🔭 astrophysics

Fast and accurate Gaia-unWISE quasar mock catalogs from LPT and Eulerian bias

This paper presents and validates 100 full-sky quasar mock catalogs generated using a novel hierarchical nonlocal nonlinear bias scheme (Hicobian) on lightcone dark matter fields, which accurately reproduce the Gaia-unWISE Quaia catalog's observational characteristics and summary statistics for future cosmological analyses.

Original authors: Francesco Sinigaglia, Francisco-Shu Kitaura, Mahlet Shiferaw, Ginevra Favole, Kate Storey-Fisher, Nestor Arsenov

Published 2026-04-15

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CC BY 4.0

Original authors: Francesco Sinigaglia, Francisco-Shu Kitaura, Mahlet Shiferaw, Ginevra Favole, Kate Storey-Fisher, Nestor Arsenov

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are an architect trying to design a skyscraper that will stand for a thousand years. Before you pour a single drop of concrete, you need to know: Will it sway in the wind? Will the foundation crack? How will it look from different angles?

In the world of cosmology, the "skyscraper" is the Universe, and the "wind" is the complex data we collect from telescopes. To test our theories, scientists need to build a perfect simulation (a "mock catalog") that looks and behaves exactly like the real Universe.

This paper is about building a massive, ultra-accurate digital twin of a specific cosmic dataset called Quaia (a catalog of quasars, which are the brilliant, glowing hearts of ancient galaxies).

Here is the story of how they built it, explained simply:

1. The Challenge: Mapping the Whole Sky

The Quaia catalog is special because it covers the entire sky and looks back in time to when the Universe was very young (redshift $z \sim 4$ ).

The Problem: To simulate this, you can't just build a small model of a neighborhood; you need to build a model of the entire planet, stretching from the ground to the stratosphere.
The Solution: The team used a supercomputer to generate 100 full-sky universes. They didn't just make a static snapshot; they created a "movie" of the universe evolving smoothly from today back to the distant past.

2. The Engine: "Augmented Lagrangian Perturbation Theory" (ALPT)

How do you simulate gravity without running a simulation that takes a million years?

The Analogy: Imagine trying to predict how a crowd of people will move in a stadium. You could simulate every single person's footsteps (too slow!), or you could use a smart algorithm that predicts the general flow of the crowd based on where they started and how fast they are moving.
The Method: The authors used a clever mathematical shortcut called ALPT. It's like a "smart GPS" for dark matter. It calculates how the invisible "scaffolding" of the universe (dark matter) stretches and twists over time, creating the cosmic web of filaments and voids where galaxies live.

3. The "Painting" Process: Hicobian

Once they had the dark matter "scaffolding," they needed to place the quasars (the bright lights) on it. But quasars don't just pop up randomly; they prefer to live in specific environments, like high towers (dense clusters) or quiet suburbs (voids).

The Analogy: Think of the dark matter as a landscape with mountains, valleys, and rivers. The team used a new "painting recipe" called Hicobian.
- Instead of just saying "put a quasar here," Hicobian looks at the landscape and asks: "Is this a mountain peak? A river valley? A flat plain?"
- It then decides exactly how many quasars to place in each spot based on the local "terrain." This ensures the quasars look and behave exactly like the real ones found in the Quaia catalog.

4. Adding the "Glitch": Simulating Real-World Messiness

A perfect simulation is useless if it's too perfect. Real telescopes make mistakes. They get blurry, they miss faint objects, and they sometimes guess the distance wrong.

The Analogy: Imagine taking a perfect, high-definition photo of a city, but then deliberately adding camera shake, fog, and pixel noise to make it look like a photo taken with an old, shaky camera.
The Execution: The team took their perfect digital quasars and "injected" the specific errors of the Quaia telescope:
- Redshift Uncertainty: They made the distance measurements slightly "fuzzy," just like the real data.
- The "Mask": They hid parts of the sky that the telescope couldn't see (like the dusty plane of our own Milky Way).
- Selection Bias: They made sure the simulation only included the types of quasars the telescope is actually good at finding.

