We present an analytic model for the interaction between planetary
atmospheres and stellar winds from main sequence M stars, with the purpose of
obtaining a quick test-model that estimates the timescale for total atmospheric
mass loss due to this interaction. Planets in the habitable zone of M dwarfs
may be tidally locked and may have weak magnetic fields, because of this we
consider the extreme case of planets with no magnetic field. The model gives
the planetary atmosphere mass loss rate as a function of the stellar wind and
planetary properties (mass, atmospheric pressure and orbital distance) and an
entrainment efficiency coefficient Ξ±. We use a mixing layer model to
explore two different cases: a time-independent stellar mass loss and a stellar
mass loss rate that decreases with time. For both cases we consider planetary
masses within the range of 1β10 Mββ and atmospheric pressures with
values of 1, 5 and 10 atm. For the time dependent case, planets without
magnetic field in the habitable zone of M dwarfs with initial stellar mass
losses of β€MΛwβ<10β11 Mββ yrβ1, may retain their
atmospheres for at least 1 Gyr. This case may be applied to early spectral type
M dwarfs (earlier than M5). Studies have shown that late type M dwarfs (later
than M5) may be active for long periods of time (β₯4Gyr), and because of
that our model with constant stellar mass loss rate may be more accurate. For
these stars most planets may have lost their atmospheres in 1 Gyr or less
because most of the late type M dwarfs are expected to be active. We emphasize
that our model only considers planets without magnetic fields. Clearly we must
expect a higher resistance to atmospheric erosion if we include the presence of
a magnetic field.Comment: Icarus, submitted. 18 pages, 6 figure