Biasing from galaxy trough and peak profiles with the DES Y3 redMaGiC galaxies and the weak lensing mass map

Abstract

We measure the correspondence between the distribution of galaxies and matter around troughs and peaks in the projected galaxy density, by comparing \texttt{redMaGiC} galaxies ($0.15<z<0.65$) to weak lensing mass maps from the Dark Energy Survey (DES) Y3 data release. We obtain stacked profiles, as a function of angle $θ$, of the galaxy density contrast $δ_{\rm g}$ and the weak lensing convergence $κ$, in the vicinity of these identified troughs and peaks, referred to as `void' and `cluster' superstructures. The ratio of the profiles depend mildly on $θ$, indicating good consistency between the profile shapes. We model the amplitude of this ratio using a function $F(η, θ)$ that depends on cosmological parameters $η$, scaled by the galaxy bias. We construct templates of $F(η, θ)$ using a suite of $N$-body (`Gower Street') simulations forward-modelled with DES Y3-like noise and systematics. We discuss and quantify the caveats of using a linear bias model to create galaxy maps from the simulation dark matter shells. We measure the galaxy bias in three lens tomographic bins (near to far): $2.32^{+0.86}_{-0.27}, 2.18^{+0.86}_{-0.23}, 1.86^{+0.82}_{-0.23}$ for voids, and $2.46^{+0.73}_{-0.27}, 3.55^{+0.96}_{-0.55}, 4.27^{+0.36}_{-1.14}$ for clusters, assuming the best-fit \textit{Planck} cosmology. Similar values with $\sim0.1σ$ shifts are obtained assuming the mean DES Y3 cosmology. The biases from troughs and peaks are broadly consistent, although a larger bias is derived for peaks, which is also larger than those measured from the DES Y3 $3\times2$-point analysis. This method shows an interesting avenue for measuring field-level bias that can be applied to future lensing surveys.

Figures (17)

• Figure 1: Redshift distribution of the DES Y3 source sample (upper panel) and the high-density redMaGiC galaxies (lower panel). The source redshift distributions are adopted from the mean of HyperRank2022MNRAS.511.2170C. For the lens redshift distributions, we show the average distribution combining four realizations of the photometric redshift for each object. Source bins 1 and 2 are not used in the analysis due to their redshift overlap with the lens bins.
• Figure 2: Cutouts of the DES Y3 redMaGiC galaxy density maps in three tomographic bins, centred on ${\rm RA}=40^{\circ}$, ${\rm Dec}=-35^{\circ}$, smoothed by a Gaussian filter with a fixed comoving scale $R_s=20{\,h^{-1}\,\rm Mpc}$. Underdense regions are blue; overdense regions are red. The identified two-dimensional voids (resp. clusters) are shown by dashed (resp. solid) circles. The size of the cutout box is $50\times33 \,\text{deg}^2$ in Gnomonic projection. Notice that distortions are present at the edge of the boxes due to the large angular size.
• Figure 3: The distribution of the smoothed galaxy density contrast for the void/cluster finding in the DES Y3 data (first three panels), and the smoothed kappa maps (last two panels). The smoothing angles are indicated in each panel for each lens/source redshift bin. The shaded regions are the pixels used for void (blue) and cluster (red) finding, defined by the threshold contrast $\delta_c$.
• Figure 4: Various galaxy biases measured from the Gower Street simulations as a function of input bias in the simulation. The figures shows four sets of measured biases using the galaxy and dark matter density maps: $b_{C_{\ell}}$, the weighted ratio of angular power spectra (blue lines), $b_{\mathop{\mathrm{RMS}}\nolimits}$, the ratio of the standard deviation of smoothed maps (orange dashed lines), and $b^{v,c}_{\rm MP}$, the profile ratio stacked around voids (green dots) and clusters (red open squares). The three columns show this relation for three simulations with increasing $\sigma_8$ values (left to right). The black line marks the diagonal. This provides a mapping between the input galaxy bias and the actual bias measured from the ratios of several quantities directly concerning the galaxy and matter field. The deviation from diagonal for small $b_{\rm input}$ is due to shot noise, and that for large $b_{\rm input}$ is due to the clipping of under-dense pixels.
• Figure 5: The stacked galaxy density profiles $\langle \delta_{\rm g} \rangle_{\rm Ring}(\theta)$ (upper panel) and the lensing profiles $\langle \kappa \rangle_{\rm Ring}(\theta)$ (lower panel) for voids (empty points and dashed lines) and clusters (filled points and solid lines), measured in the DES Y3 data (blue) and in 16 Gower Street simulations (yellow). The lens-source combination $(i,j)$ is indicated the upper right corner. The Gower Street samples have cosmological parameters within ranges $0.27\leq\Omega_{\rm m}\leq 0.32$ and $-1<w<-0.9$, and have an input linear bias of $b_{\rm input}=1.7$. For the data $\langle \kappa \rangle_{\rm Ring}(\theta)$ profiles, the solid and dashed green lines show the template model with the best-fit bias values. Grey shading denotes angular scales omitted from the final calculations.