  The X-ray and extreme-ultraviolet (EUV) emissions from the low-mass stars
significantly affect the evolution of the planetary atmosphere. However, it is,
observationally difficult to constrain the stellar high-energy emission because
of the strong interstellar extinction of EUV photons. In this study, we
simulate the XUV (X-ray+EUV) emission from the Sun-like stars by extending the
solar coronal heating model that self-consistently solves, with sufficiently
high resolution, the surface-to-coronal energy transport, turbulent coronal
heating, and coronal thermal response by conduction and radiation. The
simulations are performed with a range of loop lengths and magnetic filling
factors at the stellar surface. With the solar parameters, the model reproduces
the observed solar XUV spectrum below the Lyman edge, thus validating its
capability of predicting the XUV spectra of other Sun-like stars. The model
also reproduces the observed nearly-linear relation between the unsigned
magnetic flux and the X-ray luminosity. From the simulation runs with various
loop lengths and filling factors, we also find a scaling relation, namely $\log
L_{\rm EUV} = 9.93 + 0.67 \log L_{\rm X}$, where $L_{\rm EUV}$ and $L_{\rm X}$
are the luminosity in the EUV and X-ray range, respectively, in cgs. By
assuming a power-law relation between the Rossby number and the magnetic
filling factor, we reproduce the renowned relation between the Rossby number
and the X-ray luminosity. We also propose an analytical description of the
energy injected into the corona, which, in combination with the conventional
Rosner-Tucker-Vaiana scaling law, semi-analytically explains the simulation
results. This study refines the concepts of solar and stellar coronal heating
and derives a theoretical relation for estimating the hidden stellar EUV
luminosity from X-ray observations.
