Quantifying resolution in cosmological N- body simulations using self-similarity

Journal Article · 11 November 2020 · Monthly Notices of the Royal Astronomical Society

DOI: https://doi.org/10.1093/mnras/staa3434 · OSTI ID:1761232

Joyce, Michael ^[1]; Garrison, Lehman  ^[2]; Eisenstein, Daniel ^[3]

---

1. Laboratoire de Physique Nucléaire et de Hautes Énergies, UPMC IN2P3 CNRS UMR 7585, Sorbonne Université, 4, place Jussieu, F-75252 Paris Cedex 05, France
2. Harvard and Smithsonian Center for Astrophysics, 60 Garden St, Cambridge, MA 02138, USA, Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Ave., New York, NY 10010, USA
3. Harvard and Smithsonian Center for Astrophysics, 60 Garden St, Cambridge, MA 02138, USA

ABSTRACT 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 per cent, 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.

• Research Organization: Omega Optics, Austin, TX (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC)
• Grant/Contract Number: SC0013178
• OSTI ID: 1761232
• Journal Information: Monthly Notices of the Royal Astronomical Society, Journal Name: Monthly Notices of the Royal Astronomical Society Journal Issue: 4 Vol. 501; ISSN 0035-8711
• Publisher: Oxford University PressCopyright Statement
• Country of Publication: United Kingdom
• Language: English