  We investigate the stability of super Earth atmospheres around M stars using
a 7-parameter, analytical framework. We construct stability diagrams in the
parameter space of exoplanetary radius versus semi-major axis and elucidate the
regions in which the atmospheres are stable against the condensation of their
major constituents, out of the gas phase, on their permanent nightside
hemispheres. We find that super Earth atmospheres which are nitrogen-dominated
("Earth-like") occupy a smaller region of allowed parameter space, compared to
hydrogen-dominated atmospheres, because of the dual effects of diminished
advection and enhanced radiative cooling. Furthermore, some super Earths which
reside within the habitable zones of M stars may not possess stable
atmospheres, depending on the mean molecular weight and infrared photospheric
pressure of their atmospheres. We apply our stability diagrams to GJ 436b and
GJ 1214b, and demonstrate that atmospheric compositions with high mean
molecular weights are disfavoured if these exoplanets possess solid surfaces
and shallow atmospheres. Finally, we construct stability diagrams tailored to
the Kepler dataset, for G and K stars, and predict that about half of the
exoplanet candidates are expected to habour stable atmospheres if Earth-like
conditions are assumed. We include 55 Cancri e and CoRoT-7b in our stability
diagram for G stars.
