Potential Surface Ice Distribution on Close-in Terrestrial Exoplanets around M dwarfs

Previous studies suggested that surface ice could be distributed on close-in terrestrial exoplanets around M-dwarfs if heat redistribution on the planets is very inefficient. In general, orbital and atmospheric parameters play an important role in the climate on terrestrial planets, including the cold-trap region where the permanent surface water reservoir can potentially be distributed. Here, we develop a simple coupled land-atmosphere model to explore the potential surface ice distribution on close-in terrestrial planets with various orbital and atmospheric parameters, assuming that the planets are airless or have a thin \ce{N2} atmosphere. We find that the most significant factors in deciding the surface cold trap region are the spin-orbit ratio and obliquity. The incident stellar flux and the surface pressure play a limited role in the thin \ce{N2} simulations for incident flux smaller than Mercury's and surface pressure lower than 10$^4$ Pa. Our result illustrates the possible distribution of surface ice on arid terrestrial planets and can help to understand the climate of these exoplanets.