# A Mean-Field Approach to Simulating the Merging of Collisionless Stellar Systems Using a Particle-Based Method

## TL;DR

This paper introduces a mean-field, particle-based simulation method using a self-consistent field approach to model the merging of collisionless stellar systems, demonstrating its accuracy and advantages over traditional tree codes.

## Contribution

The paper develops a self-consistent field (SCF) method for simulating stellar mergers, providing a softening-free, accurate alternative to tree codes with broad application potential.

## Key findings

- SCF and tree code results agree well on morphology and profiles.
- Softening in tree codes affects orbital phase timing.
- SCF method effectively models collisionless stellar mergers.

## Abstract

We present a mean-field approach to simulating merging processes of two spherical collisionless stellar systems. This approach is realized with a self-consistent field (SCF) method in which the full spatial dependence of the density and potential of a system is expanded in a set of basis functions for solving Poisson's equation. In order to apply this SCF method to a merging situation where two systems are moving in space, we assign the expansion center to the center of mass of each system, the position of which is followed by a mass-less particle placed at that position initially. Merging simulations over a wide range of impact parameters are performed using both an SCF code developed here and a tree code. The results of each simulation produced by the two codes show excellent agreement in the evolving morphology of the merging systems and in the density and velocity dispersion profiles of the merged systems. However, comparing the results generated by the tree code to those obtained with the softening-free SCF code, we have found that in large impact parameter cases, a softening length of the Plummer type introduced in the tree code has an effect of advancing the orbital phase of the two systems in the merging process at late times. We demonstrate that the faster orbital phase originates from the larger convergence length to the pure Newtonian force. Other application problems suitable to the current SCF code are also discussed.