Table 5.
Models summary.
| Model ID | N. par. | d.o.f. | Δrms [″] |  |
BIC | AIC | Description |
|---|---|---|---|---|---|---|---|
| RXJ 2129-P1 | 8 | 22 | 0.20 | 3.39 | 34.7 | 27.6 | One smooth elliptical PIEMD component |
| RXJ 2129-gNFW1 | 9 | 21 | 0.22 | 4.40 | 36.7 | 30.1 | One smooth elliptical gNFW component |
| RXJ 2129-P2 | 14 | 16 | 0.13 | 1.56 | 38.8 | 38.7 | Two smooth elliptical PIEMD components |
| RXJ 2129-P2-circular | 12 | 18 | 0.14 | 1.71 | 37.0 | 34.8 | Second smooth component with circular symmetry |
| RXJ 2129-P1-shear | 10 | 20 | 0.20 | 3.37 | 36.6 | 31.6 | Same as P1 plus an with external shear term |
| RXJ 2129-P1-BCG | 10 | 20 | 0.19 | 3.31 | 36.6 | 31.6 | Same as P1 but with free circular BCG parameters |
| RXJ 2129-P1-BCG-shear | 12 | 18 | 0.19 | 3.30 | 38.6 | 35.6 | Same as BCG but plus an external shear term |
| RXJ 2129-P1-BCGell | 12 | 18 | 0.16 | 2.37 | 37.6 | 35.1 | Same as P1 but with free elliptical BCG parameters |
| MACS J1931-P1 | 8 | 16 | 0.93 | 41.0 | 94.1 | 57.5 | One smooth elliptical PIEMD component |
| MACS J1931-P2 | 14 | 10 | 0.34 | 9.00 | 43.3 | 41.1 | Two smooth elliptical PIEMD components |
| MACS J1931-P2-circular | 12 | 12 | 0.38 | 10.9 | 43.2 | 38.0 | Second smooth component with circular symmetry |
| MACS J1931-gNFW2-curcular | 13 | 11 | 0.39 | 11.5 | 44.7 | 40.3 | Main smooth component parametrised by gNFW |
| MACS J1931-P1-shear | 10 | 14 | 0.58 | 25.4 | 55.7 | 41.3 | Same as P1 plus an external shear term |
| MACS J1931-P1-BCG | 10 | 14 | 0.69 | 36.2 | 66.5 | 46.7 | Same as P1 but with free circular BCG parameters |
| MACS J1931-P1-BCGell | 12 | 12 | 0.55 | 23.4 | 55.7 | 44.3 | Same as P1 but with free elliptical BCG parameters |
| MACS J0329-P1 | 8 | 20 | 1.74 | 278 | 310 | 165 | One smooth elliptical PIEMD component |
| MACS J0329-P2 | 14 | 14 | 0.32 | 9.15 | 47.3 | 43.0 | Two smooth elliptical PIEMD components |
| MACS J0329-P2-circular | 12 | 16 | 0.73 | 49.2 | 85.3 | 59.0 | Second smooth component with circular symmetry |
| MACS J0329-P3-circular | 18 | 10 | 0.26 | 6.04 | 48.2 | 49.4 | Same as P2 plus a 3rd circular component |
| MACS J0329-P3 | 20 | 8 | 0.25 | 5.63 | 49.7 | 53.2 | Same as P2 plus a 3rd elliptical component |
| MACS J0329-P2-shear | 16 | 12 | 0.24 | 5.18 | 45.3 | 45.0 | Same as P2 plus an external shear term |
| MACS J0329-gNFW2-shear | 17 | 11 | 0.22 | 4.43 | 45.5 | 46.6 | Main smooth component parametrised by gNFW |
| MACS J0329-P2-BCG | 16 | 12 | 0.31 | 8.71 | 48.8 | 46.7 | Same as P1 but with free circular BCG parameters |
| MACS J0329-P2-BCGell | 18 | 10 | 0.29 | 9.00 | 50.1 | 50.4 | Same as P1 but with free elliptical BCG parameters |
| MACS J2129-P1 | 8 | 46 | 1.10 | 180 | 226 | 123 | One smooth elliptical PIEMD component |
| MACS J2129-P1-shear | 10 | 44 | 1.05 | 162 | 211 | 118 | Same as P1 plus an external shear term |
| MACS J2129-P1-BCG | 10 | 44 | 0.99 | 149 | 197 | 111 | Same as P1 but with free circular BCG parameters |
| MACS J2129-P1-BCGell | 12 | 42 | 0.94 | 134 | 184 | 108 | Same as P1 but with free elliptical BCG parameters |
| MACS J2129-P2-circular | 12 | 42 | 0.71 | 77.4 | 128 | 79.9 | Second smooth component with circular symmetry |
| MACS J2129-P2 | 14 | 40 | 0.56 | 47.1 | 99.5 | 68.7 | Two smooth elliptical PIEMD components |
| MACS J2129-gNFW2 | 15 | 39 | 0.83 | 105 | 158 | 99.5 | Main smooth component parametrised by gNFW |
| MACS J2129-P2-circular-shear | 14 | 40 | 0.65 | 62.8 | 115 | 76.5 | Same as P2-circular plus an external shear term |
| MACS J2129-P3-circular | 16 | 38 | 0.64 | 62.0 | 116 | 80.1 | Three smooth components with circular symmetry |
| Cluster sample with small number of constraints | |||||||
| MACS J1115-P1 | 9 | 3 | 0.61 | 13.2 | 32.8 | 28.7 | One smooth elliptical PIEMD component |
| MACS J0429-P1 | 9 | 7 | 0.32 | 4.38 | 26.1 | 25.2 | One smooth elliptical PIEMD component |
| RX J1347-P2 | 18 | 6 | 1.05 | 87.7 | 127 | 88.9 | Two smooth elliptical PIEMD |
| RX J1347-P2-shear | 20 | 4 | 0.36 | 10.1 | 51.1 | 54.1 | Two smooth elliptical PIEMD plus an external shear term |
| MACS J1311-P1 | 10 | 0 | 0.88 | 24.9 | 44.4 | 36.1 | One smooth elliptical PIEMD component |
| Previous models | |||||||
| Abell 1063 | 14 | 62 | 0.44 | 44.5 | 125 | 84.1 | Updated model from Caminha et al. (2016b) |
| MACS J1206 | 22 | 88 | 0.44 | 41.0 | 225 | 143 | Model from Caminha et al. (2017b) |
| MACS J0416 | 26 | 104 | 0.59 | 143 | 266 | 169 | Model from Caminha et al. (2017a) |
Notes. For each model, we present the number of free parameters (N. par.), the degree of freedom (d.o.f.), the root-mean-square difference between the model predicted and observed multiple image positions (Δrms), the minimum χ2 (see Eq. (2)), the Bayesian and Akaike information criteria (BIC and AIC, respectively), and a short description of the model parametrization. Rows in boldface are our reference models, since they have the lowest BIC and AIC values. Model IDs in italics have the main smooth component parametrised by a gNFW mass profile.
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