  TRAPPIST-1 planets are invaluable for the study of comparative planetary
science outside our Solar System and possibly habitability. First, we derive
from N-body simulations possible planetary evolution scenarios, and show that
each of the planets are likely to be in synchronous rotation. We then use a 3-D
Global Climate Model to explore the possible climates of cool planets of the
TRAPPIST-1 system. In particular, we look at the conditions required for cool
planets to prevent possible volatile species to be lost by permanent
condensation, irreversible burying or photochemical destruction. We also
explore the resilience of the same volatiles (when in condensed phase) to a
runaway greenhouse process. We find that background atmospheres made of N2, CO
or O2 are resistant to atmospheric collapse. However, it should be difficult
for TRAPPIST-1 planets to accumulate significant greenhouse gases like CO2,
CH4, or NH3. CO2 can easily condense on the nightside, forming glaciers that
would flow toward the substellar region. A complete CO2 ice cover is possible
on TRAPPIST-1g and h only, although CO2 ice deposits could be gravitationally
unstable and get buried beneath the water ice shell in geologically short
timescales. Given TRAPPIST-1 planets large EUV irradiation (at least 1000x
Titan's flux), CH4 and NH3 should be photodissociated rapidly and thus be hard
to accumulate in the atmosphere. Photochemical hazes could then sedimentate and
form a surface layer of tholins. Regarding habitability, we confirm that few
bars of CO2 would suffice to warm the surface of TRAPPIST-1f and g above the
melting point of water. We also show that TRAPPIST-1e is a remarkable candidate
for surface habitability. If the planet is today synchronous and abundant in
water, then it should always sustain surface liquid water at least in the
substellar region, whatever the atmosphere considered.
