Euclid Q1 Strong Lensing Discovery Engine

[image to be added on Wed 19th]

This repository shares catalogues, images, and modelling results for strong lens candidates found in the Euclid Q1 data release as part of the Strong Lensing Discovery Engine. Lenses were found through a combined machine learning, citizen science, and expert visual inspection campaign. The sample is described and presented in the following five discovery papers:

(paper links to be added on Wed 19th).
(candidates from paper B are listed separately)

If you use Euclid Q1 data in your research, please cite the five core Euclid Q1 papers.

Euclid is a space telescope surveying 14k square degrees over the next six years. Q1 is the first major data release, covering 63 square degrees in the Euclid Deep Fields (see the paper). It is representative of the ongoing Euclid Wide Survey. Euclid images include a VIS optical image (400-900nm) and 3 NIR images (Y, J, H). The Euclid VIS PSF FWHM is approx. 0.16 arcsec per pixel.

We are continuing to search for strong lenses in the ongoing survey. We expect around 10k candidates in Euclid DR1. 

Strong Lens Candidate Catalogue

The list of strong lens candidates is strong_lens_candidates.csv.

This table combines three sets of candidates, identified with the subset column.

- Most (250 grade A, 247 grade B) candidates are from the discovery_engine subset. These were identified by our main search and follow the selection reported in our papers.
- We also include 56 grade A and 19 grade B candidates identified by Galaxy Zoo Euclid volunteers as part of a campaign to measure visual morphology; these are outside of the Q1 footprint and have a different selection function.
- Finally, we include 3 grade A candidates missed by our search but identified serendiptously. These are inside Q1.

All subsets have filled values for the following columns

The discovery_engine subset also includes filled values, copied from the MERge Q1 catalogue, for

For the other subsets, each source was not originally drawn from the MERge Q1 catalogue, and so these values are not filled.

Lens Modeling

We attempted to fit lens models to all candidates identified by the Discovery Engine (discovery_engine in subset column above) and rated above 2.0 (Grade B or better). The rest of this README discusses those results.

Modeling was performed by fitting the VIS image as the "primary" wavelength image and then using that mass model to reconstruct the source in the NIR images.

The following lens model is used:

- A Multi Gaussian Expansion (MGE) lens light model (see He et al. 2024).
- An SIE with external shear mass model.
- A source galaxy reconstructed using an adaptive Voronoi mesh (see PyAutoLens docs).

The Euclid Strong Lens Modeling Pipeline is publicly available here. It is built with the modeling code PyAutoLens.

Modelling Parameter Catalogues

336 candidates were successfully fit with a lens model. We hope that nearly all are strong lenses.

Catalogues of lens modeling results are provided in five .csv files. Each .csv can be joined with the lens catalogue (q1_discovery_engine_lens_catalog.csv) on id_str. 

All results for all parameters are given using six different values:

- `max_lh`: Maximum likelihood value.
- `median_pdf`: Median value of the posterior PDF.
- `upper_3_sigma`: Upper 3-sigma value (99.7% percentile).
- `lower_3_sigma`: Lower 3-sigma value (0.3% percentile).
- `upper_1_sigma`: Upper 1-sigma value (68.3% percentile).
- `lower_1_sigma`: Lower 1-sigma value (31.7% percentile).

The file `modelling_lens_mass.csv` summarizes the lens mass model properties of all 336 high-quality candidates:

The file modelling_lens_mge.csv summarizes the MGE lens light model properties.

The file modelling_lens_sersic.csv summarizes the Sersic lens light model properties.

The file modelling_mge_magnitude.csv summarizes the magnitudes of the lens and source galaxies. Includes values for VIS / Y / J / H.

The file modelling_lens_sersic_magnitude.csv contains similar information as above but for the specific lens.

Individual Lens Data

The four .zip files contain cutouts and modeling results (where successful) for the four sets of candidates described below.

Lens

The archive lens.zip contains folders for each candidate with a .fits file with the lens's ID ("id_str" in the catalogue), for example `102018665_NEG570040238507752998/102018665_NEG570040238507752998.fits`.

Folders also contain various .png and .fits files, including:

- `rgb_0.png` and `rgb_1.png`: RGB images of the lens.
- `mask_extra_galaxies.fits`: A mask of extra galaxies in the imaging data.
- `sie_fit_pix.png`, `source_reconstruction.png`, `sie_fit_mge.png`: Lens modeling results.
- `lens_light.fits`, `source_light.fits`, `source_reconstruction.fits`, etc.: Files summarizing model data.

Unsuccessful Lens Candidates and Models

The archive unsuccess.zip contains images of 144 unsuccessful lens candidates for various reasons, including modeling failures, non-lens status, or ambiguity.

