  At distances from the active galaxy nucleus (AGN) where the ambient
temperature falls below ~1500-1800 K, dust is able to survive. It is thus
possible to have a large dusty structure present which surrounds the AGN. This
is the first of two papers aiming at comparing six dusty torus models with
available SEDs, namely Fritz et al. (2006), Nenkova et al. (2008B), Hoenig &
Kishimoto (2010), Siebenmorgen et al. (2015), Stalevski et al. (2016), and
Hoenig & Kishimoto (2017). In this first paper we use synthetic spectra to
explore the discrimination between these models and under which circumstances
they allow to restrict the torus parameters, while our second paper analyzes
the best model to describe the mid-infrared spectroscopic data. We have
produced synthetic spectra from current instruments: GTC/CanariCam and Spitzer
/IRS and future JWST/MIRI and JWST/NIRSpec instruments. We find that for a
reasonable brightness (F12um > 100mJy) we can actually distinguish among models
except for the two pair of parent models. We show that these models can be
distinguished based on the continuum slopes and the strength of the silicate
features. Moreover, their parameters can be constrained within 15% of error,
irrespective of the instrument used, for all the models but Hoenig & Kishimoto
(2017). However, the parameter estimates are ruined when more than 50% of
circumnuclear contributors are included. Therefore, future high spatial
resolution spectra as those expected from JWST will provide enough coverage and
spatial resolution to tackle this topic.
