Table summarizing the main properties of the reconstructions of Ares and Hera. The columns correspond to (1) name of the model; (2) name of the cluster; (3) plane where the optimization is performed (source or image plane); (4) profile used to model the dark matter halo components; (5) number of dark matter haloes assumed; (6) type of constraints used (SL, WL); (7) number of multiple images used as constraints; (8) number of additional constraints (e.g. image ellipticity, flux, etc.); (9) number of free parameters. In the case of free-form methods, the number of grid points of the reconstructed map is given; (10) density profile used to model the cluster galaxies; (11) shape of the cluster galaxies (circular or elliptical); (12) scaling relations used to model the ensemble of cluster galaxies; (13) number of free parameters used to model the cluster galaxies; (14) catalogue of cluster galaxies used; (15) number of cluster galaxies optimized individually (i.e. independently on the scaling relations); (16) external shear (yes or no); (17) high-order perturbations (yes or no) and (18) regularization term (yes or no).
| Model . | Cluster . | Opt. plane . | Halo prof. . | No. of haloes . | Type of constr. . | Mult. images . | Other constr. . | No. of free par. . | Gal. profiles . | Gal. shape . | Scaling rel. . | Free par. . | Gal. catalogue . | Opt. galaxies . | Ext. shear . | High-order pert. . | Reg. . |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Bradac-Hoag | Ares | Image | – | – | SL+WL | 242 | 574 | 1959(a) | – | – | – | – | – | – | No | No | Yes |
| Bradac-Hoag | Hera | Image | – | – | SL+WL | 65 | 2102 | 5497 | – | – | – | – | – | – | No | No | Yes |
| Diego-multires | Hera | Source | Gaussians(b) | – | SL | 65 | 161(c) | 304 | LTM | ell. | M/L = const | 3 | Official | 2 | No | No | No |
| Diego-overfit | Hera | Source | Gaussians | – | SL | 65 | 161 | 1027 | LTM | ell. | M/L = const | 3 | Official | 2 | No | No | No |
| Diego-reggrid | Ares | Source | Gaussians | – | SL | 242 | 643 | 1027 | LTM | ell. | M/L = const | 3 | Official | 2 | No | No | No |
| Diego-reggrid | Hera | Source | Gaussians | – | SL | 65 | 161 | 1027 | LTM | ell. | M/L = const | 3 | Official | 2 | No | No | No |
| Lam | Hera | Source | Gaussians | – | SL | 65 | – | 1027 | NFW | circ. | M ∝ M★ | 20 | Official | 10 | No | No | No |
| GRALE | Ares | Source | Plummer(d) | – | SL | 183(e) | – | >600(f) | – | – | – | – | – | – | No | No | No |
| GRALE | Hera | Source | Plummer | – | SL | 65 | – | >600 | – | – | – | – | – | – | No | No | No |
| Coe | Ares | Image | RBFs(g) | – | SL | 242 | – | 170 | – | – | – | – | – | – | No | No | Yes |
| CATS | Ares | Source | PIEMD | 2 | SL | 242 | – | 35 | PIEMD | circ. | σ ∝ L1/4 rt ∝ L1/2 | 2 | CATS Ares(h) | 5 | No | No | No |
| CATS | Hera | Source | PIEMD | 2 | SL | 65 | – | 34 | PIEMD | circ. | σ ∝ L1/4 rt ∝ L1/2 | 2 | Official | 6 | No | No | No |
| Johnson-Sharon | Ares | Source | PIEMD | 2 | SL | 242 | – | 18 | PIEMD | ell. | σ ∝ L1/4 rt ∝ L1/2 | 1 | Official | 2 | No | No | No |
| Johnson-Sharon | Hera | Source | PIEMD | 2 | SL | 65 | – | 13 | PIEMD | ell. | σ ∝ L1/4 rt ∝ L1/2 | 1 | Official | 2 | No | No | No |
