Large-scale non-Gaussian mass function and halo bias: tests on N-body simulations

TL;DR

Large-scale structure offers a powerful probe of primordial non-Gaussianity through the abundance and clustering of halos. The authors test analytic predictions for non-Gaussian halo mass functions and halo bias against large N-body simulations with local-type non-Gaussianity parameterized by $f_{\rm NL}$, calibrating corrections due to non-spherical collapse. They show that applying a $q$-dependent correction with $q\simeq0.75$, specifically $\delta_c \rightarrow \delta_c \sqrt{q}$ for the mass function and $\delta_c \rightarrow \delta_c q$ for the bias, yields excellent agreement with simulations for MVJ00 and Loverde07 mass functions and for the large-scale bias, respectively. The results imply that non-Gaussian halo bias remains a robust and competitive constraint on primordial non-Gaussianity, with practical formulae and tabulated quantities enabling interpolation across cosmologies. These findings refine the interpretation of current and future surveys and emphasize the importance of accounting for ellipsoidal collapse effects in non-Gaussian models.

Abstract

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 --> δ_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.

Figures (12)

• Figure 1: Skewness $S_3$ of the smoothed initial density field for $f_{\rm NL}=100,200,500,1000$. Symbols show the numerical results of the initial conditions code (averaged over 5 realizations) and are plotted against the analytical predictions for smoothing radii $r_s=4, 6, 8, 10 Mpc/h$ of a spherical top-hat filter.
• Figure 2: The bias of the halo power spectrum $b_{hh}$ compared to the bias of the cross (halo-matter) power spectrum $b_{hm}$. As expected, when the number density of halos is high there is good agreement between the two quantities. At low halo number densities the two quantities are affected differently by shot noise, with $b_{hm}$ being the least affected.
• Figure 3: Multiplicity mass function for the Gaussian simulation computed using a Friends-of-Friends halo finder. Points denote the simulations results at different redshift: $z=0,0.44,1.02,1.53,2.26$ and $3.23$ (top to bottom). Solid (green) lines are the Sheth & Tormen (1999) formula, dashed (red) lines are the Warren et al. (2006) one and dotted (blue) are the Jenkins et al. (2001).
• Figure 4: Comparison between the halo mass function recovered in our simulations with the work of Desjaques and Pillepich at $z=0$. We show the ratio between our non-Gaussian and Gaussian simulation with $f_{NL}=\pm 100$, few points we read out from Figure 1 of Desjaques(black points) at the values of $\nu$ corresponding to $1\times 10^{13}$,$1\times 10^{14}$ and $1\times 10^{15}$$M_{\odot}/h$ and the points from Pillepich. We plot the reciprocal of the results for $f_{NL}=-100$.
• Figure 5: Comparison between the halo mass function recovered in our simulations with the work of Desjaques and Pillepich. In the left panel we show the ratio between the non-Gaussian and Gaussian simulation at redshift $1$ for our simulations with $f_{NL}=\pm 100$, three points we read out from Figure 1 of Desjaques(black points) at the values of $\nu$ corresponding to $1\times 10^{13}$,$1\times 10^{14}$ and $1\times 10^{15}$$M_{\odot}/h$. We plot the reciprocal of the results for $f_{NL}=-100$. In the right panel we show the data of Pillepich, Porciani, Hahn (2008) at $z=0.5$ and we compare them with our simulation results for the two closest available redshifts : $z=0.44$ and $z=0.61$ and with Desjaques. All points are rescaled to $|f_{NL}=100|$ in our notation. The three independent simulations are in good agreement.