Approximate Methods for the Generation of Dark Matter Halo Catalogs in the Age of Precision Cosmology
Abstract
:1. Introduction
2. Foundations of Approximate Methods
2.1. Perturbation Theories
2.2. The Need for Smoothing
2.3. Press and Schechter and Its Extensions
2.4. Ellipsoidal Collapse
2.5. Halo Bias
3. Approximate Methods in the 1990s
3.1. Lognormal Model
3.2. Adhesion Theory
3.3. Extensions of ZA
3.4. Truncated Zeldovich Approximation and Beyond
3.5. Reconstruction of Initial Conditions
4. The age of Precision Cosmology
4.1. Recent Development of the Foundations
4.2. The Universal Mass Function
4.3. Lagrangian Methods to Produce Mock Catalogs
4.3.1. PINOCCHIO
4.3.2. PTHALOS
4.3.3. Methods Based on the Particle-Mesh Scheme
4.4. Bias-Based Methods
4.4.1. PATCHY
4.4.2. EZmocks
4.4.3. Halogen
5. Comparison of Methods
5.1. The nIFTy Comparison Project
5.2. Generating Displacement Fields of Halos without Worrying about Particle Assignments to Halos
- (1)
- For the matter power spectrum, the wavenumber at which power drops below a % level does not overtake 0.2 h Mpc for all models, with the exception of COLA, that can reach 0.8 h Mpc for all meshes but the coarsest one. Moreover, going from lower to higher orders provides only some modest improvement, and this is true for all LPT flavours. This quantifies the trend, noticed in Figure 2, that higher LPT orders may give better convergence before orbit crossing, but they add to the spreading of the multi-stream region.
- (2)
- All approximate methods are able to recover the halo power spectrum at a higher wavenumber than the matter power spectrum. For the straight LPT series, power drops below a % level at k ∼0.13, and h Mpc for the three orders, showing that the improvement achieved going to higher orders is significant.
- (3)
- No advantage is found by adopting the truncated LPT scheme. As noticed in Section 3.4, in the original paper of Coles et al. [102] the advantage of the truncated scheme was found to be good for a power spectrum of positive or flat slope ≥ but marginal for a slope , that is shallower than the slope of a ΛCDM spectrum at k ∼0.5.
- (4)
- Augmentation contributes to the improvement of the LPT series. This trend is more apparent for the halo power spectrum, in which case the improvement in going from 2LPT to A2LPT is of the same order as the improvement in going from 2LPT to 3LPT. A3LPT is only marginally better than 3LPT.
- (5)
- COLA gives percent accurate results for the matter power spectrum up to k ∼0.5 h Mpc, and is 10% accurate up to h Mpc. Very good results are obtained for halos, where some excess power at the 2% level is found at , but 10% accuracy is achieved up to h Mpc. Results are stable with the grid dimension, with the exception of the coarsest grid that gives poor performance; for halos, finer grids give some excess of power, the grid gives the best performance. Clearly, finer grids are needed by COLA to allow proper identification of halos, but not to achieve better accuracy in their clustering.
6. Concluding Remarks
Acknowledgments
Conflicts of Interest
Abbreviations
BAO | baryonic acoustic oscillations |
CDM | cold dark matter |
DM | dark matter |
EPT | Eulerian Perturbation Theory |
FFT | fast Fourier transform |
FoF | friends-of-friends |
LPT | Lagrangian Perturbation Theory |
2LPT | 2nd-order LPT |
3LPT | 3rd-order LPT |
ALPT | augmented LPT |
probability distribution function | |
SAM | semi-analytic model |
ZA | Zeldovich approximation |
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Method | Memory | N. Cores | Elapsed Time | CPU Time | 1000 Realizations |
---|---|---|---|---|---|
EZmocks | 40 GB | 16 | 7.5 m | 2 h + calibration N-body | 822,000 h |
PATCHY | 40 GB | 16 | 7.5 m | 2 h + calibration N-body | 822,000 h |
PINOCCHIO | 14 TB | 2048 | 30 m | 1024 h | 1,024,000 h |
COLA | 33 TB | 4096 | 2.5 h | 10,240 h | 10,240,000 h |
N-body (HugeMDPL) | 6.5 TB | 2000 | 410 h | 820,000 h | 820,000,000 h |
© 2016 by the author; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).
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Monaco, P. Approximate Methods for the Generation of Dark Matter Halo Catalogs in the Age of Precision Cosmology. Galaxies 2016, 4, 53. https://doi.org/10.3390/galaxies4040053
Monaco P. Approximate Methods for the Generation of Dark Matter Halo Catalogs in the Age of Precision Cosmology. Galaxies. 2016; 4(4):53. https://doi.org/10.3390/galaxies4040053
Chicago/Turabian StyleMonaco, Pierluigi. 2016. "Approximate Methods for the Generation of Dark Matter Halo Catalogs in the Age of Precision Cosmology" Galaxies 4, no. 4: 53. https://doi.org/10.3390/galaxies4040053