| GLAFIC | Ares | Source | eNFW | 5 | SL | 242 | – | 32 | PIEMD | ell. | σ ∝ L1/4 rt ∝ L1/2 | 2 | GLAFIC(i) | – | No | No | No |
| GLAFIC | Hera | Source | eNFW | 2 | SL | 65 | – | 23 | PIEMD+Hernquist(j) | ell. | σ ∝ L1/4 rt ∝ Lη | 3 | GLAFIC | 2 | Yes | Yes | No |
| Zitrin-LTM-gauss | Ares | Image | LTM | – | SL | 242 | – | 19 | LTM | circ. | Same LTM scaling | 12 | Official | 4 | Yes | No | No |
| Zitrin-LTM-gauss | Hera | Image | LTM | – | SL | 65 | – | 17 | LTM | circ. | Same LTM scaling | 10 | Official | 4 | Yes | No | No |
| Zitrin-NFW | Ares | Image | eNFW | 2 | SL | 242 | – | 25 | PIEMD | circ. | σ ∝ L1/4 rt ∝ L1/2 | 13 | Official | 4 | No | No | No |
| Zitrin-NFW | Hera | Image | eNFW | 3 | SL | 65 | – | 24 | PIEMD | circ. | σ ∝ L1/4 rt ∝ L1/2 | 11 | Official | 4 | No | No | No |
| Model . | Cluster . | Opt. plane . | Halo prof. . | No. of haloes . | Type of constr. . | Mult. images . | Other constr. . | No. of free par. . | Gal. profiles . | Gal. shape . | Scaling rel. . | Free par. . | Gal. catalogue . | Opt. galaxies . | Ext. shear . | High-order pert. . | Reg. . |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Bradac-Hoag | Ares | Image | – | – | SL+WL | 242 | 574 | 1959(a) | – | – | – | – | – | – | No | No | Yes |
| Bradac-Hoag | Hera | Image | – | – | SL+WL | 65 | 2102 | 5497 | – | – | – | – | – | – | No | No | Yes |
| Diego-multires | Hera | Source | Gaussians(b) | – | SL | 65 | 161(c) | 304 | LTM | ell. | M/L = const | 3 | Official | 2 | No | No | No |
| Diego-overfit | Hera | Source | Gaussians | – | SL | 65 | 161 | 1027 | LTM | ell. | M/L = const | 3 | Official | 2 | No | No | No |
| Diego-reggrid | Ares | Source | Gaussians | – | SL | 242 | 643 | 1027 | LTM | ell. | M/L = const | 3 | Official | 2 | No | No | No |
| Diego-reggrid | Hera | Source | Gaussians | – | SL | 65 | 161 | 1027 | LTM | ell. | M/L = const | 3 | Official | 2 | No | No | No |
| Lam | Hera | Source | Gaussians | – | SL | 65 | – | 1027 | NFW | circ. | M ∝ M★ | 20 | Official | 10 | No | No | No |
| GRALE | Ares | Source | Plummer(d) | – | SL | 183(e) | – | >600(f) | – | – | – | – | – | – | No | No | No |
| GRALE | Hera | Source | Plummer | – | SL | 65 | – | >600 | – | – | – | – | – | – | No | No | No |
| Coe | Ares | Image | RBFs(g) | – | SL | 242 | – | 170 | – | – | – | – | – | – | No | No | Yes |
| CATS | Ares | Source | PIEMD | 2 | SL | 242 | – | 35 | PIEMD | circ. | σ ∝ L1/4 rt ∝ L1/2 | 2 | CATS Ares(h) | 5 | No | No | No |
| CATS | Hera | Source | PIEMD | 2 | SL | 65 | – | 34 | PIEMD | circ. | σ ∝ L1/4 rt ∝ L1/2 | 2 | Official | 6 | No | No | No |
| Johnson-Sharon | Ares | Source | PIEMD | 2 | SL | 242 | – | 18 | PIEMD | ell. | σ ∝ L1/4 rt ∝ L1/2 | 1 | Official | 2 | No | No | No |
| Johnson-Sharon | Hera | Source | PIEMD | 2 | SL | 65 | – | 13 | PIEMD | ell. | σ ∝ L1/4 rt ∝ L1/2 | 1 | Official | 2 | No | No | No |
| GLAFIC | Ares | Source | eNFW | 5 | SL | 242 | – | 32 | PIEMD | ell. | σ ∝ L1/4 rt ∝ L1/2 | 2 | GLAFIC(i) | – | No | No | No |
| GLAFIC | Hera | Source | eNFW | 2 | SL | 65 | – | 23 | PIEMD+Hernquist(j) | ell. | σ ∝ L1/4 rt ∝ Lη | 3 | GLAFIC | 2 | Yes | Yes | No |
| Zitrin-LTM-gauss | Ares | Image | LTM | – | SL | 242 | – | 19 | LTM | circ. | Same LTM scaling | 12 | Official | 4 | Yes | No | No |
