On the equivalent width of the Fe K$\alpha$ line produced by a dusty
  absorber in active galactic nuclei
  Obscured AGNs provide an opportunity to study the material surrounding the
central engine. Geometric and physical constraints on the absorber can be
deduced from the reprocessed AGN emission. In particular, the obscuring gas may
reprocess the nuclear X-ray emission producing a narrow Fe K$\alpha$ line and a
Compton reflection hump. In recent years, models of the X-ray reflection from
an obscuring torus have been computed; however, although the reflecting gas may
be dusty, the models do not yet take into account the effects of dust on the
predicted spectrum. We study this problem by analyzing two sets of models, with
and without the presence of dust, using the one dimensional photo-ionization
code Cloudy. The calculations are performed for a range of column densities
($22 <{\rm log}[N_H(\rm cm^{-2})]< 24.5$ ) and hydrogen densities ( $6 <{\rm
log}[n_H(\rm cm^{-3})]< 8$). The calculations show the presence of dust can
enhance the Fe K$\alpha$ equivalent width (EW) in the reflected spectrum by
factors up to $\approx$ 8 for Compton thick (CT) gas and a typical ISM grain
size distribution. The enhancement in EW with respect to the reflection
continuum is due to the reduction in the reflected continuum intensity caused
by the anisotropic scattering behaviour of dust grains. This effect will be
most relevant for reflection from distant, predominately neutral gas, and is a
possible explanation for AGNs which show a strong Fe K$\alpha$ EW and a
relatively weak reflection continuum. Our results show it is an important to
take into account dust while modeling the X-ray reflection spectrum, and that
inferring a CT column density from an observed Fe K$\alpha$ EW may not always
be valid. Multi-dimensional models are needed to fully explore the magnitude of
the effect.
