  Absorption of stellar X-ray and Extreme Ultraviolet radiation in the upper
atmosphere of close-in exoplanets can give rise to hydrodynamic outflows, which
may lead to the gradual shedding of their primordial, light element envelopes.
Excess absorption by neutral helium atoms in the metastable state has recently
emerged as a viable diagnostic of atmospheric escape. Here we present a public
module to the 1D photo-ionization hydrodynamic code ATES, designed to calculate
the HeI triplet transmission probability for a broad range of planetary
parameters. By relaxing the isothermal outflow assumption, the code enables a
self-consistent assessment of the HeI triplet absorption depth along with the
atmospheric mass loss rate and the outflow temperature profile, which strongly
affects the recombination rate of HeII into HeI triplet. We investigate how the
transit signal can be expected to depend upon known system parameters,
including host spectral type, orbital distance, as well as planet gravity. At
variance with previous studies, which identified K-type stars as favorable
hosts, we conclude that late M-dwarfs with Neptune-sized planets orbiting at
~0.05-0.1 AU can be expected to yield the strongest transit signal well in
excess of 30% for near-cosmological He/H abundances. More generally, we show
that the physics which regulates the population and depletion of the metastable
state, combined with geometrical effects, can yield somewhat counter-intuitive
results, such as a non-monotonic dependence of the transit depth on orbital
distance. These are compounded by a strong degeneracy between the stellar EUV
flux intensity and the atmospheric He/H abundance, both of which are highly
uncertain. Compared against spectroscopy data our modelling suggests that
either a large fraction of the targets have helium depleted envelopes, or, that
the input stellar EUV spectra are systematically overestimated.