| Zitrin-LTM-gauss | Hera | Image | LTM | – | SL | 65 | – | 17 | LTM | circ. | Same LTM scaling | 10 | Official | 4 | Yes | No | No |
| Zitrin-NFW | Ares | Image | eNFW | 2 | SL | 242 | – | 25 | PIEMD | circ. | σ ∝ L1/4 rt ∝ L1/2 | 13 | Official | 4 | No | No | No |
| Zitrin-NFW | Hera | Image | eNFW | 3 | SL | 65 | – | 24 | PIEMD | circ. | σ ∝ L1/4 rt ∝ L1/2 | 11 | Official | 4 | No | No | No |
Notes. (a) This number corresponds to the total number of grid points at the end of the refinements in the map of the lensing potential. Note that these points are highly correlated, as the lensing constraints measure higher order derivatives of the potential; (b) The diffuse, halo component of the cluster mass distribution in the Diego and Lam models is fitted with a combination of Gaussians on a regular or adaptive grid; (c) In the Diego and Lam models, constraints other than image positions are derived from the sizes and shapes of the spatially resolved images; (d) The cluster mass distribution in the GRALE models is given by a combination of Plummer spheres; (e) Systems composed by two images only were not used in the reconstruction; (f) The number of free parameters depends on the number of Plummer spheres effectively used. This is not known a priori as it is determined by the genetic algorithm during each run. The starting number of Plummer spheres is 600–1000 depending on the run; (g) The cluster mass distribution is described by a combination of RBFs whose form is given in equations 17, 20 and 21 of Coe et al. (2008); (h) The CATS Ares catalogue of cluster members is obtained by selecting the galaxies with mF160W < 22; (i) Positions and luminosities were taken from the official catalogue of cluster members distributed to all teams. Ellipticity and position angle of each galaxy were measured using SExtractor; (j) The two brightest galaxies are modelled with Hernquist profiles and optimized individually. The other galaxies are modelled with PIEMDs and their masses and sizes scale with luminosity.
Table summarizing the main properties of the reconstructions of Ares and Hera. The columns correspond to (1) name of the model; (2) name of the cluster; (3) plane where the optimization is performed (source or image plane); (4) profile used to model the dark matter halo components; (5) number of dark matter haloes assumed; (6) type of constraints used (SL, WL); (7) number of multiple images used as constraints; (8) number of additional constraints (e.g. image ellipticity, flux, etc.); (9) number of free parameters. In the case of free-form methods, the number of grid points of the reconstructed map is given; (10) density profile used to model the cluster galaxies; (11) shape of the cluster galaxies (circular or elliptical); (12) scaling relations used to model the ensemble of cluster galaxies; (13) number of free parameters used to model the cluster galaxies; (14) catalogue of cluster galaxies used; (15) number of cluster galaxies optimized individually (i.e. independently on the scaling relations); (16) external shear (yes or no); (17) high-order perturbations (yes or no) and (18) regularization term (yes or no).
