Recent observations which resolved the mid-infrared (MIR) emission of nearby active galactic nuclei (AGN), surprisingly revealed that their dust emission appears prominently extended in the polar direction, at odds with the expectations from the canonical dusty torus. This polar dust, tentatively associated with dusty winds driven by radiation pressure, is found to have a major contribution to the MIR flux from scales of a few to hundreds of parsecs. When facing a potential change of paradigm, case studies of objects with the best intrinsic resolution are essential. One such source with a clear detection of polar dust is a nearby, well-known AGN in the Circinus galaxy. In the first paper, we successfully explained the peculiar MIR morphology of Circinus observed on large, tens of parsec scales with a model consisting of a compact dusty disc and an extended hollow dusty cone. In this work, we further refine the model on smaller, parsecs scales to test whether it can also explain the MIR interferometric data. We find that a model composed of a thin dusty disc seen almost edge-on and a polar outflow in the form of a hyperboloid shell can reproduce well the VLTI/MIDI observations at all wavelengths, baselines and position angles. In contrast, while providing a good fit to the integrated MIR spectrum, the dusty torus model fails to reproduce the spatially resolved interferometric data. We put forth the disc$+$hyperboloid wind model of Circinus AGN as a prototype for the dust structure in the AGN population with polar dust.
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