  We modeled the transit signatures in the Lya line of a putative Earth-sized
planet orbiting in the HZ of the M dwarf GJ436. We estimated the transit depth
in the Lya line for an exo-Earth with three types of atmospheres: a
hydrogen-dominated atmosphere, a nitrogen-dominated atmosphere, and a
nitrogen-dominated atmosphere with an amount of hydrogen equal to that of the
Earth. We calculated the in-transit absorption they would produce in the Lya
line. We applied it to the out-of-transit Lya observations of GJ 436 obtained
by the HST and compared the calculated in-transit absorption with observational
uncertainties to determine if it would be detectable. To validate the model, we
also used our method to simulate the deep absorption signature observed during
the transit of GJ 436b and showed that our model is capable of reproducing the
observations. We used a DSMC code to model the planetary exospheres. The code
includes several species and traces neutral particles and ions. At the lower
boundary of the DSMC model we assumed an atmosphere density, temperature, and
velocity obtained with a hydrodynamic model for the lower atmosphere. We showed
that for a small rocky Earth-like planet orbiting in the HZ of GJ436 only the
hydrogen-dominated atmosphere is marginally detectable with the STIS/HST.
Neither a pure nitrogen atmosphere nor a nitrogen-dominated atmosphere with an
Earth-like hydrogen concentration in the upper atmosphere are detectable. We
also showed that the Lya observations of GJ436b can be reproduced reasonably
well assuming a hydrogen-dominated atmosphere, both in the blue and red wings
of the Lya line, which indicates that warm Neptune-like planets are a suitable
target for Lya observations. Terrestrial planets can be observed in the Lya
line if they orbit very nearby stars, or if several observational visits are
available.
