Velocity-inverted Three-dimensional Distribution of the Gas Clouds in the Type 2 AGN NGC 1068

Spatially resolved velocity maps at high resolutions of 1-10 pc are becoming available for many nearby active galactic nuclei (AGNs) in both optical/infrared atomic emission lines and submillimeter molecular lines. For the former, it is known that a linear relationship appears to exist between the velocity of the ionized gas clouds and the distance from the nucleus in the inner similar to 100 pc region, where these clouds are outflowing. Here we demonstrate that, in such a case, we can actually derive the three-dimensional (3D) geometrical distribution of the clouds directly from the velocity map. Revisiting such a velocity map taken by the Hubble Space Telescope for the prototypical Type 2 AGN NGC 1068, we implement the visualization of the 3D distribution derived from the map, and show that this inner narrow-line region has indeed a hollow-cone structure, consistent with previous modeling results. Quite possibly, this is the outer extended part of the polar elongated dusty material seen in the recent mid-infrared interferometry at parsec scale. Conversely, the latter small-scale geometry is inferred to have a hollow-cone outflowing structure as the inward extension of the derived 3D distribution above. The AGN obscuring "torus" is argued to be the inner optically thick part of this hollow-cone outflow, and its shadowed side would probably be associated with the molecular outflow seen in certain submillimeter lines. We discuss the nature of the linear velocity field, which could be from an episodic acceleration that occurred similar to 10(5) yr ago.