| Model . | Cluster . | Opt. plane . | Halo prof. . | No. of haloes . | Type of constr. . | Mult. images . | Other constr. . | No. of free par. . | Gal. profiles . | Gal. shape . | Scaling rel. . | Free par. . | Gal. catalogue . | Opt. galaxies . | Ext. shear . | High-order pert. . | Reg. . |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Bradac-Hoag | Ares | Image | – | – | SL+WL | 242 | 574 | 1959(a) | – | – | – | – | – | – | No | No | Yes |
| Bradac-Hoag | Hera | Image | – | – | SL+WL | 65 | 2102 | 5497 | – | – | – | – | – | – | No | No | Yes |
| Diego-multires | Hera | Source | Gaussians(b) | – | SL | 65 | 161(c) | 304 | LTM | ell. | M/L = const | 3 | Official | 2 | No | No | No |
| Diego-overfit | Hera | Source | Gaussians | – | SL | 65 | 161 | 1027 | LTM | ell. | M/L = const | 3 | Official | 2 | No | No | No |
| Diego-reggrid | Ares | Source | Gaussians | – | SL | 242 | 643 | 1027 | LTM | ell. | M/L = const | 3 | Official | 2 | No | No | No |
| Diego-reggrid | Hera | Source | Gaussians | – | SL | 65 | 161 | 1027 | LTM | ell. | M/L = const | 3 | Official | 2 | No | No | No |
| Lam | Hera | Source | Gaussians | – | SL | 65 | – | 1027 | NFW | circ. | M ∝ M★ | 20 | Official | 10 | No | No | No |
| GRALE | Ares | Source | Plummer(d) | – | SL | 183(e) | – | >600(f) | – | – | – | – | – | – | No | No | No |
| GRALE | Hera | Source | Plummer | – | SL | 65 | – | >600 | – | – | – | – | – | – | No | No | No |
| Coe | Ares | Image | RBFs(g) | – | SL | 242 | – | 170 | – | – | – | – | – | – | No | No | Yes |
| CATS | Ares | Source | PIEMD | 2 | SL | 242 | – | 35 | PIEMD | circ. | σ ∝ L1/4 rt ∝ L1/2 | 2 | CATS Ares(h) | 5 | No | No | No |
| CATS | Hera | Source | PIEMD | 2 | SL | 65 | – | 34 | PIEMD | circ. | σ ∝ L1/4 rt ∝ L1/2 | 2 | Official | 6 | No | No | No |
| Johnson-Sharon | Ares | Source | PIEMD | 2 | SL | 242 | – | 18 | PIEMD | ell. | σ ∝ L1/4 rt ∝ L1/2 | 1 | Official | 2 | No | No | No |
| Johnson-Sharon | Hera | Source | PIEMD | 2 | SL | 65 | – | 13 | PIEMD | ell. | σ ∝ L1/4 rt ∝ L1/2 | 1 | Official | 2 | No | No | No |
| GLAFIC | Ares | Source | eNFW | 5 | SL | 242 | – | 32 | PIEMD | ell. | σ ∝ L1/4 rt ∝ L1/2 | 2 | GLAFIC(i) | – | No | No | No |
| GLAFIC | Hera | Source | eNFW | 2 | SL | 65 | – | 23 | PIEMD+Hernquist(j) | ell. | σ ∝ L1/4 rt ∝ Lη | 3 | GLAFIC | 2 | Yes | Yes | No |
| Zitrin-LTM-gauss | Ares | Image | LTM | – | SL | 242 | – | 19 | LTM | circ. | Same LTM scaling | 12 | Official | 4 | Yes | No | No |
| Zitrin-LTM-gauss | Hera | Image | LTM | – | SL | 65 | – | 17 | LTM | circ. | Same LTM scaling | 10 | Official | 4 | Yes | No | No |
| Zitrin-NFW | Ares | Image | eNFW | 2 | SL | 242 | – | 25 | PIEMD | circ. | σ ∝ L1/4 rt ∝ L1/2 | 13 | Official | 4 | No | No | No |
| Zitrin-NFW | Hera | Image | eNFW | 3 | SL | 65 | – | 24 | PIEMD | circ. | σ ∝ L1/4 rt ∝ L1/2 | 11 | Official | 4 | No | No | No |
| Model . | Cluster . | Opt. plane . | Halo prof. . | No. of haloes . | Type of constr. . | Mult. images . | Other constr. . | No. of free par. . | Gal. profiles . | Gal. shape . | Scaling rel. . | Free par. . | Gal. catalogue . | Opt. galaxies . | Ext. shear . | High-order pert. . | Reg. . |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Bradac-Hoag | Ares | Image | – | – | SL+WL | 242 | 574 | 1959(a) | – | – | – | – | – | – | No | No | Yes |
| Bradac-Hoag | Hera | Image | – | – | SL+WL | 65 | 2102 | 5497 | – | – | – | – | – | – | No | No | Yes |
| Diego-multires | Hera | Source | Gaussians(b) | – | SL | 65 | 161(c) | 304 | LTM | ell. | M/L = const | 3 | Official | 2 | No | No | No |
| Diego-overfit | Hera | Source | Gaussians | – | SL | 65 | 161 | 1027 | LTM | ell. | M/L = const | 3 | Official | 2 | No | No | No |
