Recent progress in transit photometry opened a new window to the interior of super-Earths. From measured radii and masses, we can infer planetary internal compositions. It has been recently revealed that super-Earths are diverse in composition. Such a diversity is thought to arise from diversity in volatile content. The stability of the volatile components is to be examined, because hot super-Earths undergo photo-evaporative mass loss. While several studies investigated the impact of photo-evaporative mass loss on hydrogen-helium envelopes, there are few studies as to the impact on water-vapor envelopes. To obtain theoretical prediction to future observations, we also investigate the relationships among masses, radii, and semimajor axes of water-rich sub/super-Earths that have undergone photo-evaporative mass loss. We simulate the interior structure and evolution of sub/super-Earths that consist of a rocky core surrounded by a water envelope, including mass loss due to the stellar XUV-driven energy-limited hydrodynamic escape. We find that the photo-evaporative mass loss has a significant impact on the evolution of hot sub/super-Earths. We then derive the threshold planetary mass and radius below which the planet loses its water envelope completely as a function of the initial water content, and find that there are minimums of the threshold mass and radius. We constrain the domain in the parameter space of planetary mass, radius, and semimajor axis in which sub/super-Earths never retain water envelopes in 1-10 Gyr. This would provide an essential piece of information for understanding the origin of close-in low-mass planets. The current uncertainties in stellar XUV flux and its heating efficiency, however, prevent us from deriving robust conclusions. Nevertheless, it seems to be a robust conclusion that Kepler planet candidates contain a significant number of rocky sub/super-Earths.
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