  Distant planets in globally ice-covered, "snowball", states may depend on
increases in their host stars' luminosity to become hospitable for surface
life. Using a General Circulation Model (GCM), we simulated the equilibrium
climate response of a planet to a range of instellations from an F-, G-, or M-
dwarf star. The range of instellation that permits both complete ice cover and
at least partially ice-free climate states is a measure of the climate
hysteresis that a planet can exhibit. An ice-covered planet with high climate
hysteresis would show a higher resistance to the initial loss of surface ice
coverage with increases in instellation, and abrupt, extreme ice loss once
deglaciation begins. Our simulations indicate that the climate hysteresis
depends sensitively on the host star spectral energy distribution. Under fixed
CO2 conditions, a planet orbiting an M-dwarf star exhibits a smaller climate
hysteresis, requiring a smaller instellation to initiate deglaciation than
planets orbiting hotter, brighter stars. This is due to the higher absorption
of near-IR radiation by ice on the surfaces and greenhouse gases and clouds in
the atmosphere of an M-dwarf planet. Increases in atmospheric CO2 further lower
the climate hysteresis, as M-dwarf snowball planets exhibit a larger radiative
response than G-dwarf snowball planets for the same increase in CO2. For a
smaller hysteresis, planets near the outer edge of the habitable zone will thaw
earlier in their evolutionary history, and will experience a less abrupt
transition out of global ice cover.