5. The "Stress Test": Does It Match Reality?

Now comes the most important part: Validation.
The team compared their 100 fake universes against the real Quaia data. They checked:

The Map: Do the fake quasars cluster in the same shapes as the real ones? (Yes!)
The Distances: Do the fake distance errors look like the real ones? (Yes!)
The Statistics: If they run complex math on the fake data, does it produce the same results as the real data? (Yes!)

The Result: The fake universes were indistinguishable from the real thing. The "fake" maps looked exactly like the "real" maps, and the statistical patterns matched perfectly.

Why Does This Matter?

Think of these mock catalogs as a flight simulator for cosmologists.
Before scientists try to extract deep secrets about Dark Energy or the expansion of the universe from the real Quaia data, they can "fly" their analysis tools through these 100 fake universes first.

If their tool crashes in the simulator, they know to fix it before touching the real data.
If the tool works perfectly in the simulator, they can trust it when they analyze the real universe.

In short: This paper provides the scientific community with a perfectly calibrated, full-sky, time-traveling video game of quasars. It allows astronomers to test their theories and tools with confidence, ensuring that when they look at the real universe, they aren't being fooled by the telescope's imperfections.

1. Problem Statement

The paper addresses the critical need for accurate, large-volume mock catalogs to analyze the Gaia-unWISE Quasar Catalog (Quaia). The Quaia catalog is a full-sky dataset covering redshifts $z \sim 0$ to $z \sim 4$ , combining data from Gaia and unWISE surveys. Generating mocks for this dataset presents four specific challenges:

Volume: The full-sky coverage up to $z \sim 4$ requires a cosmological volume of $V \approx (10 \, h^{-1} \text{Gpc})^3$ . Running full $N$ -body simulations for 100 realizations of this volume is computationally prohibitive.
Redshift Evolution: The mocks must capture the smooth evolution of the dark matter (DM) field and bias across a wide redshift range, rather than relying on single redshift snapshots.
Bias Connection: There must be an accurate physical link between the underlying DM field and the quasar population, requiring calibration against high-fidelity reference catalogs.
Resolution vs. Memory: To handle the large volume, a coarse mesh ( $l \sim 5.5 \, h^{-1} \text{Mpc}$ ) is necessary, which demands a sophisticated subgrid model to correctly populate cells with quasar positions without losing small-scale clustering information.
Systematics: The mocks must replicate complex observational effects specific to Quaia, including spectrophotometric redshift uncertainties, angular selection functions (masking), and redshift number counts ( $n(z)$ ).

2. Methodology

The authors developed an end-to-end workflow using the WebON code and a novel bias model to generate 100 full-sky mock catalogs. The process involves four main stages:

A. Dark Matter Lightcones

Solver: They use Augmented Lagrangian Perturbation Theory (ALPT) implemented in the WebON code. ALPT combines long-range 2nd-order LPT (2LPT) with a short-range component based on the spherical collapse model.
Lightcone Construction: The code generates DM fields on a lightcone geometry by interpolating displacement fields from fixed redshift snapshots ( $z = 0, 0.5, \dots, 3.5$ ). A Zel'dovich approximation correction ensures smooth redshift evolution between snapshots.
Resolution: The simulation uses a $1800^3$ cell mesh in a $(10 \, h^{-1} \text{Gpc})^3$ volume, resulting in a cell size of $\sim 5.5 \, h^{-1} \text{Mpc}$ .

B. Reference Catalogs and Bias Calibration

Reference: The bias model is calibrated against AbacusSummit $N$ -body simulations (Planck cosmology) using a Halo Occupation Distribution (HOD) tuned to DESI Early Data Release (EDR) quasar clustering.
Bias Model (Hicobian): The authors apply a novel hierarchical nonlocal nonlinear stochastic bias scheme called Hicobian.
- Cosmic Web Classification: Cells are classified into 16 distinct environments based on a hierarchical "T-web" (tidal field) and "D-web" (curvature tensor) classification.
- Stochasticity: The number of quasars per cell follows a Negative Binomial Distribution to account for overdispersion.
- Deterministic Bias: The mean density is modeled via a power law and exponential factors accounting for high/low-density thresholds.
Fine-Tuning: The bias parameters are initially fitted to DESI-like clustering. They are then fine-tuned (specifically the power-law exponent $\alpha$ ) to match the angular clustering amplitude of the Quaia catalog, which has a higher bias due to its brighter magnitude cuts ( $G < 20.5$ and $G < 20$ ) compared to DESI.

