Solving Large Scale Structure in Ten Easy Steps with COLA

TL;DR

The paper introduces the COLA method, an efficient N-body simulation technique that combines Lagrangian Perturbation Theory with N-body calculations to accurately model large-scale structure with significantly reduced computational cost.

Contribution

The paper presents the COLA method, a novel approach that accelerates large-scale structure simulations by trading small-scale accuracy for computational efficiency while maintaining large-scale precision.

Findings

COLA achieves accurate halo statistics with only 10 timesteps.

The method is significantly faster than traditional N-body simulations.

COLA maintains large-scale accuracy comparable to full N-body runs.

Abstract

We present the COmoving Lagrangian Acceleration (COLA) method: an N-body method for solving for Large Scale Structure (LSS) in a frame that is comoving with observers following trajectories calculated in Lagrangian Perturbation Theory (LPT). Unlike standard N-body methods, the COLA method can straightforwardly trade accuracy at small-scales in order to gain computational speed without sacrificing accuracy at large scales. This is especially useful for cheaply generating large ensembles of accurate mock halo catalogs required to study galaxy clustering and weak lensing, as those catalogs are essential for performing detailed error analysis for ongoing and future surveys of LSS. As an illustration, we ran a COLA-based N-body code on a box of size 100Mpc/h with particles of mass ~5*10^9Msolar/h. Running the code with only 10 timesteps was sufficient to obtain an accurate description of halo statistics down to halo masses of at least 10^11Msolar/h. This is only at a modest speed penalty when compared to mocks obtained with LPT. A standard detailed N-body run is orders of magnitude slower than our COLA-based code. The speed-up we obtain with COLA is due to the fact that we calculate the large-scale dynamics exactly using LPT, while letting the N-body code solve for the small scales, without requiring it to capture exactly the internal dynamics of halos. Achieving a similar level of accuracy in halo statistics without the COLA method requires at least 3 times more timesteps than when COLA is employed.