Group Scale Lenses

The archive group.zip contains images of 41 group-scale lens candidates requiring multiple mass components, which was beyond the scope of the current modeling pipeline.

Recenter

The archive recenter.zip contains images of lenses which were not centered correctly, breaking lens modeling. We hope to update these in future.

Important Caveat: PSF Quality

The VIS PSF used for lens modeling is produced by OU-MER, not utilizing the full Euclid PSF model of OU-SHE. While suitable for Einstein radii and source reconstructions, it may be inadequate for more detailed science such as dark matter substructure studies.

Appendix A: Modelling Details

Geometry

Lens modeling results involve several geometric quantities, defined as follows:

To begin, a $(y,x)$ Cartesian coordinate system is established, centered on the light or mass profile:

$$y_{shift} = y - y_{centre}, \quad x_{shift} = x - x_{centre}$$

The shifted coordinates are then rotated by the position angle $\phi$, defined counter-clockwise from the positive x-axis:

$$y_{rot} = y' \cos(\phi) - x' \sin(\phi), \quad x_{rot} = y' \sin(\phi) + x' \cos(\phi)$$

The rotated coordinates are converted to elliptical coordinates using the axis-ratio $q$ of the light or mass profile:

$$\xi = \sqrt{(x_{rot})^2 + \frac{(y_{rot})^2}{q^2}}$$

Instead of defining geometry using $\phi$ and $q$, the following "elliptical components" are used:

$$\epsilon_{1} = \frac{1 - q}{1 + q} \sin(2\phi), \quad \epsilon_{2} = \frac{1 - q}{1 + q} \cos(2\phi)$$

To convert between these components and the position angle / axis-ratio:

$$q = \frac{1 - \text{fac}}{1 + \text{fac}}, \quad \phi = \frac{1}{2} \arctan\left(\frac{\epsilon_{2}}{\epsilon_{1}}\right)$$

where:

$$\text{fac} = \sqrt{1 - \epsilon_{1}^2 - \epsilon_{2}^2}$$

Mass Model

The SIE lens mass model is defined by:

$$\kappa(\xi) = \frac{1}{1 + q^{\text{mass}}} \left( \frac{\theta^{\text{mass}}_{\text{E}}}{\xi} \right)$$

where $\theta^{\text{mass}}_{\text{E}}$ is the Einstein radius of the mass model. Note that this is a scaled Einstein radius to improve modeling efficiency in PyAutoLens.

The **effective** Einstein radius, $R_{\text{Ein,eff}}$, which is the definition of Einstein radius more commonly used in the literature, is defined as:

$$R_{\text{Ein,eff}} = \sqrt{\frac{A}{\pi}}$$

where $A$ is the area enclosed by the tangential critical curve, ensuring consistency across various mass density profiles.

External Shear

The external shear field is parameterized by two components $\gamma_{1}^{\text{ext}}$ and $\gamma_{2}^{\text{ext}}$. The magnitude and orientation are given by:

$$\gamma^{\text{ext}} = \sqrt{(\gamma_{1}^{\text{ext}})^2 + (\gamma_{2}^{\text{ext}})^2}, \quad \tan(2\phi^{\text{ext}}) = \frac{\gamma_{2}^{\text{ext}}}{\gamma_{1}^{\text{ext}}}$$

Magnitudes

For the MGE lens light and Voronoi source reconstruction, refer to the papers and PyAutoLens documentation for detailed descriptions of the profiles.

The magnitudes of the lens and source galaxies are calculated in AB magnitudes:

$$M_{\text{lens}} = 2.5 \times \log_{10}(F\_{lens}) + Z$$

$$M_{\text{source}} = 2.5 \times \log_{10}(F\_{source}) + Z$$

where $F\_{lens}$ and $F\_{source}$ are the fluxes of the lens and source galaxies, respectively, and $Z$ is the zero-point.

The magnification factor $\mu$ is defined as:

$$\mu = \frac{F\_{lensed}}{F\_{source}}$$

where $F\_{lensed}$ is the total flux of the lensed source galaxy in the image-plane (e.g. it is magnified by the lens galaxy).

The `zero_point` corresponds to the calibration of the data.

Sersic

Results for a Sersic lens light model are also provided, which is given as:

$$I(\xi) = I_{\text{eff}} \exp\left(-b_n \left[ \left( \frac{\xi}{R_{\text{eff}}} \right)^{1/n} - 1 \right] \right)$$

where $I_{\text{eff}}$ is the effective intensity, $R_{\text{eff}}$ is the effective radius, $n$ is the Sersic index, and $b_n$ is a constant that depends on $n$.