Unclustered tracers remain unclustered: the lack of primordial non-Gaussianity response of bias-zero tracers

TL;DR

The paper critically tests the idea that bias-zero tracers, selected by local density, can maximize sensitivity to local PNG characterized by $f_{\rm NL}$. Using PNG-UNITsim simulations with $f_{\rm NL}=100$ and $-20$, tracers are binned by $\delta_{t,R}$ (with $R=8\,h^{-1}\mathrm{Mpc}$) and their linear bias $b_1$ and PNG response $b_{\phi}$ are inferred from cross- and auto-power spectra against the matter field. Across all parent samples (all halos, halo mass bins, and DESI-like LRG/QSO galaxies), the results show $b_{\phi}\approx0$ for tracers with $b_1\approx0$, with only mild PNG signals for $|b_1|>1$ and significant deviations from the universal relation $b_{\phi}=2\delta_{\rm crit}(b_1-1)$; shot noise is strongly non-Poissonian ($A_{\rm sn}$ typically large). These findings imply that density-selected bias-zero tracers do not enhance PNG constraints and underscore the need for realistic simulation-based modelling in PNG forecast studies and multi-tracer analyses.

Abstract

Constraining primordial non-Gaussianities (PNG) is one of the main goals of new-generation large-scale galaxy surveys. It had been proposed that unclustered tracers (with bias $b_1=0$) could be optimal for PNG studies, and that these could be found by selecting galaxies in bins of their local density. Here, we test this hypothesis in state-of-the-art simulations from the PNG-UNITsim suite with local $f_{\rm NL}=100$ and $f_{\rm NL}=-20$. We consider different parent tracer catalogues: all halos together, halos in large mass bins, and HOD models for LRGs and QSO. We then classify these tracers by their local density ($δ_{t,R}$) and measure the linear bias ($b_1$) and PNG-response ($b_φ$). Most $δ_{t,R}$ bins show a PNG-response compatible with $b_φ=0$ for all halos or the low-mass bin (log$M<11$). For high-mass halos (log$M>$12), QSO or LRG, we recover a trend closer to the universality relation ($b_φ= 2 δ_{\rm crit}(b_1-1)$) for $b_1>1$, but the $b_φ(b_1)$ curve flattens to 0 below $\vert b_1\lvert<1$. Hence, we find $b_φ\approx0$ for all bias-zero tracers considered. The complex $δ_{t,R}$-based selection causes their clustering to strongly deviate from simple assumptions, namely the universality relation and Poisson shot noise, hindering their capability to constrain PNG.

Figures (6)

• Figure 1: Theoretical auto-power spectra for matter ($b = 1$, $f_{\rm NL}$ = 0), a biased tracer in a Gaussian Universe ($b_g=2$, $f_{\rm NL}$$=0$), a biased universal tracer with PNG ($b_g=2$, $f_{\rm NL}$$=100$, $p=1$), an unclustered but universal tracer ($b_g=0$, $f_{\rm NL}$$=100$, $p=1$), and an unclustered and non-PNG-responsive tracer ($b_g=0$, $b_\phi=0$).
• Figure 2: Measured linear halo bias $b_1$ (68% c.l.) as a function of halo overdensity $\delta_{h,R}$ in spheres of $R=8 h^{-1}$Mpc for the UNIT simulation ($f_{\rm NL}$ =0). Similar results are found for $f_{\rm NL}$$=100$.
• Figure 3: We show the PNG-response ($b_\phi$) as a function of the measured bias ($b_1$) for the tracers binned in their local overdensity. Top: Results for all halos (purple band) above $M=2\times10^{11}$ together of the PNG-UNITsim, based on the matter-halo cross-power spectrum. The black dot-dashed line shows the universality relation. We find that the PNG-response is well-below the universality relation and compatible with no response ($b_\phi\sim0$) for all the $\delta_R$-bins. We also show (as markers with errorbars) the results using mass bins as parent catalogues. Bottom: Same results but for the LRG and QSO from PNG-UNITsim-XL.
• Figure 4: PNG response ($b_\phi$) and linear bias ($b_1$) measurements for the closest case to $b_1=0$ for the density bins (blue) and density split (red) samples. We consider different parent catalogues: all halos, halos in mass bins, and HODs (\ref{['sec:density_classification']}). For all cases, the PNG response is clearly smaller than predicted by universality (dot-dashed line) and compatible with $b_\phi=0$.
• Figure 5: Power spectrum of a bin with $b_1\sim 3.2$ selected by halo mass ($M_h$, left) and by local halo overdensity ($\delta_{h,R}$, right). Whereas the effect of introducing PNG ($f_{\rm NL}$$=100$) has a strong effect on mass-selected bins, the $\delta_{h,R}$-bins show near identical clustering for $f_{\rm NL}$ = 0 and $f_{\rm NL}$ = 100.