Dust radiative transfer modelling of the infrared ring around the magnetar SGR 1900$+$14

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.