Euclid Galaxy Lens Catalog

• Euclid Galaxy Lens Catalog is a comprehensive database of galaxy-scale strong gravitational lenses identified via high-resolution Euclid imaging and verified through machine learning and citizen science.
• It leverages wide-area surveys and advanced deep learning methods like ResNets and Vision Transformers to catalog hundreds of lenses with projections reaching up to 110,000 over the mission.
• The catalog underpins precision cosmology and dark matter studies by providing critical metrics such as Einstein radii, lensing masses, and redshift distributions.

The Euclid Galaxy Lens Catalog is the definitive listing of galaxy-scale strong gravitational lenses discovered by the Euclid space mission. Leveraging Euclid’s high-resolution space-based imaging across wide sky areas, the catalog employs machine learning, citizen science, and expert validation to identify and characterize strong lensing systems. This collection underpins emerging research in precision cosmology, the structure of dark matter, galaxy evolution, and the mass distribution of galaxies and clusters.

1. Scope and Statistical Properties

The Euclid Galaxy Lens Catalog originates from the Euclid space telescope's wide survey, initially with 63 deg² released in Quick Data Release 1 (Q1), scaling to ≃15,000 deg² over the full 6-year mission. In Q1, ~500 high-quality galaxy-galaxy strong lenses were cataloged at a density of ≃7.9 lenses deg⁻². Projections estimate ≃15,000 lenses by DR1 (~4.5% sky), and a final tally of ≃110,000–120,000 lenses. This increases the known lens population by two orders of magnitude relative to pre-Euclid space-based catalogs (Collaboration et al., 19 Mar 2025, Lines et al., 20 Aug 2025).

The Q1 statistical breakdown is:

• Lens redshift ($z_l$): Mean ≃ 0.48, median ≃ 0.45 (range 0.2–1.0)
• Source redshift ($z_s$): Mean ≃ 2.1, median ≃ 1.9 (range 0.8–4.2)
• Einstein radius ($\theta_E$): Mean ≃ 1.05″, median ≃ 1.00″ (range 0.4″–2.5″)
• Enclosed lensing mass (within $\theta_E$): Mean $\sim$ 6 × 10¹¹ $M_\odot$, with 0.4 dex dispersion

Exotic configurations in Q1 include 4 compound (double-source-plane) systems, ~40 edge-on disk-galaxy lenses, several quadruple-image ("Einstein cross") lenses, and systems with rare or complex morphology (Collaboration et al., 19 Mar 2025, Collaboration et al., 19 Mar 2025, Lines et al., 20 Aug 2025).

2. Catalog Structure and Fields

The core catalog is provided in tabular form, with each entry comprising essential lensing and photometric attributes. Primary columns, as standardized in Euclid releases, include:

Field name	Units	Description
lens_id	—	Unique identifier (e.g. “EUCLID_Q1_Jhhmmss±ddmmss”)
ra, dec	degrees (J2000)	Right ascension and declination (ICRS)
z_l	—	Photometric lens redshift (typical error $\sigma_z\simeq 0.05(1+z)$)
z_s	—	Photometric (or spectroscopic, if available) source redshift
θ_E	arcseconds	Einstein radius from lens modeling
M_lens	$M_\odot$	Projected lens mass within θ_E (assuming SIS or SIE)
Δθ	arcseconds	Max image separation
morph_class	—	Morphological class (early-type, edge-on disk, compound, etc.)
p_confidence	[0,1]	Confidence score (machine learning ensemble probability)
notes	—	Flags and comments (e.g., “quad,” “double-plane,” “spec-z needed”)

All positions use the ICRS reference frame. Selection confidence is calibrated by an ensemble ML score, citizen science consensus, and expert panel grading (Collaboration et al., 19 Mar 2025, Lines et al., 20 Aug 2025).

3. Detection Pipeline and Methodology

The catalog construction is a multi-stage process:

1. Machine Learning Preselection: An ensemble of deep neural networks (including ResNets, Vision Transformers, and fine-tuned Zoobot foundation models) is trained on simulated lenses (“painted” arcs injected into real Euclid images) and non-lens galaxies. Model outputs are continuous lens probabilities ($p_\text{ml}$) for each candidate (Collaboration et al., 19 Mar 2025, Lines et al., 20 Aug 2025).
2. Citizen Science Validation: The “Space Warps” Zooniverse platform presents top ML-ranked candidates to volunteers. Each cutout undergoes ~150 independent classifications, with Bayesian consensus scores ($p_\text{cs}$) derived per candidate. Known simulated and non-lens systems are injected in real time for performance calibration (Collaboration et al., 19 Mar 2025).
3. Expert Visual Inspection: Candidates surpassing ML ($p_\text{ml}>0.5$) or citizen ($p_\text{cs}>0.3$) thresholds are examined by multiple lensing experts. Grading protocol aggregates scores, corrects for expert biases, and assigns final catalog grades (A: confident; B: probable) (Collaboration et al., 19 Mar 2025, Lines et al., 20 Aug 2025).
4. Quantitative Lens Modeling: Confirmed candidates are modeled with SIE+shear mass models and Multi-Gaussian Expansion (MGE) light profiles. Source reconstruction is performed with adaptive pixelization frameworks such as PyAutoLens and inference tools like nautilus and dynesty nested samplers (Collaboration et al., 19 Mar 2025). Models yield $\theta_E$, mass profile parameters, and lensing configuration details.

