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Register a new userLarge-scale non-Gaussian mass function and halo bias: tests on N-body simulations
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M. Grossi
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The description of the abundance and clustering of halos for non-Gaussian initial conditions has recently received renewed interest, motivated by the forthcoming large galaxy and cluster surveys, which can potentially yield constraints of order unity on the non-Gaussianity parameter f_{NL}. We present tests on N-body simulations of analytical formulae describing the halo abundance and clustering for non-Gaussian initial conditions. We calibrate the analytic non-Gaussian mass function of Matarrese et al.(2000) and LoVerde et al.(2008) and the analytic description of clustering of halos for non-Gaussian initial conditions on N-body simulations. We find excellent agreement between the simulations and the analytic predictions if we make the corrections delta_c --> delta_c X sqrt{q} and delta_c --> delta_c X q where q ~ 0.75, in the density threshold for gravitational collapse and in the non-Gaussian fractional correction to the halo bias, respectively. We discuss the implications of this correction on present and forecasted primordial non-Gaussianity constraints. We confirm that the non-Gaussian halo bias offers a robust and highly competitive test of primordial non-Gaussianity.
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We perform a series of high-resolution N-body simulations of cosmological structure formation starting from Gaussian and non-Gaussian initial conditions. We adopt the best-fitting cosmological parameters of WMAP (3rd- and 5th-year) and we consider non-Gaussianity of the local type parameterised by 8 different values of the non-linearity parameter F_NL. Building upon previous work based on the Gaussian case, we show that, expressed in terms of suitable variables, the mass function of friends-of-friends haloes is approximately universal (i.e. independent of redshift, cosmology, and matter transfer function) to good precision (nearly 10 per cent) also in non-Gaussian scenarios. We provide fitting formulae for the high-mass end (M>10^13 M_sol/h) of the universal mass function in terms of F_NL, and we also present a non-universal fit in terms of both F_NL and z to be used for applications requiring higher accuracy. In the Gaussian case, we extend our fit to a wider range of halo masses (M>2.4 x 10^10 M_sol/h) and we also provide a consistent fit of the linear halo bias. We show that, for realistic values of F_NL, the matter power-spectrum in non-Gaussian cosmologies departs from the Gaussian one by up to 2 per cent on the scales where the baryonic- oscillation features are imprinted on the 2-point statistics. We confirm the strong k-dependence of the halo bias on large scales (k<0.05 h Mpc^-1) which was already detected in previous studies. However, we find that commonly used parameterisations based on the peak-background split do not provide an accurate description of our simulations which present extra dependencies on the wavenumber, the non-linearity parameter and, possibly, the clustering strength. We provide an accurate fit of the simulation data that can be used as a benchmark for future determinations of F_NL with galaxy surveys.
The interpretation of redshift surveys requires modeling the relationship between large-scale fluctuations in the observed number density of tracers, $delta_mathrm{h}$, and the underlying matter density, $delta$. Bias models often express $delta_mathrm{h}$ as a truncated series of integro-differential operators acting on $delta$, each weighted by a bias parameter. Due to the presence of `composite operators (obtained by multiplying fields evaluated at the same spatial location), the linear bias parameter measured from clustering statistics does not coincide with that appearing in the bias expansion. This issue can be cured by re-writing the expansion in terms of `renormalised operators. After providing a pedagogical and comprehensive review of bias renormalisation in perturbation theory, we generalize the concept to non-perturbative dynamics and successfully apply it to dark-matter haloes extracted from a large suite of N-body simulations. When comparing numerical and perturbative results, we highlight the effect of the window function employed to smooth the random fields. We then measure the bias parameters as a function of halo mass by fitting a non-perturbative bias model (both before and after applying renormalisation) to the cross spectrum $P_{delta_mathrm{h}delta}(k)$. Finally, we employ Bayesian model selection to determine the optimal operator set to describe $P_{delta_mathrm{h}delta}(k)$ for $k<0.2,h$ Mpc$^{-1}$ at redshift $z=0$. We find that it includes $delta, abla^2delta, delta^2$ and the square of the traceless tidal tensor, $s^2$. Considering higher-order terms (in $delta$) leads to overfitting as they cannot be precisely constrained by our data. We also notice that next-to-leading-order perturbative solutions are inaccurate for $kgtrsim 0.1,h$ Mpc$^{-1}$.
We discuss the relation between the output of Newtonian N-body simulations on scales that approach or exceed the particle horizon to the description of General Relativity. At leading order, the Zeldovich approximation is correct on large scales, coinciding with the General Relativistic result. At second order in the initial metric potential, the trajectories of particles deviate from the second order Newtonian result and hence the validity of 2LPT initial conditions should be reassessed when used in very large simulations. We also advocate using the expression for the synchronous gauge density as a well behaved measure of density fluctuations on such scales.
The strong dependence of the large-scale dark matter halo bias on the (local) non-Gaussianity parameter, f_NL, offers a promising avenue towards constraining primordial non-Gaussianity with large-scale structure surveys. In this paper, we present the first detection of the dependence of the non-Gaussian halo bias on halo formation history using N-body simulations. We also present an analytic derivation of the expected signal based on the extended Press-Schechter formalism. In excellent agreement with our analytic prediction, we find that the halo formation history-dependent contribution to the non-Gaussian halo bias (which we call non-Gaussian halo assembly bias) can be factorized in a form approximately independent of redshift and halo mass. The correction to the non-Gaussian halo bias due to the halo formation history can be as large as 100%, with a suppression of the signal for recently formed halos and enhancement for old halos. This could in principle be a problem for realistic galaxy surveys if observational selection effects were to pick galaxies occupying only recently formed halos. Current semi-analytic galaxy formation models, for example, imply an enhancement in the expected signal of ~23% and ~48% for galaxies at z=1 selected by stellar mass and star formation rate, respectively.
In this paper we present the implementation of an efficient formalism for the generation of arbitrary non-Gaussian initial conditions for use in N-body simulations. The methodology involves the use of a separable modal approach for decomposing a primordial bispectrum or trispectrum. This approach allows for the far more efficient generation of the non-Gaussian initial conditions already described in the literature, as well as the generation for the first time of non-separable bispectra and the special class of diagonal-free trispectra. The modal approach also allows for the reconstruction of the spectra from given realisations, a fact which is exploited to provide an accurate consistency check of the simulations.
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