An Accurate P${}^3$M Algorithm for Gravitational Lensing Studies in Simulations

Abstract

We present a two-dimensional (2D) Particle-Particle-Particle-Mesh (P${}^3$M) algorithm with an optimized Green function and adaptive softening length for gravitational lensing studies in N-Body simulations. The analytical form of the optimized Green function $\hat{G}(\mathrm{k})$ is given. The softening schemes ($S$) are studied for both the PM and the PP calculations in order for accurate force calculation and suppression of the particle discreteness effect. Our method is two orders of magnitude more accurate than the simple PM algorithm with the {\it poor man's} Green function ($\propto 1/k^2$) at a scale of a few mesh cells or smaller. The force anisotropy is also much smaller than the conventional PM calculation. We can achieve a force accuracy better than 0.1 percent at all scales with our algorithm, which makes it an ideal (accurate and fast) algorithm for {\textit{micro}} lensing studies . When we apply the algorithm to computing {\textit{weak}} and {\textit{strong}} lensing quantities in N-Body simulations, the errors are dominated by the Poisson noise caused by particle discreteness. The Poisson noise can be suppressed by smoothing out the particle distribution, which can be achieved by simply choosing an adaptive softening length in the PP calculation. We have presented a criterion to set the adaptive softening length. Our algorithm is also applicable to cosmological simulations. We provide a \textsc{python} implementation \texttt{P3Mlens} for this algorithm.

arXiv comment11 pages, 6 figures, accepted for publication on ApJ

References in corpus (15)

• A Universal Density Profile from Hierarchical Clustering
• LSST: from Science Drivers to Reference Design and Anticipated Data Products
• Overview of the DESI Legacy Imaging Surveys
• The Hyper Suprime-Cam SSP Survey: Overview and Survey Design
• Cold dark matter haloes in the Planck era: evolution of structural parameters for Einasto and NFW profiles
• Extragalactic Science, Cosmology and Galactic Archaeology with the Subaru Prime Focus Spectrograph (PFS)
• Strong Lensing by Galaxies
• Weak lensing for precision cosmology
• Ray Tracing Simulations of Weak Lensing by Large-Scale Structure
• The Three-Point Correlation Function in Cosmology
• Potential sources of contamination to weak lensing measurements: constraints from N-body simulations
• Three-Point Correlations in Weak Lensing Surveys: Model Predictions and Applications
• The onion universe: all sky lightcone simulations in spherical shells
• The signature of substructure on gravitational lensing in the LCDM cosmological model
• Smoothing Algorithms and High-order Singularities in Gravitational Lensing

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