This pipeline achieves >90% catalog purity, with ~0.85 completeness for visually confirmed strong lenses at $p_\text{ml}>0.5$ on Q1 data. ROC curves show AUC ≃ 0.98 on held-out simulated data (Lines et al., 20 Aug 2025).

4. Special System Types and Cosmological Applications

The catalog includes several rare and scientifically valuable system subtypes:

• Double-Source-Plane Lenses (DSPLs): Four new galaxy-scale DSPLs in Q1, with projected survey-wide yield of ~1700. DSPLs are identified by concentric arcs at distinct radii and colors, modelled via multiplane lensing extensions. Their Einstein radii ratio probes the cosmological scaling factor $\beta$ and constrains dark energy equation-of-state $w$ (Collaboration et al., 19 Mar 2025).
• Edge-on Disk Lenses: $\sim$40 Q1 detections, sensitive to disk/bulge mass decomposition.
• Einstein Crosses and Radial Arcs: Systems with rare image geometry, enabling substructure and profile tests.

DSPL identification relies on presence of inner and outer arcs with distinct properties, selection thresholds on arc length ($\ell_\text{arc}>0.3''$), and color, with expert consensus confirmation. Model parameters include lens and source $I_E$-band magnitudes, Einstein radii for both planes, mass profile slopes, shear, and ellipticity.

For DSPLs, $\beta$ is defined as:

$\beta = \frac{D_{ls1}\,D_{s2}}{D_{s1}\,D_{ls2}}$

where $D_{ij}$ are angular diameter distances between observer, lens, and sources. A 1% error in $\beta$ propagates to $\Delta w \sim 0.3$ at fixed cosmology (Collaboration et al., 19 Mar 2025).

5. Forecasts, Statistical Methodologies, and Mock Catalogs

Extrapolation of Q1 results scales with survey area and depth. Predictive models (e.g., LensPop, integral lensing count equations) incorporate observed lensing surface densities, source redshift distributions, and halo mass functions:

$$N_\mathrm{lenses} = S_\mathrm{sky} \int dz \frac{dV}{dz} \int d\sigma_v\, n(\sigma_v,z) \sigma_\mathrm{lens}(\sigma_v,z) \int_{z}^{z_s^\mathrm{max}} dz_s\, n_S(z_s)$$

with $\sigma_\mathrm{lens} \propto \theta_E^2$ for SIS/ellipsoid models (Lines et al., 20 Aug 2025).

HST-based surveys indicate empirical surface densities of $N_\mathrm{obs} \approx 7\,\mathrm{deg}^{-2}$ at $I\approx26$ AB mag, consistent with Q1 results and supporting the forecast of at least $6\times10^4$–$10^5$ Euclid strong lenses (Pawase et al., 2012).

The Euclid Flagship mock catalog underpins selection functions, completeness corrections, and cosmic variance impact assessments. This simulated dataset consists of 3.4 billion galaxies (complete to $H_E < 26$, $0$\kappa$), and shear ($\gamma_{1,2}$), and validates expected weak-lensing and clustering statistics (Collaboration et al., 22 May 2024).

6. Catalog Validation, Limitations, and Prospects

Catalog purity—defined as $p = \mathrm{TP}/(\mathrm{TP}+\mathrm{FP})$—exceeds 90% after multi-level vetting. Completeness is currently $\sim$75–85% for grade A/B (confident/probable) lenses, with particular incompleteness at low arc radii ($\theta_E < 0.7''$) and lower surface brightness (Lines et al., 20 Aug 2025, Pawase et al., 2012). Early HST-based morphology-only samples exhibited high purity (≥75%) but lower absolute completeness.

Potential systematic limitations arise from:

• Training set representation of rare morphologies
• Photometric redshift uncertainties (especially for sources, $\sigma_{z_s} \sim 0.1(1+z)$)
• Model assumptions (SIE+shear, no substructure by default)
• Spectroscopic confirmation needs, especially for exotic/multiple-source systems

Comprehensive simulation suites (Flagship, painted arcs, abundance- and HOD-matched mocks) mitigate various biases and provide robust end-to-end validation (Collaboration et al., 22 May 2024).

Prospective directions include extending the catalog with multi-band photometry, spectroscopically confirmed redshift assignments, automated substructure analysis, and adaptation of pipelines to faint, small-radius or compound lenses as survey depth increases (Collaboration et al., 19 Mar 2025, Lines et al., 20 Aug 2025).

7. Scientific Impact and Usage

The Euclid Galaxy Lens Catalog enables diverse research agendas:

• Measurement of the mass profiles of galaxies and their evolution
• Tests for dark matter substructure via anomalous image configurations
• Cosmological parameter estimation: $H_0$ via time delays, $w$ via DSPLs and arc statistics
• Galaxy–galaxy lensing analyses at unprecedented sample sizes
• Calibration and benchmarking of machine learning methodologies for future astrophysical surveys

The catalog’s comprehensive format and rigorous vetting standards establish it as the reference database for strong-lensing studies over the coming decade (Collaboration et al., 19 Mar 2025, Collaboration et al., 19 Mar 2025, Lines et al., 20 Aug 2025, Collaboration et al., 22 May 2024, Pawase et al., 2012).