Modeling the [Fe II]{\lambda}1.644{\mu}m outflow and comparison with H${}_2$ and H${}^{+}$ kinematics in the inner 200 pc of NGC 1068

We map the kinematics of the inner (200 pc) narrow-line region (NLR) of the Seyfert 2 galaxy NGC 1068 using the instrument NIFS and adaptative optics at the Gemini North Telescope. Channel maps and position-velocity diagrams are presented at a spatial resolution of $\sim$ 10 pc and spectral resolution $\sim$ 5300 in the emission lines [Fe II] {\lambda} 1.644 {\mu}m, H${}_2$ {\lambda} 2.122 {\mu}m and Br{\gamma}. The [Fe II] emission line provides a better coverage of the NLR outflow than the previously used [O III] {\lambda} 5007 emission line, extending beyond the area of the bi-polar cone observed in Br{\gamma} and [O III]. This is mainly due to the contribution of the redshifted channels to the NE of the nucleus, supporting its origin in a partial ionized zone with additional contribution from shocks of the outflowing gas with the galactic disc. We modeled the kinematics and geometry of the [Fe II] emitting gas finding good agreement with the data for outflow models with conical and lemniscate (or hourglass) geometry. We calculate a mass outflow rate $1.9_{-0.7}^{+1.9}$ M${}_{\odot }$yr${}^{-1}$ but a power for the outflow of only 0.08% L${}_{Bol}$. The molecular (H${}_2$) gas kinematics is completely distinct from that of [Fe II] and Br{\gamma}, showing radial expansion in an off-centered $\sim$ 100 pc radius ring in the galaxy plane. The expansion velocity decelerates from $\sim$ 200 km/s in the inner border of the ring to approximately zero at the outer border where our previous studies found a 10 Myr stellar population.