  (abridged) We investigate the long-term evolution of X-ray coronae of solar
analogs based on high-resolution X-ray spectroscopy and photometry with
XMM-Newton. Six nearby main-sequence G stars with ages between ~0.1 Gyr and
\~1.6 Gyr and rotation periods between ~1d and 12.4d have been observed. We
derive coronal element abundances and the coronal emission measure distribution
(EMD). The abundances change from an inverse-First Ionization Potential (FIP)
distribution in stars with ages around 0.1 Gyr to a solar-type FIP distribution
in stars at ages of 0.3 Gyr and beyond. The coronal EMDs show shapes
characterized by power-laws on each side of the EMD peak. The latter shifts
from temperatures of about 10 MK in the most rapidly rotating, young stars to
temperatures around 4 MK in the oldest target considered here. The power-law
index on the cooler side of the EMD exceeds expected slopes for static loops,
with typical values being 1.5-3. We interpret this slope with a model in which
the coronal emission is due to a superposition of stochastically occurring
flares, with an occurrence rate that is distributed in radiated energy E as a
power-law, dN/dE ~ E^-a. Our EMDs indicate a ~ 2.2-2.8, in excellent agreement
with values previously derived from light curves of magnetically active stars.
We derive the range of flare energies required to explain the light-curve
modulation. In an overall scenario, we propose that flaring activity plays a
larger role in more active stars. In this model, the higher flare rate is
responsible both for the higher average coronal temperature and the high
coronal X-ray luminosity, two parameters that are indeed found to be
correlated.
