How Faithful Are N - Body Simulations of Disc Galaxies

1. I n t r o d u c t i o n N-body simulations employing particle-mesh codes have nowadays become a very powerful tool for investigating the dynamics of disc galaxies. In particular, two-dimensional N-body models in which the stars and the cold interstellar gas are treated as two different components have successfully been applied in studies of spiral structure (e.g., Salo 1991; Thomasson 1991). A correct interpretation of computational results in terms of real phenomena poses serious problems, also because there are quantities introduced for numerical reasons which do not have clear physical counterparts. One of such artificial quantities is the softening length of the modified (non-Newtonian) gravitational interaction between the computer particles, and its value can critically affect the results of N-body experiments. It is thus of fundamental importance to have a prescription for choosing meaningful values of the softening length. From the stability point of view, it has been suggested that softening introduces a quite reasonable thickness correction for a twodimensional model (e.g., Sellwood 1986, 1987; see also Byrd et al. 1986). In this paper the analogy between numerical softening and finite-thickness effects is investigated in detail on the basis of a local linear stability analysis, and in particular the question "How faithfully does the softening mimic the thickness of galactic discs?" is addressed. It is found that high-softening two-dimensional models, frequently employed in N-body experiments, do not provide faithful simulations of real gMactic discs. A prescription (6) is given for choosing meaningful values of the softening length. 258 Alessandro B. ROMEO Strictly connected with that problem is the choice of meaningful input values of the local stability parameter for a given softening length. In contrast to the softening length, the Toomre parameter is directly related to observable quantities, has a clear physical meaning, and its output values in N-body experiments can be compared to those predicted by theories of spiral structure and secular heating. In this paper a local stability criterion (8) is found in virtue of the descriptive similarity between numerical softening and finite-thickness effects. Such a criterion should indeed provide a key to this problem. A more thorough discussion is given by Romeo (1993). In this short paper we just focus on a few points.