| Diego-reggrid | Ares | Source | Gaussians | – | SL | 242 | 643 | 1027 | LTM | ell. | M/L = const | 3 | Official | 2 | No | No | No |
| Diego-reggrid | Hera | Source | Gaussians | – | SL | 65 | 161 | 1027 | LTM | ell. | M/L = const | 3 | Official | 2 | No | No | No |
| Lam | Hera | Source | Gaussians | – | SL | 65 | – | 1027 | NFW | circ. | M ∝ M★ | 20 | Official | 10 | No | No | No |
| GRALE | Ares | Source | Plummer(d) | – | SL | 183(e) | – | >600(f) | – | – | – | – | – | – | No | No | No |
| GRALE | Hera | Source | Plummer | – | SL | 65 | – | >600 | – | – | – | – | – | – | No | No | No |
| Coe | Ares | Image | RBFs(g) | – | SL | 242 | – | 170 | – | – | – | – | – | – | No | No | Yes |
| CATS | Ares | Source | PIEMD | 2 | SL | 242 | – | 35 | PIEMD | circ. | σ ∝ L1/4 rt ∝ L1/2 | 2 | CATS Ares(h) | 5 | No | No | No |
| CATS | Hera | Source | PIEMD | 2 | SL | 65 | – | 34 | PIEMD | circ. | σ ∝ L1/4 rt ∝ L1/2 | 2 | Official | 6 | No | No | No |
| Johnson-Sharon | Ares | Source | PIEMD | 2 | SL | 242 | – | 18 | PIEMD | ell. | σ ∝ L1/4 rt ∝ L1/2 | 1 | Official | 2 | No | No | No |
| Johnson-Sharon | Hera | Source | PIEMD | 2 | SL | 65 | – | 13 | PIEMD | ell. | σ ∝ L1/4 rt ∝ L1/2 | 1 | Official | 2 | No | No | No |
| GLAFIC | Ares | Source | eNFW | 5 | SL | 242 | – | 32 | PIEMD | ell. | σ ∝ L1/4 rt ∝ L1/2 | 2 | GLAFIC(i) | – | No | No | No |
| GLAFIC | Hera | Source | eNFW | 2 | SL | 65 | – | 23 | PIEMD+Hernquist(j) | ell. | σ ∝ L1/4 rt ∝ Lη | 3 | GLAFIC | 2 | Yes | Yes | No |
| Zitrin-LTM-gauss | Ares | Image | LTM | – | SL | 242 | – | 19 | LTM | circ. | Same LTM scaling | 12 | Official | 4 | Yes | No | No |
| Zitrin-LTM-gauss | Hera | Image | LTM | – | SL | 65 | – | 17 | LTM | circ. | Same LTM scaling | 10 | Official | 4 | Yes | No | No |
| Zitrin-NFW | Ares | Image | eNFW | 2 | SL | 242 | – | 25 | PIEMD | circ. | σ ∝ L1/4 rt ∝ L1/2 | 13 | Official | 4 | No | No | No |
| Zitrin-NFW | Hera | Image | eNFW | 3 | SL | 65 | – | 24 | PIEMD | circ. | σ ∝ L1/4 rt ∝ L1/2 | 11 | Official | 4 | No | No | No |
Notes. (a) This number corresponds to the total number of grid points at the end of the refinements in the map of the lensing potential. Note that these points are highly correlated, as the lensing constraints measure higher order derivatives of the potential; (b) The diffuse, halo component of the cluster mass distribution in the Diego and Lam models is fitted with a combination of Gaussians on a regular or adaptive grid; (c) In the Diego and Lam models, constraints other than image positions are derived from the sizes and shapes of the spatially resolved images; (d) The cluster mass distribution in the GRALE models is given by a combination of Plummer spheres; (e) Systems composed by two images only were not used in the reconstruction; (f) The number of free parameters depends on the number of Plummer spheres effectively used. This is not known a priori as it is determined by the genetic algorithm during each run. The starting number of Plummer spheres is 600–1000 depending on the run; (g) The cluster mass distribution is described by a combination of RBFs whose form is given in equations 17, 20 and 21 of Coe et al. (2008); (h) The CATS Ares catalogue of cluster members is obtained by selecting the galaxies with mF160W < 22; (i) Positions and luminosities were taken from the official catalogue of cluster members distributed to all teams. Ellipticity and position angle of each galaxy were measured using SExtractor; (j) The two brightest galaxies are modelled with Hernquist profiles and optimized individually. The other galaxies are modelled with PIEMDs and their masses and sizes scale with luminosity.
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