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Authors
Adrian L. Melott
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It is shown that the historical summary of the growth in size of N-body simulations as measured by particle number in this review is missing some key milestones. Size matters, because particle number with appropriate force smoothing is a key method to suppress unwanted discreteness, so that the initial conditions and equations of motion are appropriate to growth by gravitational instability in a Poisson-Vlasov system appropriate to a Universe with dark matter. Published strong constraints on what can be done are not included in the review.
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As an entry for the 2012 Gordon-Bell performance prize, we report performance results of astrophysical N-body simulations of one trillion particles performed on the full system of K computer. This is the first gravitational trillion-body simulation in the world. We describe the scientific motivation, the numerical algorithm, the parallelization strategy, and the performance analysis. Unlike many previous Gordon-Bell prize winners that used the tree algorithm for astrophysical N-body simulations, we used the hybrid TreePM method, for similar level of accuracy in which the short-range force is calculated by the tree algorithm, and the long-range force is solved by the particle-mesh algorithm. We developed a highly-tuned gravity kernel for short-range forces, and a novel communication algorithm for long-range forces. The average performance on 24576 and 82944 nodes of K computer are 1.53 and 4.45 Pflops, which correspond to 49% and 42% of the peak speed.
Large redshift surveys of galaxies and clusters are providing the first opportunities to search for distortions in the observed pattern of large-scale structure due to such effects as gravitational redshift. We focus on non-linear scales and apply a quasi-Newtonian approach using N-body simulations to predict the small asymmetries in the cross-correlation function of two galaxy different populations. Following recent work by Bonvin et al., Zhao and Peacock and Kaiser on galaxy clusters, we include effects which enter at the same order as gravitational redshift: the transverse Doppler effect, light-cone effects, relativistic beaming, luminosity distance perturbation and wide-angle effects. We find that all these effects cause asymmetries in the cross-correlation functions. Quantifying these asymmetries, we find that the total effect is dominated by the gravitational redshift and luminosity distance perturbation at small and large scales, respectively. By adding additional subresolution modelling of galaxy structure to the large-scale structure information, we find that the signal is significantly increased, indicating that structure on the smallest scales is important and should be included. We report on comparison of our simulation results with measurements from the SDSS/BOSS galaxy redshift survey in a companion paper.
Gravitational softening length is one of the key parameters to properly set up a cosmological $N$-body simulation. In this paper, we perform a large suit of high-resolution $N$-body simulations to revise the optimal softening scheme proposed by Power et al. (P03). Our finding is that P03 optimal scheme works well but is over conservative. Using smaller softening lengths than that of P03 can achieve higher spatial resolution and numerically convergent results on both circular velocity and density profiles. However using an over small softening length overpredicts matter density at the inner most region of dark matter haloes. We empirically explore a better optimal softening scheme based on P03 form and find that a small modification works well. This work will be useful for setting up cosmological simulations.
Gravitational N-body simulations, that is numerical solutions of the equations of motions for N particles interacting gravitationally, are widely used tools in astrophysics, with applications from few body or solar system like systems all the way up to galactic and cosmological scales. In this article we present a summary review of the field highlighting the main methods for N-body simulations and the astrophysical context in which they are usually applied.
In the next decade, cosmological surveys will have the statistical power to detect the absolute neutrino mass scale. N-body simulations of large-scale structure formation play a central role in interpreting data from such surveys. Yet these simulations are Newtonian in nature. We provide a quantitative study of the limitations to treating neutrinos, implemented as N-body particles, in N-body codes, focusing on the error introduced by neglecting special relativistic effects. Special relativistic effects are potentially important due to the large thermal velocities of neutrino particles in the simulation box. We derive a self-consistent theory of linear perturbations in Newtonian and non-relativistic neutrinos and use this to demonstrate that N-body simulations overestimate the neutrino free-streaming scale, and cause errors in the matter power spectrum that depend on the initial redshift of the simulations. For $z_{i} lesssim 100$, and neutrino masses within the currently allowed range, this error is $lesssim 0.5%$, though represents an up to $sim 10%$ correction to the shape of the neutrino-induced suppression to the cold dark matter power spectrum. We argue that the simulations accurately model non-linear clustering of neutrinos so that the error is confined to linear scales.
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