Multi-scale initial conditions for cosmological simulations

TL;DR

This paper introduces a new multi-scale initial condition algorithm for cosmological simulations that significantly reduces errors and improves accuracy in generating initial displacements and velocities, especially for zoom-in simulations.

Contribution

The paper presents a novel adaptive convolution-based algorithm for multi-scale initial conditions, achieving two orders of magnitude lower errors than previous methods and handling baryon-dark matter simulations effectively.

Findings

Achieves RMS relative errors of 10^(-4) in displacements and velocities.

Reproduces halo properties and subhalo abundances with percent-level accuracy.

Power spectrum evolution matches linear perturbation theory well.

Abstract

We discuss a new algorithm to generate multi-scale initial conditions with multiple levels of refinements for cosmological "zoom-in" simulations. The method uses an adaptive convolution of Gaussian white noise with a real space transfer function kernel together with an adaptive multi-grid Poisson solver to generate displacements and velocities following first (1LPT) or second order Lagrangian perturbation theory (2LPT). The new algorithm achieves RMS relative errors of order 10^(-4) for displacements and velocities in the refinement region and thus improves in terms of errors by about two orders of magnitude over previous approaches. In addition, errors are localized at coarse-fine boundaries and do not suffer from Fourier-space induced interference ringing. An optional hybrid multi-grid and Fast Fourier Transform (FFT) based scheme is introduced which has identical Fourier space behaviour as traditional approaches. Using a suite of re-simulations of a galaxy cluster halo our real space based approach is found to reproduce correlation functions, density profiles, key halo properties and subhalo abundances with per cent level accuracy. Finally, we generalize our approach for two-component baryon and dark-matter simulations and demonstrate that the power spectrum evolution is in excellent agreement with linear perturbation theory. For initial baryon density fields, it is suggested to use the local Lagrangian approximation in order to generate a density field for mesh based codes that is consistent with Lagrangian perturbation theory instead of the current practice of using the Eulerian linearly scaled densities.