Impact of photo-evaporative mass loss on masses and radii of water-rich sub/super-Earths

Context. Recent progress in transit photometry opened a new window to the interior of super-Earths. From measured radii and masses, we can infer constraints on planetary internal compositions. It has been recently revealed that super-Earths orbiting close to host stars (i.e., hot super-Earths) are diverse in composition. This diversity is thought to arise from diversity in volatile content. Aims. The stability of the volatile components, which we call the envelopes, is to be examined, because hot super-Earths, which are exposed to strong irradiation, 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, which we investigate in this study. To obtain theoretical prediction to future observations, we also investigate the relationships among masses, radii, and semi-major axes of water-rich super-Earths and also sub-Earths that have undergone photo-evaporative mass loss. Methods. We simulate the interior structure and evolution of highly-irradiated sub/super-Earths that consist of a rocky core surrounded by a water envelope, which include mass loss due to the stellar XUV-driven energy-limited hydrodynamic escape. Results. We find that the photo-evaporative mass loss has a significant impact on the evolution of hot sub/super-Earths. With a widely-used empirical formula for XUV flux from typical G-stars and the heating efficiency of 0.1 for example, the planets of less than 3 Earth masses orbiting 0.03 AU have their water envelopes completely stripped off. 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. Conclusions. We constrain the domain in the parameter space of planetary mass, radius, and the semi-major 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.