  We investigated the coronal properties of G-dwarf stars including the Sun
over a wide range of X-ray luminosity $L_{\rm X}$ ($3\times 10^{26}$ to
$2\times 10^{30}~{\rm erg~s^{-1}}$). We analyzed the archival data of ten X-ray
bright ($L_{\it X}>10^{28}~{\rm erg~s^{-1}}$) G-dwarf stars to derive their
emission measure (EM) and the coronal temperature ($T$) during the periods when
no prominent stellar flares were observed. We attempted to explain the relation
on the basis of our understanding of the present Sun: a steady corona model
based on the so-called RTV scaling laws and the observed power-law distribution
function of surface magnetic features. We derived a theoretical scaling law of
the EM--$T$ relation for a star with multiple active regions, and applied it to
the observations combined with data in literature. We found that with the solar
parameters, our scaling law seems to be consistent with the data of
slowly-rotating stars. However, more X-ray bright stars are located well above
the scaling law based on the solar parameter. The scaling law may explain the
observations if those stars show a power-law distribution function of active
regions with the same power-law index but a 10-100 times larger coefficient.
This suggests that X-ray bright stars show more active regions for a given size
than the Sun. Since our samples include rapidly-rotating stars, we infer that
the offset of the X-ray bright stars from the present-Sun-based scaling law is
due to the enhancement of the surface magnetic field generation by their rapid
rotation.
