  Rocky planets orbiting M-dwarf stars are among the most promising and
abundant astronomical targets for detecting habitable climates. Planets in the
M-dwarf habitable zone are likely synchronously rotating, such that we expect
significant day-night temperature differences, and potentially limited
fractional habitability. Previous studies have focused on scenarios where
fractional habitability is confined to the substellar or "eye" region, but in
this paper we explore the possibility of planets with terminator habitability,
defined by the existence of a habitable band at the transition between a
scorching dayside and a glacial nightside. Using a global climate model, we
show that for water-limited planets it is possible to have scorching
temperatures in the "eye" and freezing temperatures on the nightside, while
maintaining a temperate climate in the terminator region, due to a reduced
atmospheric energy transport. Whereas on water-rich planets, increasing stellar
flux leads to increased atmospheric energy transport and a reduction in
day-night temperature differences, such that the terminator does not remain
habitable once the dayside temperatures approach runaway or moist greenhouse
limits. We also show that, while water-abundant simulations may result in
larger fractional habitability, they are vulnerable to water loss through
cold-trapping on the nightside surface or atmospheric water vapor escape,
suggesting that even if planets were formed with abundant water, their climates
could become water-limited and subject to terminator habitability.
