The influence of numerical parameters on tidally triggered bar formation

¹ Depto. de Física, Instituto Nacional de Investigaciones Nucleares, Apdo. Postal 18-1027, México DF 11801, México e-mail: ruslan@nuclear.inin.mx
² Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto Literario 100, CP 50000, Toluca, México
³ Universität Konstanz, Fachbereich Physik, Fach M568, 78457 Konstanz, Germany

Received: 24 September 2005
Accepted: 19 December 2005

Abstract

The joint influence of numerical parameters such as the number of particles N, the gravitational softening length ε and the time-step is investigated in the context of galaxy simulations. For isolated galaxy models we have performed a convergence study and estimated the numerical parameters ranges for which the relaxed models do not deviate significantly from its initial configuration. By fixing N, we calculate the range of the mean interparticle separation  along the disc radius. Uniformly spaced values of λ are used as ε in numerical tests of disc heating. We have found that in the simulations with particles λ varies by a factor of 6, and the corresponding final Toomre's parameters Q change by only about 5 per cent. By decreasing N, the λ and Q ranges broaden. Large ε and small N cause an earlier bar formation. In addition, the numerical experiments indicate, that for a given set of parameters the disc heating is smaller with the Plummer softening than with the spline softening. For galaxy collision models we have studied the influence of the selected numerical parameters on the formation of tidally triggered bars in galactic discs and their properties, such as their dimensions, shape, amplitude and rotational velocity. Numerical simulations indicate that the properties of the formed bars strongly depend upon the selection of N and ε. Large values of the gravitational softening parameter and a small number of particles result in the rapid formation of a well defined, slowly rotating bar. On the other hand, small values of ε produce a small, rapidly rotating disc with tightly wound spiral arms, and subsequently a weak bar emerges. We have found that by increasing N, the bar properties converge and the effect of the softening parameter diminishes. Finally, in some cases short spiral arms are observed at the ends of the bar that change periodically from trailing to leading and vice-versa – the wiggle.