Variation of Bar Strength with Central Velocity Dispersion in Spiral Galaxies

We investigate the variation of bar strength with central velocity dispersion in a sample of barred spiral galaxies. The bar strength is characterized by $Q_g$, the maximal tangential perturbation associated with the bar, normalized by the mean axisymmetric force. It is derived from the galaxy potentials which are obtained using near-infrared images of the galaxies. However, $Q_g$ is sensitive to bulge mass. Hence we also estimated bar strengths from the relative Fourier intensity amplitude ($A_{2}$) of bars in near-infrared images. The central velocity dispersions were obtained from integral field spectroscopy observations of the velocity fields in the centers of these galaxies; it was normalized by the rotation curve amplitude obtained from HI line width for each galaxy. We found a correlation between bar strengths (both $Q_g$ and $A_{2}$) and the normalized central velocity dispersions in our sample. This suggests that bars weaken as their central components become kinematically hotter. This may have important implications for the secular evolution of barred galaxies.