Pattern Speeds in Barred Galaxies

Abstract

The ratio R of the corotation radius to the bar radius ranges from 1 to 1.8 in theoretical models that fit the observed dynamics of gas or stars in the bar and spiral regions of galaxies. Most models cluster around a ratio R = 1.2 for early type galaxies. This ratio confirms the bar-aligned orbit theory long held by Contopoulos and others, which requires that R < 1, but it also suggests that bars do not end exactly at corotation, as is often assumed, but significantly inside. The difference between R = 1 in the old interpretation and R = 1.2 or 1.4 in the fitted models is critical for our interpretation of bar-spiral morphologies. It appears that the bar-to-spiral transition in early Hubble types occurs between the inner 4:1 resonance and corotation, in the range corresponding to R = 1.55 to 1 for a flat rotation curve, because of orbit stochasticity where the 2m: 1 orbits in the x₁ family cluster together in space. Corotation then occurs relatively far out in the arms, at an angle from the bar end that may exceed 60° for tightly wrapped spirals. This position sometimes corresponds to the crossing of a dust lane from inside the arms to outside (NGC 1300, NGC 1365) or to a spiral arm bifurcation as in non-barred galaxies. The relatively high value of R is also consistent with the identification of inner rings with the inner 4:1 resonance, outer rings with the outer Lindblad resonance, and offset bar dust lanes and nuclear rings with the inner Lindblad resonance. In contrast to this clear interpretation for early type galaxies, there is little consensus on the location of corotation in late type galaxies, which usually lack an inner Lindblad resonance interior to the bar. It is also not known whether late type spirals corotate with their bars, although this appears to be the case for early type galaxies based on the ubiquity and location of outer spirals and rings.