10. THEORIES OF RING FORMATION

10.1. Some Historical Points

From the beginning, the problem of rings in galaxies has been associated with that of spiral arms, because like spiral arms, rings are very similar thin structures, more prominent in the blue, and the sites of star formation. Quite often, the rings are only pseudorings, clearly formed by spiral arms in the way of winding up into a ring (see Figure 3 and Figure 17). It is then natural that early theories of rings closely accompanied theories of spiral structure. The same temptation to attribute them only to gas dynamics in a magnetic field, instead of gravitational dynamics, appeared from the 1930's-60's. However, as the idea of density waves was developed by Bertil Lindblad in the 1950s to explain spiral structure, he noticed the existence of ``dispersion orbits'' with m = 2 symmetry that precessed at a rate almost constant with radius (Lindblad 1962, 1964). From the epicyclic theory, we can consider stellar orbits as closed ellipses precessing at the rate - / 2, where is the epicylic frequency. This precession rate appears to be almost constant in a certain range of radii in the Galaxy, which suggests that a ring could be formed by an accumulation of such dispersion orbits, slowly precessing as a whole around the galactic center (cf. the early N-body experiments of P.O. Lindblad 1960).

It is interesting to note that in the pre-density wave era, Randers (1940) proposed a theory of ring formation based on viscous torques. This theory was developed again in the 1970's and 80's for gas flows (Icke 1979; Lesch et al. 1990), and we will discuss it in section 12. The principle is that viscous torques act in regions of differential rotation, and accumulate matter where the angular velocity becomes constant, i.e., rings are expected at the turnover point of the rotation curves. Randers applied this theory to the stellar population, where he claimed that collisions and scatterings were equivalent to a viscosity effect. The problem of diffusion and heating of the stellar component was debated much later (Wielen 1977; Lacey 1984; Zhang 1996).

More recently, Danby (1965) discussed the existence of ringlike structures in barred galaxies, associated with the equipotential surfaces in the rotating frame of the bar; this might be the closest approach to the modern theory of ring formation, as resonant accumulation of gas in a non-axisymmetric potential.

The considerable success of the density wave theory of Lin & Shu (1964) led to the abandonment of the non-gravitational approaches, and the growing importance of N-body simulations focussed attention on bars, which were the only robust density waves found numerically in a self-consistent stellar disk (e.g Miller et al. 1970; Hohl 1971). With this advance, bars were no longer considered as solid body entities in rotation around the center, but as waves interacting with the rest of the disk and possibly triggering spiral structure. Simulations of gas flows in barred galaxies were initiated by Sanders & Huntley (1976), who showed convincingly that a long-lived spiral structure could be generated in the gas component by the stellar bar, owing to the properties of periodic orbits in a non-axisymmetric potential. No resonant rings were formed in these simulations, which could be an effect of the gas viscosity, as will be discussed in section 12. The first work where resonance rings were formed, and explained through gravitational torques on the gas, was done by Schwarz (1981, 1984b), who modelled the gas component by ballistic particles undergoing collisions. This representation, which corresponds much better to the cloudy and clumpy interstellar medium, minimizes the artificial viscosity, and strongly helps the formation of highly contrasted rings.

We will discuss in detail the mechanism of ring formation in section 11; since it is intimately linked to the bar, the dynamics of barred galaxies and their orbital structure will be detailed as a preliminary in section 11. Let us first emphasize the observational facts that support the proposed mechanism.