  (abridged) Our long-term XMM-Newton program of long-term monitoring of a
solar-like star with a well-studied chromospheric cycle, HD 81809 aims to study
whether an X-ray cycle is present, along with studying its characteristics and
its relation to the chromospheric cycle. Regular observations of HD 81809 were
performed with XMM-Newton, spaced by 6 months from 2001 to 2007. We studied the
variations in the resulting coronal luminosity and temperature, and compared
them with the chromospheric CaII variations. We also modeled the observations
in terms of a mixture of active regions, using a methodology originally
developed to study the solar corona. Our observations show a well-defined cycle
with an amplitude exceeding 1 dex and an average luminosity approximately one
order of magnitude higher than in the Sun. The behavior of the corona of HD
81809 can be modeled well in terms of varying coverage of solar-like active
regions, with a larger coverage than for the Sun, showing it to be compatible
with a simple extension of the solar case.
