Table 3
Parameterization and priors used in the joint Kepler and GTC light curve and RV modeling.
| Parameter name | Units | Prior | |
|
|
|||
| System property priors for Kepler-418b | |||
| Zero epoch | T c1 | d | U(Tc1b ± 0.05a) |
| Period | P 1 | d | U(P1b ± 0.005a) |
| Area ratio |
|
|
U(0.082, 0.502) |
| Impact parameter | b 1 | U(0.0, 0.99) | |
| Eccentricity | e 1 | U(0.0, 0.6) | |
| Arg. of periastron | ω 1 | U(0, 2π) | |
| RV semi-amplitude | K 1 | km s-1 | U(0.0, 0.2) |
|
|
|||
| System property priors for KOI-1089.02 | |||
| Zero epoch | T c2 | d | U(Tc2b ± 0.05a) |
| Period | P 2 | d | U(P2b ± 0.005a) |
| Area ratio |
|
|
U(0.042, 0.502) |
| Impact parameter | b 2 | U(0.0, 0.99) | |
| Eccentricity | e 2 | U(0.0, 0.6) | |
| Arg. of periastron | ω 2 | U(0, 2π) | |
| RV semi-amplitude | K 2 | km s-1 | U(0.0, 0.2) |
| stellar density | ρ ⋆ | g/cm3 | U(0.1, 5.0) |
| systemic velocity | C | km s-1 | U(−18.4, −18.5) |
| RV scatter | e RV | km s-1 | U(0.01, 0.17) |
| Kepler LC scatter | e Kl | U(0.0005, 0.0006) | |
| Kepler SC scatter | e Ks | U(0.0028, 0.0029) | |
| GTC z′ scatter | e z ′ | U(0.0025, 0.0045) | |
| GTC g′ scatter | e g ′ | U(0.0025, 0.0045) | |
| GTC z′ baseline | z z ′ | U(0.95, 1.05) | |
| GTC g′ baseline | z g ′ | U(0.95, 1.05) | |
| z′ contamination | C | U(0.00, 0.99) | |
| contaminant temperature | T c | K | U(2000, 15 000) |
|
|
|||
| Stellar property priors: unconstrained quadratic limb darkening | |||
| K limb darkening u | u a,K | U(0.00, 1.00) | |
| K limb darkening v | v a,K | U(–0.35, 0.50) | |
| z′ limb darkening u | u a, z ′ | U(0.00, 1.00) | |
| z′ limb darkening v | v a, z ′ | U(–0.35, 0.50) | |
| g′ limb darkening u | u a, g ′ | U(0.00, 1.00) | |
| g′ limb darkening v | v a, g ′ | U(–0.35, 0.50) | |
|
|
|||
| Stellar property priors: constrained quadratic limb darkening | |||
| K limb darkening u | u b,K | N(0.12, 0.03) | |
| K limb darkening v | v b,K | N(0.19, 0.06) | |
| z′ limb darkening u | u b, z ′ | N(0.32, 0.06) | |
| z′ limb darkening v | v b, z ′ | N(0.19, 0.06) | |
| g′ limb darkening u | u b, g ′ | N(0.64, 0.09) | |
| g′ limb darkening v | v b, g ′ | N(0.13, 0.09) | |
Notes. The two basic prior distributions used are uniform (U) and normal (N), where the uniform distribution is defined by its lower and upper bounds, while the normal distribution is defined by its mean and standard deviation. The two limb darkening cases are described in detail in Sect. 6.4.
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