Quantifying resolution in cosmological N-body simulations using self-similarity. (arXiv:2004.07256v2 [astro-ph.CO] UPDATED)

<a href="http://arxiv.org/find/astro-ph/1/au:+Joyce_M/0/1/0/all/0/1">Michael Joyce</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Garrison_L/0/1/0/all/0/1">Lehman Garrison</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Eisenstein_D/0/1/0/all/0/1">Daniel Eisenstein</a>

We demonstrate that testing for self-similarity in scale-free simulations

provides an excellent tool to quantify the resolution at small scales of

cosmological N-body simulations. Analysing two-point correlation functions

measured in simulations using ABACUS, we show how observed deviations from

self-similarity reveal the range of time and distance scales in which

convergence is obtained. While the well-converged scales show accuracy below 1

percent, our results show that, with a small force softening length, the

spatial resolution is essentially determined by the mass resolution. At later

times the lower cut-off scale on convergence evolves in comoving units as

$a^{-1/2}$ ($a$ being the scale factor), consistent with a hypothesis that it

is set by two-body collisionality. A corollary of our results is that N-body

simulations, particularly at high red-shift, contain a significant spatial

range in which clustering appears converged with respect to the time-stepping

and force softening but has not actually converged to the physical continuum

result. The method developed can be applied to determine the resolution of any

clustering statistic and extended to infer resolution limits for non-scale-free

simulations.

We demonstrate that testing for self-similarity in scale-free simulations

provides an excellent tool to quantify the resolution at small scales of

cosmological N-body simulations. Analysing two-point correlation functions

measured in simulations using ABACUS, we show how observed deviations from

self-similarity reveal the range of time and distance scales in which

convergence is obtained. While the well-converged scales show accuracy below 1

percent, our results show that, with a small force softening length, the

spatial resolution is essentially determined by the mass resolution. At later

times the lower cut-off scale on convergence evolves in comoving units as

$a^{-1/2}$ ($a$ being the scale factor), consistent with a hypothesis that it

is set by two-body collisionality. A corollary of our results is that N-body

simulations, particularly at high red-shift, contain a significant spatial

range in which clustering appears converged with respect to the time-stepping

and force softening but has not actually converged to the physical continuum

result. The method developed can be applied to determine the resolution of any

clustering statistic and extended to infer resolution limits for non-scale-free

simulations.

http://arxiv.org/icons/sfx.gif