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Hydrodynamical Simulations of Nuclear Rings in Barred Galaxies

Dust lanes, nuclear rings, and nuclear spirals are typical gas structures in the inner region of barred galaxies. Their shapes and properties are linked to the physical parameters of the host galaxy. We use high-resolution hydrodynamical simulations to study 2D gas flows in simple barred galaxy models. The nuclear rings formed in our simulations can be divided into two groups: one group is nearly round and the other is highly elongated. We find that roundish rings may not form when the bar pattern speed is too high or the bulge central density is too low. We also study the periodic orbits in our galaxy models, and find that the concept of inner Lindblad resonance (ILR) may be generalized by the extent of $x_2$ orbits. All roundish nuclear rings in our simulations settle in the range of $x_2$ orbits (or ILRs). However, knowing the resonances is insufficient to pin down the exact location of these nuclear rings. We suggest that the backbone of round nuclear rings is the $x_2$ orbital family, i.e. round nuclear rings are allowed only in the radial range of $x_2$ orbits. A round nuclear ring forms exactly at the radius where the residual angular momentum of infalling gas balances the centrifugal force, which can be described by a parameter $f_{\rm ring}$ measured from the rotation curve. The gravitational torque on gas in high pattern speed models is larger, leading to a smaller ring size than in the low pattern speed models. Our result may have important implications for using nuclear rings to measure the parameters of real barred galaxies with 2D gas kinematics.