  Recent results showed that the magnetic field of M-dwarf (dM) stars,
currently the main targets in searches for terrestrial planets, is very
different from the solar one, both in topology as well as in intensity. In
particular, the magnetised environment surrounding a planet orbiting in the
habitable zone (HZ) of dM stars can differ substantially to the one encountered
around the Earth. These extreme magnetic fields can compress planetary
magnetospheres to such an extent that a significant fraction of the planet's
atmosphere may be exposed to erosion by the stellar wind. Using observed
surface magnetic maps for a sample of 15 dM stars, we investigate the minimum
degree of planetary magnetospheric compression caused by the intense stellar
magnetic fields. We show that hypothetical Earth-like planets with similar
terrestrial magnetisation (~1G) orbiting at the inner (outer) edge of the HZ of
these stars would present magnetospheres that extend at most up to 6.1 (11.7)
planetary radii. To be able to sustain an Earth-sized magnetosphere, the
terrestrial planet would either need to orbit significantly farther out than
the traditional limits of the HZ; or else, if it were orbiting within the
life-bearing region, it would require a minimum magnetic field ranging from a
few G to up to a few thousand G.
