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.
