Scale-dependent bias induced by local non-Gaussianity: A comparison to N-body simulations

TL;DR

The authors test the impact of local-type primordial non-Gaussianity, parameterized by $f_{ m NL}$, on halo clustering using large-volume N-body simulations in a $ m \Lambda CDM$ framework. They verify that the non-Gaussian bias shift can be written as a sum of a scale-dependent term $ riangle b_ abla$, a scale-independent term $ riangle b_{ m I}$, and a matter-power response term $b(M)eta_{ m m}$, with inclusion of $ riangle b_{ m I}$ and $eta_{ m m}$ substantially improving agreement with simulations across $k\, o\,0.03$ h/Mpc for moderately biased haloes. The results show consistency between halo-halo and halo-matter measurements and support (to first order) linear scaling in $f_{ m NL}$, reinforcing the viability of LSS clustering as a probe of primordial non-Gaussianity, though limitations arise for low-bias samples and on smaller scales. These findings help interpret previous constraints from large-scale surveys and guide future analyses accounting for scale-independent bias and matter-power corrections.

Abstract

We investigate the effect of primordial non-Gaussianity of the local f_NL type on the auto- and cross-power spectrum of dark matter haloes using simulations of the LCDM cosmology. We perform a series of large N-body simulations of both positive and negative f_NL, spanning the range between 10 and 100. Theoretical models predict a scale-dependent bias correction Δb(k,f_NL) that depends on the linear halo bias b(M). We measure the power spectra for a range of halo mass and redshifts covering the relevant range of existing galaxy and quasar populations. We show that auto and cross-correlation analyses of bias are consistent with each other. We find that for low wavenumbers with k<0.03 h/Mpc the theory and the simulations agree well with each other for biased haloes with b(M)>1.5. We show that a scale-independent bias correction improves the comparison between theory and simulations on smaller scales, where the scale-dependent effect rapidly becomes negligible. The current limits on f_NL from Slosar et al. (2008) come mostly from very large scales k<0.01 h/Mpc and, therefore, remain valid. For the halo samples with b(M)<1.5-2 we find that the scale- dependent bias from non-Gaussianity actually exceeds the theoretical predictions. Our results are consistent with the bias correction scaling linearly with f_NL.

Figures (10)

• Figure 1: Top panel : multiplicity function $f(\nu,0)$ for the Gaussian simulations. Different symbols refer to different redshifts as indicated. Results are shown relative to the Sheth-Tormen fitting formula to emphasise deviation from the latter. Bottom panel : ratio between the non-Gaussian and the fiducial Gaussian mass functions. The dotted and dotted-dashed curves are the theoretical prediction at $z=0$ and 2, which is based on an Edgeworth expansion of the dark matter probability distribution function (see text). In both panels, error bars denote Poisson errors. For illustration, $M=10^{15}\ {\rm M_\odot/{\it h}}$ corresponds to $\nu=3.2$, 5.2, 7.7 at redshift $z=0$, 1 and 2, respectively. Similarly, $M=10^{14}\ {\rm M_\odot/{\it h}}$ and $10^{13}\ {\rm M_\odot/{\it h}}$ correspond to $\nu=1.9$, 3, 4.5 and 1.2, 1.9, 2.9 respectively.
• Figure 2: Halo bias as a function of wavenumber. Results are shown at redshift $z=0.3$, 0.5, 1, 1.4 and 2 (from bottom to top) for haloes with mass above $2\times 10^{13}\ {\rm M_\odot/{\it h}}$. Filled and empty symbols represent the bias estimators $b_{\rm hh}=\sqrt{P_{\rm hh}/P_{\rm mm}}$ and $b_{\rm mh}=P_{\rm mh}/P_{\rm mm}$, respectively. The bins are equally spaced in logarithmic space with a bin width $\Delta\log k=0.1$. Measurements of $b_{\rm hh}$ have been slightly shifted horizontally for clarity. The horizontal lines indicate our estimate of the linear bias $b(M)$ (see text). Notice that $P_{\rm hh}(k)$ is corrected for shot-noise.
• Figure 3: Top panel : Non-Gaussian correction $\beta_{\rm m}(k,f_{\rm NL})=\Delta P_{\rm mm}(k,f_{\rm NL})/P_{\rm mm}(k,0)$ to the matter power spectrum that originates from primordial non-Gaussianity of the local type. Results are shown at redshift $z=0$ and 2 for $f_{\rm NL}=\pm 100$. The dashed curves indicate the prediction from a leading-order perturbative expansion. Bottom panel : Non-Gaussian bias correction for the haloes of mass $M>2\times 10^{13}\ {\rm M_\odot/{\it h}}$ extracted from the snapshot at $z=0.5$ (filled symbols). The solid curve represents our theoretical model eq. (\ref{['eq:dbias']}). The dashed, dotted and dashed-dotted curves show the three separate contributions that arise at first order in $f_{\rm NL}$. Our theoretical scaling agrees very well with the data for $k~\hbox{$<$}{\hbox{$\sim$}} 0.05\ {\rm {\it h}Mpc^{-1}}$.
• Figure 4: Top panel : A comparison between the auto-power spectrum with and without the shot-noise correction. $P_{\rm hh}(k,f_{\rm NL})$ is measured at $z=1$ for haloes of mass $M>2\times 10^{13}\ {\rm M_\odot/{\it h}}$. From top to bottom, the various symbols represent the simulation results with $f_{\rm NL}=+100$ (blue), 0 (green) and -100 (red). The linear bias of this sample is $b(M)\approx 2.5$. Bottom panel : $P_{\rm hh}(k,f_{\rm NL})/P_{\rm hh}(k,0)$ as a function of wavenumber. The dashed curves denote the theoretical prediction (see text). In both panels, measurements without the shot-noise correction have been shifted horizontally for clarity.
• Figure 5: Non-Gaussian bias correction measured in the simulations at various redshifts for haloes of mass $M>2\times 10^{13}\ {\rm M_\odot/{\it h}}$ (colors as in Fig. \ref{['fig:fig4']}). In each panel, the upper plot shows the ratio $P_{\rm hh}(k,f_{\rm NL})/P_{\rm hh}(k,0)-1$ (dotted curves, empty symbols) and $P_{\rm mh}(k,f_{\rm NL})/P_{\rm mh}(k,0)-1$ (solid curves, filled symbols). The error bars represent the scatter among 5 realisations. The respective output redshift and linear halo bias are also quoted. The bottom of each panel displays the departure from the theoretical prediction, $\Delta b^{s}/\Delta b^{t}$ (see text). The shaded area indicates the domain where the deviation is less than 20 percent. The theory agrees reasonably well with the measurements at wavenumber $k~\hbox{$<$}{\hbox{$\sim$}} 0.03\ {\rm {\it h}Mpc^{-1}}$.