N-body simulations with generic non-Gaussian initial conditions II: Halo bias

TL;DR

This work extends N-body simulations to generic non-Gaussian initial conditions to study halo bias on large scales, addressing previous issues with spurious large-scale power. By refining the initial-condition construction and using very large simulation volumes, the authors validate analytic predictions for halo mass functions and halo bias across several bispectrum shapes, finding that a shape-dependent calibration factor q is essential. They show that physical inflationary shapes differ in squeezed-limit scaling from common templates, with equilateral templates approximating amplitude but not always scaling, and orthogonal/enfolded templates performing poorly for bias predictions. The study provides calibrated, shape-aware predictions and prepares public data resources, strengthening the use of halo bias as a probe of primordial non-Gaussianity.

Abstract

We present N-body simulations for generic non-Gaussian initial conditions with the aim of exploring and modelling the scale-dependent halo bias. This effect is evident at very large scales requiring large simulation boxes. In addition, the previously available prescription to implement generic non-Gaussian initial conditions has been improved to keep under control higher-order terms which were spoiling the power spectrum on large scales. We pay particular attention to the differences between physical, inflation-motivated primordial bispectra and their factorizable templates, and to the operational definition of the non-Gaussian halo bias (which has both a scale-dependent and an approximately scale-independent contributions). We find that analytic predictions for both the non-Gaussian halo mass function and halo bias work well once a calibration factor (which was introduced before) is calibrated on simulations. The halo bias remains therefore an extremely promising tool to probe primordial non-Gaussianity and thus to give insights into the physical mechanism that generated the primordial perturbations. The simulation outputs and tables of the analytic predictions will be made publicly available via the non-Gaussian comparison project web site http://icc.ub.edu/~liciaverde/NGSCP.html

Figures (16)

• Figure 1: Scale-dependent part of the non-Gaussian halo bias, $\mathcal{F}_M(k)/\mathcal{M}_M(k)$, for the equilateral types of non-Gaussianity. Solid and dashed lines correspond to a spectral index of $n_s=0.95$ and $n_s=1$, respectively. In both cases, the amplitude of the power spectrum is set by keeping the mass variance fixed, $\sigma_8=0.7913$.
• Figure 2: Scale-dependent part of the non-Gaussian halo bias, $\mathcal{F}_M(k)/\mathcal{M}_M(k)$, for different inflationary models and their corresponding templates. The solid and dashed lines show the results for halos of mass $3\times 10^{14}\,{\rm M}_{\odot}/h$ and $3\times 10^{11}\,{\rm M}_{\odot}/h$, respectively.
• Figure 3: Halo bias for different halo masses computed by the ratio of the halo-matter cross power spectrum to the matter power spectrum obtained from N-body simulations with local non-Gaussianities with $f_{\rm NL}=250$. The solid and dashed lines correspond to local-1024-1024 and local-1024-400, respectively. The masses are given in units of ${\rm M}_{\odot}/h$.
• Figure 4: The ratio of the number density of halos found in the simulation local-1024-400 and in the simulation local-1024-1024 as a function of halo mass. The error bars show the Poisson error. For clarity, the green circles are shifted slightly along the x-axis.
• Figure 5: Fractional difference in the mass function derived from non-Gaussian simulations of the local type and from Gaussian simulations. Different realizations are depicted with symbols of different shapes. For clarity, the data points of different realizations are shifted slightly along the x-axis. The solid and dashed lines show the predictions of MVJ (MVJ) and LV (LV) using the best-fit fudge factor of $q=0.75$ and $q=0.9$, respectively.