Efficiently estimating mean, uncertainty, and unconstrained large-scale fraction of local Universe simulations with paired fixed fields

ABSTRACT Provided a random realization of the cosmological model, observations of our cosmic neighbourhood 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 per cent of the power spectrum on large scales (> tens of megaparsecs) is purely random. Namely 80 per cent 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 modelling limits and uncertainties.

Merger Rates in Simulated and Observed Groups of Galaxies

The occurrence of mergers in simulated loose groups of galaxies (Barnes 1985; Mamon 1987) has generated the concern that mergers may be significantly more frequent in simulated groups than in observed groups (Ostriker 1987). I compare here quantitatively the rates of merging between a subset of 102 groups (Mamon 1986) of the CfA group catalog (Geller and Huchra 1983) and samples of 50 dynamically simulated groups of given initial density. The simulated groups start out virialized with galaxy luminosities pseudo-randomly generated from a Schechter function of index −1 and cutoff 0.5 L* (giving an average luminosity ∼ L*, close to the average in the CfA group catalog). The groups are evolved with the N-body code described in Mamon (1987). The merging time of the sample of 50 simulated groups is defined as the time at which the Tremaine-Richstone (1977) statistic T1 = σ(M1)/〈ΔM12〉 becomes smaller than 0.8. This value of T1 is significantly smaller than expected from a random realization of groups with the luminosity function given above (Mamon 1987).