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Register a new userStatistical properties of paired fixed fields
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Added by
Francisco Villaescusa-Navarro
Publication date
2018
fields
Physics
and research's language is
English
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The initial conditions of cosmological simulations are commonly drawn from a Gaussian ensemble. The limited number of modes inside a simulation volume gives rise to statistical fluctuations known as textit{sample variance}, limiting the accuracy of simulation predictions. Fixed fields offer an alternative initialization strategy; they have the same power spectrum as standard Gaussian fields but without intrinsic amplitude scatter at linear order. Paired fixed fields consists of two fixed fields with opposite phases that cancel phase correlations which otherwise induce second-order scatter in the non-linear power spectrum. We study the statistical properties of those fields for 19 different quantities at different redshifts through a large set of 600 N-body and 506 state-of-the-art magneto-hydrodynamic simulations covering a wide range of scales, mass and spatial resolutions. We find that paired fixed simulations do not introduce a bias on any of the examined quantities. We quantify the statistical improvement brought by these simulations, over standard ones, on different power spectra such as matter, halos, CDM, gas, stars, black-holes and magnetic fields, finding that they can reduce their variance by factors as large as $10^6$. We quantify the improvement achieved by fixing and by pairing, showing that sample variance in some quantities can be highly suppressed by pairing after fixing. Paired fixed simulations do not change the scatter in quantities such as the probability distribution function of matter density, or the halo, void or stellar mass functions. We argue that procedures aiming at reducing the sample variance of those quantities are unlikely to work. Our results show that paired fixed simulations do not affect either mean relations or scatter of galaxy properties, and suggest that the information embedded in 1-pt statistics is highly complementary to that in clustering.
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Provided a random realization of the cosmological model, observations of our cosmic neighborhood now allow us to build simulations of the latter down to the non-linear threshold. The resulting local Universe models are thus accurate up to a given residual cosmic variance. Namely some regions and scales are apparently not constrained by the data and seem purely random. Drawing conclusions together with their uncertainties involves then statistics implying a considerable amount of computing time. By applying the constraining algorithm to paired fixed fields, this paper diverts the original techniques from their first use to efficiently disentangle and estimate uncertainties on local Universe simulations obtained with random fields. Paired fixed fields differ from random realizations in the sense that their Fourier mode amplitudes are fixed and they are exactly out of phase. Constrained paired fixed fields show that only 20% of the power spectrum on large scales (> tens of megaparsecs) is purely random. Namely 80% of it is partly constrained by the large scale / small scale data correlations. Additionally, two realizations of our local environment obtained with paired fixed fields of the same pair constitute an excellent non-biased average or quasi-linear realization of the latter, namely the equivalent of hundreds of constrained simulations. The variance between these two realizations gives the uncertainty on the achievable local Universe simulations. These two simulations will permit enhancing faster our local cosmic web understanding thanks to a drastically reduced required computational time to appreciate its modeling limits and uncertainties.
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