Long-lived spiral waves in N-body simulations

Summary

Description of simulation

In an effort to better understand disc galaxies, we have developed a Cartesian, 2-D, N-body and hydrodynamic computer code. The results presented here use only the N-body portion of the code. To accommodate the variable time-step length required by the Courant condition for hydrodynamic flows, we use a second order predictorcorrector integration scheme (Schroeder & Comins 1989) with the same accuracy as the more familiar time-centred leap frog scheme.

The particles are distributed as a Kuz'min disc, and we add a fixed ‘halo’, having between 65% and 75% of the total gravitational potential, to stabilize the system against bar-mode instabilities. Tangential and radial velocity dispersions establish an initial Toomre Q of 1.0 over the disc. The resulting disc appears to be stable to nonaxisymmetric perturbations.

We add a rotating, logarithmic, two-armed, spiral perturbation to the potential. The amplitude of this spiral is ramped up and down as a Gaussian (Toomre 1981). This spiral perturbation grows from 2% of its maximum amplitude to full strength in 1/2 a rotation period and then decays in the same manner. Both trailing arm spirals (TASs) and leading arm spirals (LASs) are used with varieties of pitch angles and pattern speeds. All such perturbations lead to strong non-axisymmetric responses in the disc. Unless indicated otherwise, the pattern speed of the perturbation is 1/2 the co-rotation speed of the particles at the half-mass radius. Final Qs range between 1.1 in the interior and 3.5 near the disc edge.