On the evolution of shape in N-body simulations

TL;DR

This study investigates the shape evolution of N-body models of galaxy formation, revealing three distinct phases influenced by initial conditions and numerical parameters, with implications for understanding elliptical galaxy development.

Contribution

It provides a detailed analysis of shape evolution phases in N-body simulations and examines how numerical and physical parameters affect the results.

Findings

Three phases of shape evolution identified: collapse, violent relaxation, and shape relaxation.

Proper softening and particle number are crucial to avoid erroneous results.

Secular shape relaxation time matches two-body relaxation time when parameters are correctly set.

Abstract

A database on shape evolution of direct N-body models formed out of cold, dissipationless collapse is generated using GRAPE and HARP special purpose computers. Such models are important to understand the formation of elliptical galaxies. Three dynamically distinct phases of shape evolution were found, first a fast dynamical collapse which gives rise to the radial orbit instability (ROI) and generates at its end the maximal triaxiality of the system. Subsequently, two phases of violent and two-body shape relaxation occur, which drive the system first towards axisymmetry, finally to spherical symmetry (the final state, however, is still much more concentrated than the initial model). In a sequence of models the influence of numerical and physical parameters, like particle number, softening, initial virial ratio, timestep choice, different N-body codes, are examined. We find that an improper combination of softening and particle number can produce erroneous results. Selected models were evolved on the secular timescale until they became spherically symmetric again. The secular shape relaxation time scale is shown to agree very well with the two-body relaxation time, if softening is properly taken into account for the latter. Finally, we argue, that the intermediate phase of violent shape relaxation after collapse is induced by strong core oscillations in the centre, which cause potential fluctuations, dampening out the triaxiality.