Table 3.
Model parameters and prior for the joint modeling.
| Description | Parameters | Mock input | Prior | Prior range |
|---|---|---|---|---|
| Flat ΛCDM | ||||
| Hubble constant [km s−1 Mpc−1] | H0 | 82.5 | Flat | [50, 120] |
| Matter density parameter | Ωm | 0.27 | Flat | [0.05, 0.5] |
| Distances | ||||
| Model time-delay distance [Mpc] | DΔt, int | 1823 | Flat | [1000, 4000] |
| Model lens distance [Mpc] | Dd | 775 | Flat | [600, 1000] |
| Composite | ||||
| Position Angle [°] | φPA | 30 | – | – |
| Stellar M/L | Υ* | 1.95 | Flat | [0.5, 3.5] |
| Axis ratio | qenfw | 0.56 | Flat | [0.2, 1.0] |
| Characteristic density [-] | ρs | 0.24 | Flat | [0., 1.] |
| Scale radius [″] | rs | 23.0 | Gaussian | [23.0, 2.6] |
| External shear strength | γext | 0.09 | Flat | [0.0, 0.2] |
| External shear position angle | ϕext | 1.42 | Flat | [0.0, 2π] |
| BH mass [M⊙] | MBH | 5 × 109 | Discrete | [109 M⊙, 1010 M⊙] |
| Mass Sheet | λint | 1 | Flat | [0.5, 1.5] |
| External convergence | κext | 0.079 | – | – |
| Dynamics | ||||
| Anisotropy | βani | 0.15 | Flat | [ − 0.3, 0.3] |
| Inclination [°] | i | 84.3 | Flat | [80, 90] |
Notes. The value of Dd was determined from zd = 0.295, assuming H0 = 82.5 km s−1 Mpc−1, Ωm = 0.27, and ΩΛ = 0.73. The value of DΔt, int, in contrast, must be corrected for external convergence (see Eq. (12)) to obtain the true distance. Applying this correction, we find DΔt,int = 1980.14 Mpc, given the assumed cosmology. The position angle θPA defines the orientation of both the light and mass profiles of the lens galaxy, measured counterclockwise from the +x-axis and is fixed during modeling process. The scale radius rs in the dark matter profile indicates the slope transition of the density profile from −1 (inner region) to −3 (outer region), which cannot be well constrained by either SL or kinematic data due to its large distance from the galaxy centroid. For this reason, a Gaussian prior is used in the joint modeling (Gavazzi et al. 2007). In each joint modeling, the BH mass is fixed, but we explore different models by probing MBH within the range of [109, 1010] M⊙. Note that H0 and Ωm are not directly modeled in the joint analysis. The prior in the table indicates the range from which the samples are drawn and then evaluated by the posterior of the distances.
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