  Recent exoplanet statistics indicate that photo-evaporation has a great
impact on the mass and bulk composition of close-in low-mass planets. While
there are many studies addressing photo-evaporation of hydrogen-rich or
water-rich atmospheres, no detailed investigation regarding rocky vapor
atmospheres (or mineral atmospheres) has been conducted. Here, we develop a new
1-D hydrodynamic model of the UV-irradiated mineral atmosphere composed of Na,
Mg, O, Si, their ions and electrons, includin molecular diffusion, thermal
conduction, photo-/thermo-chemistry, X--ray and UV heating, and radiative line
cooling (i.e., the effects of the optical thickness and non-LTE). The focus of
this paper is on describing our methodology but presents some new findings. Our
hydrodynamic simulations demonstrate that almost all of the incident X-ray and
UV energy from the host-star is converted into and lost by the radiative
emission of the coolant gas species such as Na, Mg, Mg$^+$, Si$^{2+}$,
Na$^{3+}$ and Si$^{3+}$. For an Earth-size planet orbiting 0.02~AU around a
young solar-type star, we find that the X-ray and UV heating efficiency is as
small as $1 \times 10^{-3}$, which corresponds to 0.3~$\Mearth$/Gyr of the mass
loss rate simply integrated over all the directions. Because of such efficient
cooling, the photo-evaporation of the mineral atmosphere on hot rocky
exoplanets with masses of $1\Mearth$ is not massive enough to exert a great
influence on the planetary mass and bulk composition. This suggests that
close-in high-density exoplanets with sizes larger than the Earth radius
survive in the high-UV environments.
