Halo mass function and scale-dependent bias from N-body simulations with non-Gaussian initial conditions

TL;DR

This study investigates how local-type primordial non-Gaussianity, parameterized by $f_{ m NL}$, alters the halo mass function and halo clustering using high-resolution N-body simulations with Gaussian and eight non-Gaussian initial conditions. The authors demonstrate that the halo mass function is approximately universal when expressed in terms of $\sigma^{-1}$ even for non-Gaussian initial conditions, and they provide accurate fits for the high-mass end as a function of $f_{ m NL}$ and redshift. They also show that non-Gaussianity induces a scale-dependent halo bias that deviates from simple peak-background-split models, and they introduce a corrected bias framework with a multiplicative $\beta(f_{ m NL},k)$ factor to match simulations across $0.01<k<0.05\;h\,{ m Mpc}^{-1}$. The results offer precise benchmarks for constraining $f_{ m NL}$ with galaxy surveys and clarify the impact of non-Gaussianity on the matter power spectrum, BAO features, and weak-lensing signals, with practical fitting formulas for cosmological analyses.

Abstract

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.

Figures (13)

• Figure 1: The universal mass function in our Gaussian simulations Run 1.0 (triangles), Run 2.0 (squares), and Run 3.0 (circles) is compared with a number of fitting formulae listed in Table \ref{['TAB_MF']}. Data are equispaced in ${\rm ln}\, \sigma^{-1}$ and only bins containing more than 30 haloes are shown. The vertical dotted lines indicate the upper mass limits used in JENK, REED, and WARR. The corresponding low-mass limits are all equal or smaller than $\rm{ln}\,\sigma^{-1} = -1.2$. The lower panel shows the residuals $\frac{\Delta f}{f} = \frac{({\rm data} - {\rm fit})}{\rm data}$ between our data points and the different fitting functions. Here we only show data with a Poisson uncertainty better than 5 per cent. For clarity only outputs from Run 1.0 (triangles, $\rm{ln}\,\sigma^{-1} > -0.3$) and Run 3.0 (circles, $\rm{ln}\,\sigma^{-1} < -0.3$ ) are plotted.
• Figure 2: Universality of the mass function arising from non-Gaussian initial conditions. Colors refer to simulations with different values of $f_{\rm NL}$ as indicated by the labels. Symbols identify the redshift of the simulation output from which the mass function has been calculated, namely $z=0$ (triangles), 0.5 (circles), 1 (squares), 1.6 (diamonds).
• Figure 3: Comparison between the halo mass function from our main series of simulations (triangles) and the corresponding fitting functions (lines). Values $-80\leq f_{\rm NL}\leq 250$ and the fit in equation (\ref{['LINEARFIT']}) are considered in the left panel. All the simulations and the polynomial fit in equations (\ref{['EQ_LARGEMFFIT1']}) and (\ref{['EQ_LARGEMFFIT2']}) are shown in the right panel. The lower panels show residuals $\frac{\Delta f}{f} = \frac{({\rm data} - {\rm fit})}{\rm data}$ for data points with a statistical uncertainty which is smaller than 5 per cent.
• Figure 4: Left panel: Mass function residuals of Run1.-80, Run1.80, Run1.250, Run1.750 with respect to the universal fit given in equations (\ref{['EQ_LARGEMFFIT1']}) and (\ref{['EQ_LARGEMFFIT2']}) at redshift $z = 0,~ 0.5,~ 1, ~1.61$ (indicated by the symbols and colors). Only data points with a statistical error smaller than 10 per cent are shown. Right panel: As in the left panel but for the non-universal fit given in equation (\ref{['EQ_ZANDFNLFIT']}). In this case, only data points with an accuracy better than 5 per cent are shown.
• Figure 5: Comparison between the halo mass functions from our simulations and from the models by MVJ, by LOVERDE, and the fit by DALAL for different values of $f_{\rm NL}$ (different panels) and for $z=0,~ 0.5,~ 1$ (triangles, circles, squares, respectively). The quantity which is plotted is the ratio $f(z, f_{\rm NL})/f(z,f_{\rm NL}=0,)$. The dotted lines indicate the models of MVJ (green) and LOVERDE (magenta), as they appear in equations (B.6) and (4.19) of LOVERDE, respectively. The corresponding solid lines indicate the same models with a reduced threshold for halo collapse: $\delta_{\rm c} \simeq 1.5$. The blue solid lines are obtained by convolving the $f_{\rm NL}$-dependent kernel given in DALAL with the mass-function fit for the Gaussian case by WARR.