  Tidally locked terrestrial planets around low-mass stars are the prime
targets for future atmospheric characterizations of potentially habitable
systems, especially the three nearby ones--Proxima b, TRAPPIST-1e, and LHS
1140b. Previous studies suggest that if these planets have surface ocean they
would be in an eyeball-like climate state: ice-free in the vicinity of the
substellar point and ice-covered in the rest regions. However, an important
component of the climate system--sea ice dynamics has not been well studied in
previous studies. A fundamental question is: would the open ocean be stable
against a globally ice-covered snowball state? Here we show that sea-ice drift
cools the ocean's surface when the ice flows to the warmer substellar region
and melts through absorbing heat from the ocean and the overlying air. As a
result, the open ocean shrinks and can even disappear when atmospheric
greenhouse gases are not much more abundant than on Earth, turning the planet
into a snowball state. This occurs for both synchronous rotation and spin-orbit
resonances (such as 3 to 2). These results suggest that sea-ice drift strongly
reduces the open ocean area and can significantly impact the habitability of
tidally locked planets.
