  We present the results of an extensive study of the detectability of
Earth-sized planets and super-Earths in the habitable zones of cool and
low-mass stars using transit timing variation method. We have considered a
system consisting of a star, a transiting giant planet, and a terrestrial-class
perturber, and calculated TTVs for different values of the parameters of the
system. To identify ranges of the parameters for which these variations would
be detectable by Kepler, we considered the analysis presented by Ford et al.
(2011, ArXiv:1102.0544) and assumed that a peak-to-peak variation of 20 seconds
would be within the range of the photometric sensitivity of this telescope. We
carried out simulations for resonant and non-resonant orbits, and identified
ranges of the semimajor axes and eccentricities of the transiting and
perturbing bodies for which an Earth-sized planet or a super-Earth in the
habitable zone of a low-mass star would produce such TTVs. Results of our
simulations indicate that in general, outer perturbers near first- and
second-order resonances show a higher prospect for detection. Inner perturbers
are potentially detectable only when near 1:2 and 1:3 mean-motion resonances.
For a typical M star with a Jupiter-mass transiting planet, for instance, an
Earth-mass perturber in the habitable zone can produce detectable TTVs when the
orbit of the transiting planet is between 15 and 80 days. We present the
details of our simulations and discuss the implication of the results for the
detection of terrestrial planets around different low-mass stars.
