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Table 3

Parameter values for the WASP-18 b system.

Fitted parameter Symbol Value Prior Unit
Time of inferior conjunction T 0 375.169847 ± 0.000019 U ( 375.1 , 375.2 ) $\mathcal{U}\!\left(375.1, 375.2\right)$ BJDTDB - 2 458 000
Orbital period P 0.941452379 ± 0.000000016 days
Planet-to-star radii ratio Rp/R 0.09757 0.00013 + 0.00012 ${0.09757}_{-{0.00013}}^{+{0.00012}}$
Normalised semi-major axis a/R 3.493 ± 0.011
Orbital inclination i 84.08 ± 0.17 U ( 0 , 90 ) $\mathcal{U}\!\left(0, 90\right)$ deg
Eccentricity / argument of periastron e cos ω 0* fixed
e sin ω 0* fixed
Stellar radius R 1.2561 ± 0.0079 N ( 1.256 , 0.008 ) $\mathcal{N}\!\left(1.256, 0.008\right)$ R
CHEOPS
 Dayside flux F max CHEOPS $F_\text{max}^\text{\cheops{}}$ 211.9 7.5 + 7.6 ${211.9}_{-{7.5}}^{+{7.6}}$ U ( 0 , + ) $\mathcal{U}\!\left(0, +\infty\right)$ ppm
 EV amplitude A EV CHEOPS $A_\text{EV}^\text{\cheops{}}$ 217.0 ± 5.0 ${217.0 - 5.0}$ U ( 0 , + ) $\mathcal{U}\!\left(0, +\infty\right)$ ppm
 DB amplitude A DB CHEOPS $A_\text{DB}^\text{\cheops{}}$ 18.8 ± 4.3 ${18.8 - 4.3}$ U ( 0 , + ) $\mathcal{U}\!\left(0, +\infty\right)$ ppm
 LDC u 1 CHEOPS $u_1^\text{\cheops{}}$ 0.357 ± 0.018
u 2 CHEOPS $u_2^\text{\cheops{}}$ 0.229 0.028 + 0.029 ${0.229}_{-{0.028}}^{+{0.029}}$
TESS
 Dayside flux F max TESS $F_\text{max}^\text{\tess{}}$ 340.4 ± 7.0 U ( 0 , + ) $\mathcal{U}\!\left(0, +\infty\right)$ ppm
 EV amplitude A EV TESS $A_\text{EV}^\text{\tess{}}$ 170.8 3.5 + 3.4 ${170.8}_{-{3.5}}^{+{3.4}}$ U ( 0 , + ) $\mathcal{U}\!\left(0, +\infty\right)$ ppm
 DB amplitude A DB TESS $A_\text{DB}^\text{\tess{}}$ 26.2 3.0 + 3.1 ${26.2}_{-{3.0}}^{+{3.1}}$ U ( 0 , + ) $\mathcal{U}\!\left(0, +\infty\right)$ ppm
 LDC u 1 TESS $u_1^\text{\tess{}}$ 0.293 ± 0.018
u 2 TESS $u_2^\text{\tess{}}$ 0.168 ± 0.031
Spitzer/IRAC
 Channel 1 dayside flux F max SPITZER 1 $F_\text{max}^\text{\spitzer{}\,1}$ 3106 111 + 112 ${3106}_{-{111}}^{+{112}}$ U ( 0 , + ) $\mathcal{U}\!\left(0, +\infty\right)$ ppm
 Channel 2 dayside flux F max SPITZER 2 $F_\text{max}^\text{\spitzer{}\,2}$ 3935 ± 25 U ( 0 , + ) $\mathcal{U}\!\left(0, +\infty\right)$ ppm
 Channel 3 dayside flux F max SPITZER 3 $F_\text{max}^\text{\spitzer{}\,3}$ 4090 ± 230 U ( 0 , + ) $\mathcal{U}\!\left(0, +\infty\right)$ ppm
 Channel 4 dayside flux F max SPITZER 4 $F_\text{max}^\text{\spitzer{}\,4}$ 4360 210 + 200 ${4360}_{-{210}}^{+{200}}$ U ( 0 , + ) $\mathcal{U}\!\left(0, +\infty\right)$ ppm
Derived parameters
Optimal time of inferior conjunction T 0 , opt $T_{0,\,\text{opt}}$ 1251.662013 ± 0.000011 BJDTDB - 2 458 000
Planetary radius Rp 1.1926 ± 0.0077 RJ
Semi-major axis a 0.02041 0.00014 + 0.00015 ${0.02041}_{-{0.00014}}^{+{0.00015}}$ au
Impact parameter b 0.3605 0.0095 + 0.0091 ${0.3605}_{-{0.0095}}^{+{0.0091}}$ R
Eccentricity e 0*
CHEOPS occultation depth δ occ CHEOPS $\delta_\text{occ}^\text{\cheops{}}$ 211.3 ± 7.5 ppm
TESS occultation depth δ occ TESS $\delta_\text{occ}^\text{\tess{}}$ 339.5 7.0 + 6.9 ${339.5}_{-{7.0}}^{+{6.9}}$ ppm
Spitzer/IRAC Ch. 1 occ. depth δ occ SPITZER 1 $\delta_\text{occ}^\text{\spitzer{}\,1}$ 3098 ± 111 ppm
Spitzer/IRAC Ch. 2 occ. depth δ occ SPITZER 2 $\delta_\text{occ}^\text{\spitzer{}\,2}$ 3925 ± 25 ppm
Spitzer/IRAC Ch. 3 occ. depth δ occ SPITZER 3 $\delta_\text{occ}^\text{\spitzer{}\,3}$ 4080 ± 230 ppm
Spitzer/IRAC Ch. 4 occ. depth δ occ SPITZER 4 $\delta_\text{occ}^\text{\spitzer{}\,4}$ 4350 210 + 200 ${4350}_{-{210}}^{+{200}}$ ppm
Transit duration T 14 2.1790 ± 0.0017 hours
Max. equilibrium dayside temperature T day, max 3061 ± 29‡ K

Notes. The top part of the table lists the fitted parameters with their corresponding prior probabilities. Uniform prior probabilities are represented with U(x min, x max), where x min and x max are the minimum and maximum allowed values, respectively. Normal (Gaussian) prior probabilities are written as N(μ, σ), where μ and σ are the mean and standard deviation of the normal distribution, respectively. The lower part of the table shows the values of parameters derived from the sampled parameter space. (*)We fixed the eccentricity to 0 despite the non-zero values reported in the literature (Hellier et al. 2009; Triaud et al. 2010; Nymeyer et al. 2011; Csizmadia et al. 2019) because of the small eccentricity value and the possible tidal origin of the eccentric radial-velocity signal (see discussion in Section 4.3). (†)The maximum values of the phase curve F max are equal to the dayside fluxes because the phase offset Δφ was fixed to 0. (‡)Equilibrium dayside temperature assuming full absorption of the incoming radiation (AB = 0), no heat redistribution (ε = 0, i.e. immediate re-radiation) and black-body spectral energy distributions for both the planet and the star, i.e. T day,\,max = ( 2 / 3 ) 0.25 R / a T eff $T_\text{day,\,max}=\left(2/3\right)^{0.25}\!\sqrt{R_\star/a}\; T_\text{eff}$.

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