C. Position Assignment and Redshift Space Distortions (RSD)

Subgrid Model: Quasar positions are assigned within cells by randomly sampling existing ALPT DM particle positions. If the required number of quasars exceeds available particles, uniform random sampling is used (rare for QSOs).
RSD: Positions are shifted to redshift space using a velocity model combining:
- Large-scale coherent flows (from ALPT).
- Small-scale dispersion (Gaussian distribution scaled by density).
- A nonlinear power-law transform ( $\vec{v}' = \vec{v}^\eta$ ) to enhance high-velocity tails, mimicking N-body "Fingers of God" effects.
- Velocity parameters are made dependent on the T-web environment.

D. Injection of Observational Effects

To transform "spectroscopic" mocks into realistic "Quaia-like" mocks, three effects are injected:

Redshift Uncertainties: Random offsets are added to spectroscopic redshifts based on the Quaia $\Delta z$ vs. $z$ error curve.
Angular Selection Function: A subsample is extracted based on the Quaia selection function (modeled via Gaussian processes) to account for Galactic dust and survey geometry.
Redshift Distribution ( $n(z)$ ): The mocks are subsampled to match the observed $n(z)$ distribution of the Quaia catalog.

3. Key Contributions

100 Full-Sky Realizations: The release of 100 independent mock catalogs covering the full sky from $z=0$ to $z \sim 4$ , specifically tailored for the Quaia survey.
Hicobian Bias Model: The application and calibration of a hierarchical, nonlocal, nonlinear bias model that successfully bridges the gap between approximate gravity solvers (ALPT) and high-fidelity HOD results.
End-to-End Systematics Injection: A robust pipeline that incorporates realistic observational systematics (redshift errors, selection functions, and $n(z)$ ) directly into the mock generation process.
Public Release: The catalogs are made publicly available for the community to use for covariance matrix estimation and analysis validation.

4. Results and Validation

The authors validated the mocks against the actual Quaia catalog using several summary statistics:

Visual Inspection: Full-sky maps of QSO number counts show excellent qualitative agreement with the cosmic web structure traced by Quaia.
Redshift Distributions: The mocks reproduce the $n(z)$ distribution and redshift error distributions ( $\Delta z$ ) of the data with high fidelity.
Angular Clustering:
- Two-Point Correlation Function ( $w(\theta)$ ): Excellent agreement between mocks and data across all angular scales and redshift bins. A minor deviation ( $<2\sigma$ ) was found at very small scales ( $\theta \lesssim 0.3^\circ$ ) due to subgrid limitations, but this is below the typical analysis scale for Quaia.
- Angular Power Spectra ( $C_\ell$ ): The mocks match the Quaia $C_\ell$ measurements well. The normalized covariance matrices derived from the 100 mocks are well-behaved (positive-definite) and show expected correlations.
Systematics Impact:
- Angular Mask: The selection function has a negligible impact on clustering for $\ell \gtrsim 50$ , with minor deviations at lower multipoles.
- Redshift Errors: The difference between using spectroscopic vs. spectrophotometric redshifts in the mocks is negligible for angular power spectra.

5. Significance

This work provides a critical tool for the precision cosmology era. By offering fast, accurate, and full-sky mock catalogs that include realistic observational systematics, the authors enable:

Robust Covariance Estimation: Essential for quantifying uncertainties in cosmological parameters derived from Quaia.
Pipeline Validation: A benchmark for testing analysis pipelines against systematics before applying them to real data.
Future Analysis: The catalogs are designed to support upcoming studies on Baryon Acoustic Oscillations (BAO), density field reconstruction, and the impact of systematics on 3D clustering.
Methodological Advancement: The successful use of ALPT combined with the Hicobian bias model demonstrates a viable path for generating high-fidelity mocks for future large-scale surveys (e.g., Euclid, LSST, Roman) where full $N$ -body simulations are infeasible.