Orthogonal Vertical Velocity Dispersion Distributions Produced by Bars

In barred galaxies, the contours of stellar velocity dispersions ( ) are generally expected to be oval and aligned with the orientation of bars. However, many double-barred (S2B) galaxies exhibit distinct peaks on the minor axis of the inner bar, which we termed " -humps," while two local minima are present close to the ends of inner bars, i.e., " -hollows." Analysis of numerical simulations shows that -humps or hollows should play an important role in generating the observed -humps+hollows in low-inclination galaxies. In order to systematically investigate the properties of in barred galaxies, we apply the vertical Jeans equation to a group of well-designed three-dimensional bar+disk(+bulge) models. A vertically thin bar can lower along the bar and enhance it perpendicular to the bar, thus generating -humps+hollows. Such a result suggests that -humps+hollows can be generated by the purely dynamical response of stars in the presence of a sufficiently massive, vertically thin bar, even without an outer bar. Using self-consistent N-body simulations, we verify the existence of vertically thin bars in the nuclear-barred and S2B models that generate prominent -humps+hollows. Thus, the ubiquitous presence of -humps+hollows in S2Bs implies that inner bars are vertically thin. The addition of a bulge makes the -humps more ambiguous and thus tends to somewhat hide the -humps+hollows. We show that may be used as a kinematic diagnostic of stellar components that have different thicknesses, providing a direct perspective on the morphology and thickness of nearly face-on bars and bulges with integral field unit spectroscopy.