Constraining the Stellar-to-Halo Mass Relation with Galaxy Clustering and Weak Lensing from DES Year 3 Data

TL;DR

The authors develop a joint Halo Occupation Distribution framework that embeds a parametric stellar-to-halo mass relation to connect DES Year 3 galaxies to their dark matter halos, modeling scales from the 1-halo to quasi-linear regimes. They introduce a new stellar-mass–selected lens sample, trainred by GalPro, and combine galaxy-galaxy lensing with galaxy clustering to constrain the SHMR, satellite fraction, and galaxy bias. Their fiducial SHMR constraints are broadly consistent with literature, with best-fit parameters showing a shallow high-mass slope and a substantial characteristic mass scale; including high-mass bins tightens the subpower-law strength at the massive end. The results demonstrate the viability of DES Y3 data to constrain the SHMR in a broad mass range and highlight the importance of modeling the 1-halo to 2-halo transition and of including clustering information for robust halo-occupation constraints; they also outline pathways for improvement with future surveys and forward-modeling approaches.

Abstract

We develop a framework to study the relation between the stellar mass of a galaxy and the total mass of its host dark matter halo using galaxy clustering and galaxy-galaxy lensing measurements. We model a wide range of scales, roughly from $\sim 100 \; {\rm kpc}$ to $\sim 100 \; {\rm Mpc}$, using a theoretical framework based on the Halo Occupation Distribution and data from Year 3 of the Dark Energy Survey (DES) dataset. The new advances of this work include: 1) the generation and validation of a new stellar mass-selected galaxy sample in the range of $\log M_\star/M_\odot \sim 9.6$ to $\sim 11.5$; 2) the joint-modeling framework of galaxy clustering and galaxy-galaxy lensing that is able to describe our stellar mass-selected sample deep into the 1-halo regime; and 3) stellar-to-halo mass relation (SHMR) constraints from this dataset. In general, our SHMR constraints agree well with existing literature with various weak lensing measurements. We constrain the free parameters in the SHMR functional form $\log M_\star (M_h) = \log(εM_1) + f\left[ \log\left( M_h / M_1 \right) \right] - f(0)$, with $f(x) \equiv -\log(10^{αx}+1) + δ[\log(1+\exp(x))]^γ/ [1+\exp(10^{-x})]$, to be $\log M_1 = 11.506^{+0.325}_{-0.404}$, $\log ε= -1.632^{+0.306}_{-0.181}$, $α= -1.638^{+0.108}_{-0.099}$, $γ= 0.596^{+0.251}_{-0.210}$ and $δ= 3.810^{+2.045}_{-1.811}$. The inferred average satellite fraction is within $\sim 5-35\%$ for our fiducial results and we do not see any clear trends with redshift or stellar mass. Furthermore, we find that the inferred average galaxy bias values follow the generally expected trends with stellar mass and redshift. Our study is the first SHMR in DES in this mass range, and we expect the stellar mass sample to be of general interest for other science cases.

Figures (19)

• Figure 1: The total HOD model prediction (thick solid blue) and the two thresholded HOD's (solid and dashed cyan) that produce it via their difference. The central (solid red) and satellite (dashed red) components of the total HOD (thick solid blue) are also presented. The HOD parameters we used in this plot are: $\sigma_{\log M_\star} = 0.3$, $\alpha_{\rm sat} = 1$, $B_{\rm sat}=25$, $\beta_{\rm sat}=0.8$, $B_{\rm cut}=10$, $\beta_{\rm cut}=1.5$, $f_{\rm cen}=1=f_{\rm sat}$, $\kappa_{\rm sat}=1.5$; the SHMR parameters are: $\log M_1=11.45$, $\log \epsilon=-1.702$, $\alpha = -1.736$, $\gamma = 0.613$, $\delta=4.273$.
• Figure 2: (Upper) The total $\gamma_t$ model prediction (solid dark blue) and its components, as described in the legend, using the HOD model from Figure \ref{['fig:SHOD_tophat']}. In addition to the HOD and SHMR parameters described in Figure \ref{['fig:SHOD_tophat']}, for this plot we set $\Delta \log M_\star=0$, $\Delta z_\ell =0 = \Delta z_s$, $m_s=0$, $\Sigma_\ell = 1$, $\kappa_c = 1$, $\alpha_{\rm lmag}=4.5$. (Lower) Similar to the left plot but for $w$.
• Figure 3: (Upper) Redshift distributions, $n(z)$, of the lenses (solid filled; different mass bins are plotted with different color per redshift bin) and of the source (dashed) galaxies. (Lower) Stellar-mass distributions, $n_\star(\log M_\star)$, of our lenses. Each panel corresponds to a different redshift bin $\ell$, and in each panel all stellar-mass bins $m$ are shown.
• Figure 4: Correlations between the $i$-band depth survey property and observed galaxy density relative to the mean density over the full footprint, before (red) and after (blue) the correction using the Neural-Network weights from Section \ref{['sec:LSSweights']}. We show this relationship for all $(\ell,m)$ lens bins as noted in each panel. The gray shaded region in every panel corresponds to 1% deviation from unity.
• Figure 5: Measurements (points) and best-fit model (thick solid outlined) predictions for galaxy-galaxy lensing as a function of angular scale in ${\rm arcmin}$ from jointly fitting $\gamma_t$ and $w$ of each individual panel. Each panel corresponds to a lens-source bin combination from the ones that we choose to model in this work, as indicated in parenthesis $(\ell,m,s)$. Each model component that makes up the total (outlined solid cyan) line is also shown: 1-halo central (${\rm 1h \; Cen}$, solid black), 2-halo central (${\rm 2h \; Cen}$, dashed black), 1-halo satellite (${\rm 1h \; Sat}$, dash-dotted black), 2-halo satellite (${\rm 2h \; Sat}$, dotted black), satellite stripping (${\rm Sat\; Strip}$, dashed magenta) and lens magnification (${\rm Lens Mag.}$, dashed gold). Gray points under the shaded areas are removed from the fits by the scales cuts. We also plot the residuals between the data points and the best-fit model below each panel.