Table 2
Fitted stellar and planetary parameters of the HD 3167 system.
| Fitted parameters | Symbols | Values | Priors | Units |
|---|---|---|---|---|
| Planet b | ||||
| Time of inferior conjunction | T0,b |  |
– | BJDTDB |
| Orbital period | Pb |  |
– | days |
| Planet-to-star radii ratios | ||||
| CHEOPS passband |  |
0.01765 ± 0.00036 | – | – |
| K2 passband |  |
 |
– | – |
| HST/WFC3/G141 passband |  |
 |
– | – |
| Spitzer/IRAC/Ch2 passband |  |
 |
– | – |
| All passbands | kb |  |
– | – |
| Orbital inclination | ib |  |
U(0, 90) | deg |
| Eccentricity / argument of periastron | eb cos ωb |  |
– | – |
| eb sin ωb |  |
– | – | |
| RV semi-amplitude | Kb |  |
– | ms−1 |
| Planet c | ||||
| Time of inferior conjunction | T0,c |  |
– | BJDTDB |
| Orbital period | Pc |  |
– | days |
| Planet-to-star radii ratios | ||||
| K2 passband |  |
 |
– | – |
| HST/WFC3/G141 passband |  |
 |
– | – |
| Spitzer/IRAC/Ch2 passband |  |
 |
– | – |
| All passbands | kc |  |
– | – |
| Orbital inclination | ic |  |
U(0, 90) | deg |
| Eccentricity/argument of periastron | ec cos ωc |  |
– | – |
| ec sin ωc |  |
– | – | |
| RV semi-amplitude | Kc |  |
– | ms−1 |
| Planet d | ||||
| Time of inferior conjunction | T0,d | 2.457 585.20 ± 0.22 | – | BJDTDB |
| Orbital period | Pd | 8.4783 ± 0.0025 | – | days |
| Eccentricity/argument of periastron | ed cos ωd |  |
– | – |
| ed sin ωd |  |
– | – | |
| RV semi-amplitude | Kd |  |
– | ms–1 |
| Planet e | ||||
| Time of inferior conjunction | T0,e |  |
– | BJDTDB |
| Orbital period(†) | Pe (†) |  |
– | days |
| Eccentricity / argument of periastron | ee cos ωe |  |
– | – |
| ee cos ωe |  |
– | – | |
| RV semi-amplitude | Ke |  |
– | ms–1 |
| Star | ||||
| Stellar density | ρ* |  |
N (1.289, 0.048) | ρ⊙ |
| Limb-darkening coefficients: | ||||
| CHEOPS passband |  |
 |
– | – |
| CHEOPS passband |  |
 |
– | – |
| K2 passband |  |
 |
– | – |
 |
 |
– | – | |
| HST/WFC3/G141 passband |  |
 |
– | – |
 |
 |
– | – | |
| Spitzer/IRAC/Ch2 passband |  |
 |
– | – |
 |
 |
– | – | |
Notes. Uniform priors between a and b are represented by U(a, b). normal priors with mean µ and variance σ2 are represented by N(µ, σ). The limb-darkening coefficients correspond to the quadratic model (Manduca et al. 1977): I(µ)/I0 = 1 − u1 (1 − µ) − u2 (1 − µ)2, where 
and x is the normalized radial coordinate on the stellar disk (x = 0 at the center, x = 1 at the limb). (†)Note that the marginalized posterior distribution of Pe has several modes spanning a large range from 79 to 125 days, and that the error bars of ~0.5 days are dominated by the main mode around 102 days.
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