Characterizing X-ray activity cycles of young solar-like stars with solar observations

Throughout an activity cycle, magnetic structures rise to the stellar surface, evolve and decay. Tracing their evolution on a stellar corona allows us to characterize the X-ray cycles. However, directly mapping magnetic structures is feasible only for the Sun, while such structures are spatially unresolved with present-day X-ray instruments on stellar coronae. We present here a new method, implemented by us, that indirectly reproduces the stellar X-ray spectrum and its variability with solar magnetic structures. The technique converts solar corona observations into a format identical to that of stellar X-ray observations and, specifically, XMM-Newton spectra. From matching these synthetic spectra with those observed for a star of interest, a fractional surface coverage with solar magnetic structures can be associated to each X-ray observation. We apply this method to two young solar-like stars: $\epsilon$ Eri ($\sim 400$ Myr), the youngest star to display a coronal cycle ($\sim 3$ yr), and Kepler 63 ($\sim 200$ Myr), for which the X-ray monitoring did not reveal a cyclic variability. We found that even during the cycle minimum a large portion of $\epsilon$ Eri's corona is covered with active structures. Therefore, there is little space for additional magnetic regions during the maximum, explaining the small observed cycle amplitude ($\Delta f \sim 0.12$) in terms of the X-ray luminosity. Kepler 63 displays an even higher coverage with magnetic structure than the corona of $\epsilon$ Eri. This supports the hypothesis that for stars younger than $