Non-Gaussian Halo Bias Re-examined: Mass-dependent Amplitude from the Peak-Background Split and Thresholding

TL;DR

This paper revisits how primordial non-Gaussianity alters the large-scale clustering of halos, focusing on NG types beyond the simplest local model. It develops three complementary theoretical routes—thresholded regions, PBS with scale separation, and PBS via conditional mass functions—and derives explicit expressions for NG-induced, scale-dependent halo bias, including a newly identified mass-dependent correction. The thresholding approach, while exact at leading order, effectively reduces to local bias and cannot account for the observed mass dependence; PBS formulations reveal a crucial additional term tied to the scale dependence of small-scale cumulants, which aligns well with N-body results across several NG templates. The findings support PBS as the robust framework for modeling NG bias in LSS analyses and have direct implications for interpreting data from current and future galaxy surveys seeking primordial NG signatures.

Abstract

Recent results of N-body simulations have shown that current theoretical models are not able to correctly predict the amplitude of the scale-dependent halo bias induced by primordial non-Gaussianity, for models going beyond the simplest, local quadratic case. Motivated by these discrepancies, we carefully examine three theoretical approaches based on (1) the statistics of thresholded regions, (2) a peak-background split method based on separation of scales, and (3) a peak-background split method using the conditional mass function. We first demonstrate that the statistics of thresholded regions, which is shown to be equivalent at leading order to a local bias expansion, cannot explain the mass-dependent deviation between theory and N-body simulations. In the two formulations of the peak-background split on the other hand, we identify an important, but previously overlooked, correction to the non-Gaussian bias that strongly depends on halo mass. This new term is in general significant for any primordial non-Gaussianity going beyond the simplest local fNL model. In a separate paper, we compare these new theoretical predictions with N-body simulations, showing good agreement for all simulated types of non-Gaussianity.

Figures (3)

• Figure 1: Ratio of the non-Gaussian correction to the linear bias predicted by the statistics of thresholded regions to that obtained in the high-peak limit. For a non-zero primordial bispectrum ($N=3$) and trispectrum ($N=4$), this ratio is equal to $b_2\sigma_{0s}^2/(b_1\delta_c)$ and $b_3\sigma_{0s}^4/(b_1\delta_c^2)$, respectively. Note that it depends on the order $N$ but not on the specific shape of the primordial correlation function. Results are shown at $z=0$ as a function of halo mass $M$. The Gaussian bias parameters $b_N$ are computed from a Sheth-Tormen mass function.
• Figure 2: Ratio of the non-Gaussian correction to the linear bias predicted by the peak-background split approach to that obtained in the high-peak limit. Results are shown at $z=0$ as a function of the halo mass $M$ for a local trispectrum with cubic parameter $g_{\rm NL}$ (solid curve), a local bispectrum with $k$-dependent quadratic parameter $f_{\rm NL}$ and index $n_f=\pm 0.6$ (dashed and dot-dashed curve), the folded and orthogonal template (long-dashed curve) and the equilateral bispectrum shape (dotted curve). In contrast to Fig. \ref{['fig:emlb']}, the ratio sensitively depends on the shape of the primordial $N$-point function.
• Figure 3: A comparison between the non-Gaussian scale-dependent bias correction Eq. (\ref{['eq:dbk']}) and its low-$k$ limit Eq. (\ref{['eq:Dbo-general']}) for some of the bispectrum shapes and the local trispectrum considered in this work. In all cases, a dotted curve represents the low-$k$ limit. Results are shown as a function of $k$ for halos of mass $M=5.3\times 10^{13}\ {\rm M_\odot/{\it h}}$ at $z=0.5$, assuming $f_{\rm NL}=100$ (for the bispectra) and $g_{\rm NL}=10^6$ (for the local trispectrum).