DESI DR2 Reference Mocks: Clustering results from UCHUU ELGs and QSOs

Technical Summary: DESI DR2 Reference Mocks from Uchuu ELGs and QSOs

Problem and Motivation
The Dark Energy Spectroscopic Instrument (DESI) aims to map the matter distribution of the universe using over 50 million galaxy and quasar spectra to constrain the expansion history and growth of structure. To fully utilize this data, particularly for the upcoming Data Release 2 (DR2) cosmology analyses, realistic mock catalogs are required. These mocks must emulate DESI's selection functions and statistical characteristics to test pipelines, assess systematic uncertainties, and validate theoretical predictions.

A specific challenge addressed in this work is the modeling of Emission Line Galaxies (ELGs) and Quasars (QSOs). Unlike Luminous Red Galaxies (LRGs), which are believed to be complete in halo mass occupation, ELGs and QSOs are incomplete tracers in known parameter spaces (such as luminosity or stellar mass). Consequently, traditional Subhalo Abundance Matching (SHAM) techniques, which rely on a one-to-one mapping between halo properties and galaxy observables, are insufficient. The authors aim to construct reference mocks that reproduce the clustering statistics of DESI DR1 and DR2 ELGs and QSOs across redshifts $0.8 < z < 2.1$ (and extending to $z=3.5$ for QSOs) to improve the construction of simulated lightcones and enhance understanding of the galaxy-halo connection.

Methodology
The study utilizes the Uchuu N-body simulation, a high-resolution, large-volume ($2 h^{-1}$Gpc box) simulation containing $12,800^3$ dark matter particles, executed within a flat $\Lambda$CDM cosmology based on Planck 15 parameters. The simulation provides snapshots from $z=14$ to $z=0$, with dark matter halos and subhalos identified using the Rockstar halo finder.

To populate these halos with tracers, the authors employ a modified Subhalo Abundance Matching (SHAM) framework:

1. QSO Modeling:

   • QSOs are assigned to halos based on the peak circular velocity ($V_{peak}$), defined as the maximum $V_{max}$ measured across all redshift outputs.
   • The model assumes a Gaussian distribution of $V_{peak}$ for both central and satellite QSOs, characterized by a mean ($V_{mean}$) and standard deviation ($\sigma_V$).
   • A free parameter, the satellite fraction ($f_{sat}$), controls the relative normalization of the central and satellite distributions.
   • To account for the large redshift uncertainties inherent in QSO spectroscopy (due to broad emission lines), Gaussian redshift errors ($\sigma \approx 500$ km/s) are applied to the mock catalogs.
   • Parameters are tuned by minimizing the $\chi^2$ statistic between the mock monopole of the two-point correlation function (2PCF) and the DESI data over scales of $3$ to $70 h^{-1}$Mpc.

2. ELG Modeling:

   • Recognizing that star formation in satellite galaxies can be quenched by ram pressure stripping if they move too rapidly relative to their central halo, the authors introduce specific selection criteria for ELG satellites.
   • Satellites are selected only if they satisfy: (i) $V_{max}/V_{peak} > 0.9$ (to avoid major mergers), and (ii) low relative velocities with respect to the central halo ($V_{xyz,pec} - V_{central} < 300$ km/s) and a low central $V_{peak}$ ($< 300$ km/s).
   • Similar to QSOs, the model uses a Gaussian $V_{peak}$ distribution with parameters $V_{mean}$, $\sigma_V$, and $f_{sat}$, but the selection criteria are applied prior to abundance matching.

3. Lightcone Construction:

   • Mock lightcones are constructed by replicating Uchuu simulation boxes and cutting them into spherical shells to cover the DESI survey volume.
   • The mocks are masked to match the DESI DR2 footprint and weighted to reproduce the observed comoving number density $n(z)$ in redshift bins of $\Delta z = 0.01$.
   • The best-fit parameters are determined independently for different redshift bins and then parameterized as functions of redshift (e.g., linear evolution for QSO $f_{sat}$ and quadratic evolution for ELG $V_{mean}$).

Key Contributions

• Reference Mocks: The paper presents the first set of reference mocks for DESI DR2 specifically tuned to reproduce the clustering of ELGs and QSOs using the Uchuu simulation.
• Modified SHAM Implementation: The authors successfully adapt the SHAM technique for incomplete tracers. For ELGs, they introduce a velocity-based selection criterion to account for environmental quenching of star formation in satellites, a modification not present in standard SHAM.
• Redshift Evolution: The study identifies and parameterizes the redshift evolution of the SHAM parameters. Specifically, the satellite fraction ($f_{sat}$) for QSOs increases linearly with redshift, while the mean velocity ($V_{mean}$) for ELGs follows a quadratic trend. This allows for a more efficient parameterization than fitting independent parameters in every bin.
• Validation: The mocks are rigorously validated against DESI DR1 and DR2 data, reproducing number densities and clustering statistics across scales from $1$ to $100 h^{-1}$Mpc.

Results

• Clustering Statistics: The modified SHAM mocks show excellent agreement with DESI DR2 data for both the monopole and quadrupole of the redshift-space two-point correlation function (2PCF) and the projected correlation function. The agreement holds across the fitting range ($3$ to $70 h^{-1}$Mpc) and extends to the BAO scale ($\sim 100 h^{-1}$Mpc).
• Power Spectrum: The mocks reproduce the power spectrum monopole and quadrupole reasonably well, with minor deviations at high wavenumbers ($k$) for ELGs, which is expected as the power spectrum was not used in the fitting process.
• Halo Occupation Distribution (HOD):
  • ELGs: The HOD consists of a Gaussian component for centrals (peaking at $M_{halo} \approx 10^{12} h^{-1}M_{\odot}$ with an occupation of 0.095) and a power-law component for satellites (dominating at $M_{halo} > 10^{12.4} h^{-1}M_{\odot}$).
  • QSOs: The HOD similarly shows a Gaussian central component (peaking at $M_{halo} \approx 10^{12.4} h^{-1}M_{\odot}$ with an occupation of 0.319) and a power-law satellite component (dominating at $M_{halo} > 10^{12.8} h^{-1}M_{\odot}$).
• Large-Scale Bias: The large-scale bias ($b$) measured from the mocks matches the bias derived from DESI DR2 data in the range $10$ to $80 h^{-1}$Mpc. Both tracers show a monotonic increase in bias with redshift, consistent with occupying more massive halos at earlier cosmic times.

Significance and Claims
The paper claims that these results provide a critical bridge between theory and observation for DESI analyses. By reproducing the observed number densities and clustering patterns of ELGs and QSOs, these mocks serve as essential tools for:

1. Covariance Matrix Estimation: They can be used to generate covariance matrices for future DESI cosmology analyses.
2. Systematic Testing: They allow for the testing of cosmological pipelines and the assessment of systematic uncertainties inherent in the survey.
3. Physical Insight: The successful application of modified SHAM techniques offers enhanced understanding of the galaxy-halo connection, particularly regarding the environmental dependence of star formation in satellite galaxies (for ELGs) and the evolution of QSO populations.

The authors emphasize that while the models are tuned to DESI data, they are built upon the Planck cosmology and the Uchuu simulation, ensuring they are physically consistent with current cosmological standards. The work does not claim to discover new physics but rather to provide the necessary infrastructure (realistic mocks) to enable precise cosmological inference from the DESI survey.