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Kinematic properties of double-barred galaxies: simulations vs. integral-field observations

Using high resolution $N$-body simulations, we recently reported that a dynamically cool inner disk embedded in a hotter outer disk can naturally generate a steady double-barred (S2B) structure. Here we study the kinematics of these S2B simulations, and compare them to integral-field observations from ATLAS$^{3D}$ and SAURON. We show that S2B galaxies exhibit several distinct kinematic features, namely: (1) significantly distorted isovelocity contours at the transition region between the two bars, (2) peaks in $σ_\mathrm{LOS}$ along the minor axis of inner bars, which we term "$σ$-humps", that are often accompanied by ring/spiral-like features of increased $σ_\mathrm{LOS}$, (3) $h_3-\bar{v}$ anti-correlations in the region of the inner bar for certain orientations, and (4) rings of positive $h_4$ when viewed at low inclinations. The most impressive of these features are the $σ$-humps, these evolve with the inner bar, oscillating in strength just as the inner bar does as it rotates relative to the outer bar. We show that, in cylindrical coordinates, the inner bar has similar streaming motions and velocity dispersion properties as normal large-scale bars, except for $σ_z$, which exhibits peaks on the minor axis, i.e., humps. These $σ_z$ humps are responsible for producing the $σ$-humps. For three well-resolved early-type S2Bs (NGC 2859, NGC 2950, and NGC 3941) and a potential S2B candidate (NGC 3384), the S2B model qualitatively matches the integral-field data well, including the "$σ$-hollows" previously identified. We also discuss the kinematic effect of a nuclear disk in S2Bs.