Barred galaxy resonance rings: analytically explaining morphology and predicting dissipative misalignment

Many barred disc galaxies show rings of gas clouds and young stars thought to be in periodic orbits near the two-fold inner and outer Lindblad resonances (ILR and OLR) plus a four-fold ultraharmonic resonance (UHR) of the turning bar with oscillations about the disc orbital motion. To confirm and extend simulations by Schwarz and by Byrd et al. of resonance ring formation, we present an analytical formulation of the clouds' orbital motion which includes dissipative damping of oscillations relative to the local interstellar medium plus the rotation curve, bar pattern speed, and strength. Observed ring morphology matches our plots of periodic orbits where the density is enhanced but clouds do not collide violently. Pairs of 'outer rings' bracket the OLR. Dimpled outer rings like that of ESO 507-16 can be matched by plots with strong bars. Slightly dimpled outer rings like that of ESO 509-98 can be matched by weak bar plots. For flat rotation curves, a pair of two-fold rings bracket the ILR; the smaller can be identified with the tiny 'nuclear rings'. We find narrow UHR rings just outside this pair as well as just inside the OLR pair. We confirm the identification of the larger ILR ring and the inner UHR ring with 'inner rings'. Disagreeing with the common identification, we associate the dimpled outer rings with the UHR just inside the OLR. See ESO 507-16 as an example. We predict that damping can misalign the ILR and OLR rings relative to the bar as seen in our match to ESO 507-16. We find that for weak bars, if the linearly rising portion of the rotation curve is a significant fraction of the corotation radius, nuclear and inner rings are absent with outer rings still present. We show this in a match to ESO 509-98. Success of the matches to ESO 507-16 and 509-98 shows how the analytic formulation can be used to estimate disc orientation and pattern speed if rotation curve observations are available.