Title: Dust radiative transfer modelling of the infrared ring around the magnetar SGR 1900$+$14,
Abstract: A peculiar infrared ring-like structure was discovered by {\em Spitzer}
around the strongly magnetised neutron star SGR 1900$+$14. This infrared
structure was suggested to be due to a dust-free cavity, produced by the SGR
Giant Flare occurred in 1998, and kept illuminated by surrounding stars. Using
a 3D dust radiative transfer code, we aimed at reproducing the emission
morphology and the integrated emission flux of this structure assuming
different spatial distributions and densities for the dust, and different
positions for the illuminating stars. We found that a dust-free ellipsoidal
cavity can reproduce the shape, flux, and spectrum of the ring-like infrared
emission, provided that the illuminating stars are inside the cavity and that
the interstellar medium has high gas density ($n_H\sim$1000 cm$^{-3}$). We
further constrain the emitting region to have a sharp inner boundary and to be
significantly extended in the radial direction, possibly even just a cavity in
a smooth molecular cloud. We discuss possible scenarios for the formation of
the dustless cavity and the particular geometry that allows it to be IR-bright.