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Table 5

TOI-3862 parameters from the transit and RV joint fit, obtained with the model without GP, as well as parameters from internal structure retrievals and the atmospheric evolution.

Parameter Prior(a) Value(b)
 Model parameters
Orbital period Porb (days) 𝒰[1.2, 1.8] 1.55745774−4.2×10−7+3.6×10−7Mathematical equation: $\[1.55745774_{-4.2 \times 10^{-7}}^{+3.6 \times 10^{-7}}\]$
Transit epoch T0 (BJD – 2 450 000) 𝒰[9662.0, 9663.0] 9662.73870−0.00014+0.00013Mathematical equation: $\[9662.73870_{-0.00014}^{+0.00013}\]$
esin⁡ω⋆Mathematical equation: $\[\sqrt{e} ~\sin~ \omega_{\star}\]$ 𝒰(−1, 1) −0.148−0.021+0.019Mathematical equation: $\[-0.148_{-0.021}^{+0.019}\]$
ecos⁡ω⋆Mathematical equation: $\[\sqrt{e} ~\cos~ \omega_{\star}\]$ 𝒰(−1, 1) 0.031−0.027+0.022Mathematical equation: $\[0.031_{-0.027}^{+0.022}\]$
Scaled planetary radius Rp/R⋆ 𝒰[0, 0.5] 0.05508−0.00033+0.00036Mathematical equation: $\[0.05508_{-0.00033}^{+0.00036}\]$
Impact parameter, b 𝒰[0, 1] 0.135−0.058+0.059Mathematical equation: $\[0.135_{-0.058}^{+0.059}\]$
Radial velocity semi-amplitude variation K (m s−1) 𝒰[0, 50] 31.77 ± 0.24
Derived parameters
Planet radius (RJ) . . . 0.493 ± 0.016
Planet radius (R⊕) . . . 5.53 ± 0.18
Planet mass (MJ) . . . 0.1688−0.0090+0.0087Mathematical equation: $\[0.1688_{-0.0090}^{+0.0087}\]$
Planet mass (M⊕) . . . 53.7−2.9+2.8Mathematical equation: $\[53.7_{-2.9}^{+2.8}\]$
Eccentricity e . . . 0.0232−0.0054+0.0071Mathematical equation: $\[0.0232_{-0.0054}^{+0.0071}\]$
Scaled semi-major axis a/R⋆ . . . 8.848−0.070+0.074Mathematical equation: $\[8.848_{-0.070}^{+0.074}\]$
Semi-major axis a (AU) . . . 0.02539−0.00068+0.00064Mathematical equation: $\[0.02539_{-0.00068}^{+0.00064}\]$
ωP (deg) . . . 278.72−0.50+0.48Mathematical equation: $\[278.72_{-0.50}^{+0.48}\]$
Orbital inclination i (deg) . . . 89.15 ± 0.37
Transit duration T41 (days) . . . 0.05871−0.00049+0.00050Mathematical equation: $\[0.05871_{-0.00049}^{+0.00050}\]$
Transit duration T32 (days) . . . 0.05243−0.00049+0.00051Mathematical equation: $\[0.05243_{-0.00049}^{+0.00051}\]$
Calculated parameters
Equilibrium Temperature Teq (K) 1539 ± 36
Planetary density ρP (g cm−3) 1.75 ± 0.20
Other system parameters
Jitter term σHARPS–N (m s−1) 𝒰[0, 60] 0.63−0.42+0.64Mathematical equation: $\[0.63_{-0.42}^{+0.64}\]$
Limb darkening q1, TESS 𝒩[0.4586, 0.1] 0.4486 ± 0.0025
Limb darkening q2, TESS 𝒩[0.1153, 0.1] 0.1035−0.0029+0.0025Mathematical equation: $\[0.1035_{-0.0029}^{+0.0025}\]$
Limb darkening q1, KeplerCam(c) 𝒩[0.4740, 0.1] 0.475−0.055+0.038Mathematical equation: $\[0.475_{-0.055}^{+0.038}\]$
Limb darkening q2, KeplerCam(c) 𝒩[0.1155, 0.1] 0.124−0.034+0.048Mathematical equation: $\[0.124_{-0.034}^{+0.048}\]$
Limb darkening q1, LCO N [0.7922, 0.1] 0.782−0.047+0.041Mathematical equation: $\[0.782_{-0.047}^{+0.041}\]$
Limb darkening q2, LCO N [0.0185, 0.1] 0.003−0.049+0.052Mathematical equation: $\[0.003_{-0.049}^{+0.052}\]$
Limb darkening q1, Muscat2g 𝒩[0.7925, 0.1] 0.850−0.023+0.040Mathematical equation: $\[0.850_{-0.023}^{+0.040}\]$
Limb darkening q2, Muscat2g 𝒩[0.0020, 0.1] 0.032−0.032+0.054Mathematical equation: $\[0.032_{-0.032}^{+0.054}\]$
Limb darkening q1, Muscat2r 𝒩[0.5699, 0.1] 0.631−0.037+0.041Mathematical equation: $\[0.631_{-0.037}^{+0.041}\]$
Limb darkening q2, Muscat2r 𝒩[0.0014, 0.1] 0.056−0.050+0.039Mathematical equation: $\[0.056_{-0.050}^{+0.039}\]$
Limb darkening q1, Muscat2z 𝒩[0.4109, 0.1] 0.384−0.046+0.040Mathematical equation: $\[0.384_{-0.046}^{+0.040}\]$
Limb darkening q2, Muscat2z 𝒩[0.0009, 0.1] 0.041−0.067+0.035Mathematical equation: $\[0.041_{-0.067}^{+0.035}\]$
Results from internal structure retrievals
Envelope-to-planet mass fraction (%) . . . 17.3−2.8+2.9Mathematical equation: $\[17.3_{-2.8}^{+2.9}\]$
Core and mantle mass fraction (%) . . . 82.7−2.8+2.9Mathematical equation: $\[82.7_{-2.8}^{+2.9}\]$
Results from atmospheric evolution
Maximum initial mass (M⊕ . . . 70.6−2.8+2.4Mathematical equation: $\[70.6_{-2.8}^{+2.4}\]$
Initial envelope mass (M⊕) . . . 25.8−1.4+2.1Mathematical equation: $\[25.8_{-1.4}^{+2.1}\]$
Initial envelope-to-planet mass fraction (%) . . . 36.5−3.1+4.6Mathematical equation: $\[36.5_{-3.1}^{+4.6}\]$
Initial radius (R⊕) . . . 8.5−0.1+0.2Mathematical equation: $\[8.5_{-0.1}^{+0.2}\]$

Notes. (a) 𝒰[a, b] refers to uniform priors between a and b, 𝒩[a, b] to Gaussian priors with median a and standard deviation b.(b) Parameter estimates and corresponding uncertainties are defined as the median and the 16th and 84th percentiles of the posterior distributions. (c) Same limb-darkening model for KeplerCam and OAAlbany data (i filter).

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