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Table 2

Summary of the different RV (DRS) + transit photometry + activity diagnostics (when specified) models tested in this work.

Model ID Description Bayesian evidence(a) (ln 𝒵) Planetary mass(b) M Planetary density g cm-3
M1 GP quasi-periodic kernel applied to RVs 103927.9 ± 0.6
M2 GP quasi-periodic kernel applied to RVs, with a different set 103925.5 ± 0.6
of hyper-parameters (h,w,λ) for each observing season
M3 GP quasi-periodic kernel trained (c) on BIS 103417.5 ± 0.6
ρc = 7.4 ± 2.8 (12.0)
M4 GP quasi-periodic trained (c) on log 104237.8 ± 0.6
mc = 18.9 ± 7.0 (30.4)
M5 Multi-dimensional GP framework (d) 836.6 ± 0.3
using log and BIS, and the quasi-periodic kernel; circular orbits
M6 Multi-dimensional GP framework (d) 565.6 ± 0.5
using log and the quasi-periodic kernel; circular orbits
M7 GP dSHO kernel applied to RVs 103923.6 ± 0.5
M8 GP QPC kernel applied to RVs 103928.1 ± 0.6
M9 Activity corrected through a linear regression fit between RVs and BIS 103991.2 ± 0.5
mc = 8.4 ± 4.9 (16.7) ρc = 3.1 ± 1.8 (6.3)

Notes. All include two Keplerians for planets b and c, except for models M5 and M6, for which we adopted circular orbits. (a) We note that the analysed datasets related to each model are not always the same, therefore model comparison based on the values of the Bayesian evidence ln 𝒵 can be performed only when the same datasets are involved. (b) The 95th percentile is provided in parenthesis. (c) With "trained" we mean that the same GP kernel is used to model the RVs and the activity diagnostic. In the case of a quasi-periodic kernel, three hyper-parameters over four, namely theta, w, and λ, are shared by the two datasets, while two distinct amplitudes h are used. (d) To speed up the analysis, we did not fit the photometric transits, and we assumed circular orbits (the results from other models show that the eccentricities are consistent with zero). The priors for the planet ephemeris are defined based on the results of the M4 model. We adopted planet radii calculated from M4 to derive the densities.

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