target, consistent with the chromospheric Ca II cycle. The average X-ray luminosity is 2 × 1028erg s−1, with an amplitude that is only a factor of 2 throughout the cycle. We apply a new method to describe the evolution of the coronal emission measure distribution of ɛ Eridani in terms of solar magnetic structures: active regions, cores of active regions, and flares covering the stellar surface at varying filling fractions. Combinations of these three types of magnetic structures can only describe the observed X-ray emission measure of ɛ Eridani if the solar flare emission measure distribution is restricted to events in the decay phase. The interpretation is that flares in the corona of ɛ Eridani last longer than their solar counterparts. We ascribe this to the lower metallicity of ɛ Eridani. Our analysis also revealed that the X-ray cycle of ɛ Eridani is strongly dominated by cores of active regions. The coverage fraction of cores throughout the cycle changes by the same factor as the X-ray luminosity. The maxima of the cycle are characterized by a high percentage of covering fraction of the flares, consistent with the fact that flaring events are seen in the corresponding short-term X-ray lightcurves predominately at the cycle maxima. The high X-ray emission throughout the cycle of ɛ Eridani is thus explained by the high percentage of magnetic structures on its surface.
Relations between photospheric structure and X-ray emission