6.2. Numerical Simulations of Ring Galaxy Hydrodynamics
6.2.1. The First Simulations: 1970s
The first models of gas dynamics in ring galaxies were those of Theys and Spiegel (1977), using Prendergast's "beam scheme" (Sanders and Prendergast 1974). Theys and Spiegel presented simulations of both the gravitational breakup of isolated rotating rings, and galaxy-galaxy collisions with both gas and stellar components modeled by particles in the target disk. The ring breakup simulations were two-dimensional with self-gravity computed on a 128 × 128 grid with particles representing individual clouds and obeying a polytropic equation of state with index = 2. The ring was set up in centrifugal equilibrium, but evidently in a marginally gravitationally unstable state. The basic result was that the ring fragmented within a few free-fall times ( 108 yr.) into dense clumps, and the number of clumps was about equal to the number of initial Jeans lengths along the circumference of the ring. The simulation also included the conversion of gas clouds to stars, but no significant differences developed between the stars and clouds over the duration of the simulation. Subsequently, this result for an idealized material ring has often been uncritically cited as proof of the existence of a bead instability in (propagating, not material) ring waves.
Theys and Spiegel carried out two types of collision simulation, one with complete cylindrical symmetry, and the other was apparently a fully self-consistent three-dimensional model. Unfortunately the primary galaxy did not include a massive halo, and by the authors' description it seems that the unperturbed disk was subject to the bar instability (see e.g., Binney and Tremaine 1987, Section 6.3), and excessive disk heating in the stellar component. The number of particles was also quite small. Nonetheless, the development of the ring was evident in the gas. The ring formation and propagation are more obvious in the symmetric models, where the disk is made up of N rings.