The Completed SDSS-IV Extended Baryon Oscillation Spectroscopic Survey: N-body Mock Challenge for Galaxy Clustering Measurements

TL;DR

This study develops a comprehensive N-body mock challenge for the final eBOSS DR16 LRG analysis, leveraging the Outer Rim simulation and a progression of HOD models (including assembly bias) to stress BAO and full-shape RSD pipelines. By comparing three RSD methods in configuration and Fourier space across multiple mock sets, the work demonstrates sub-percent accuracy in dilation parameters and f sigma8, validates the consensus DR16 clustering results, and characterizes the systematic error budget. The findings indicate HOD variations impart only sub-dominant biases, while modeling systematics remain a relevant, but manageable, component for current data and a key consideration for future surveys like DESI. The released mock products and methodologies provide a scalable framework for pre-survey validation of large-volume spectroscopic surveys and for extending to other tracers such as ELGs.

Abstract

We develop a series of N-body data challenges, functional to the final analysis of the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 16 (DR16) galaxy sample. The challenges are primarily based on high-fidelity catalogs constructed from the Outer Rim simulation - a large box size realization (3 Gpc/h) characterized by an unprecedented combination of volume and mass resolution, down to 1.85x10^9 M_sun/h. We generate synthetic galaxy mocks by populating Outer Rim halos with a variety of halo occupation distribution (HOD) schemes of increasing complexity, spanning different redshift intervals. We then assess the performance of three complementary redshift space distortion (RSD) models in configuration and Fourier space, adopted for the analysis of the complete DR16 eBOSS sample of Luminous Red Galaxies (LRGs). We find all the methods mutually consistent, with comparable systematic errors on the Alcock-Paczynski parameters and the growth of structure, and robust to different HOD prescriptions - thus validating the robustness of the models and the pipelines used for the baryon acoustic oscillation (BAO) and full shape clustering analysis. In particular, all the techniques are able to recover a_par and a_perp to within 0.9%, and fsig8 to within 1.5%. As a by-product of our work, we are also able to gain interesting insights on the galaxy-halo connection. Our study is relevant for the final eBOSS DR16 `consensus cosmology', as the systematic error budget is informed by testing the results of analyses against these high-resolution mocks. In addition, it is also useful for future large-volume surveys, since similar mock-making techniques and systematic corrections can be readily extended to model for instance the Dark Energy Spectroscopic Instrument (DESI) galaxy sample.

Figures (14)

• Figure 1: HOD shapes in the Zheng2007 model, used for the production of galaxy mocks. In the various panels, dotted lines describe the central occupation statistics (Equation \ref{['eq_zheng_hod_cens']}), dashed lines are used for the satellite occupation statistics (Equation \ref{['eq_zheng_hod_sats']}), and solid lines represent the composite HODs. Three luminosity thresholds are considered, corresponding to different HOD parameter choices, as reported in Table \ref{['table_zheng07']}. See the main text for more details.
• Figure 2: [Top] Effects of varying the main parameters controlling the SHMF for central galaxies (Equation \ref{['eq_leauthaud_fshmr']}), modeled as a mean-log relation in the Leauthaud model and heavily based on Behroozi2010. The key shape parameters are altered in turn by $10\%$ ($M_{0}$, $M_{1}$), $20\%$ ($\beta$, $\delta$), and $50\%$ ($\gamma$), respectively, from the baseline Behroozi2010 model at $z=0$ (solid black line and upper part in Table \ref{['table_leauthaud11_hod']}), when $\sigma_{\log \rm M_{*}}=0.20$. Different line styles and colors refer to such variations, as clearly indicated in the panel. [Bottom] SHMF underlying the Leauthaud model at $z=0$, and its redshift evolution at $z=0.695$ and $z=0.865$: we use these SHMRs in our mock-making procedure.
• Figure 3: SHMFs for central galaxies adopted in the Tinker model and in our mock-making procedure at $z=0$ (solid lines), $z=0.695$ (dotted lines), and $z=0.865$ (dashed lines). Active galaxies are displayed in blue, while quiescent galaxies are represented in brown.
• Figure 4: HOD shapes adopted in our mock-making procedure, at $z=0.695$, for 3 thresholds in mass, denoted as 'Thres 1' ($M^{\rm thr}_{*}=10^{10} h^{-1} M_{\odot}$), 'Standard' ($M^{\rm thr}_{*}=10^{10.5} h^{-1} M_{\odot}$), and 'Thres 2' ($M^{\rm thr}_{*}=10^{11} h^{-1} M_{\odot}$). Top panels display the various HODs in the Leauthaud model. Central panels show the Tinker model, where active and quiescent galaxy HODs are represented by different colors, as indicated in the figure. Bottom panels are for the Hearin HODs, where galaxies are split into upper- and lower-percentiles in terms of halo concentration, respectively, with different assembly bias strength for centrals and satellites ($A_{\rm bias}^{\rm cen} =1.0$ and $A_{\rm bias}^{\rm sat}=0.2$). In all the plots, the central occupation statistics is displayed with dotted lines, the satellite occupation statistics with dashed lines, and the global HOD shapes with solid lines.
• Figure 5: Small portion of the Outer Rim halo catalog at $z=0.865$. The left panel is a $100 \times 100 ~[h^{-1} {\rm Mpc}]^2$ projection along $x$ and $y$ and across $z$, with thickness $\Delta z=50~h^{-1} {\rm Mpc}$, while the middle panel is a progressive zoom into a $50 \times 50 ~[h^{-1} {\rm Mpc}]^2$ block. Points the figure are FOF halos, color coded by their mass. Zooming into a smaller $7 \times 7~[h^{-1} {\rm Mpc}]^2$ inset of the halo catalog, the right panel displays the ellipsoidal shape of a halo of mass $4.938 \times 10^{13}~h^{-1}{\rm M_{\odot}}$ contained inside that area, rendered with a 1% random particle subsample. Length units displayed in the left panel are in $h^{-1} {\rm Mpc}$. The high resolution of the simulation, down to $1.85 \times 10^9 h^{-1} {\rm M_{\odot}}$, allows one to resolve accurately also relatively low-mass halos.