Radii, masses, and transit-timing variations of the three-planet system orbiting the naked-eye star TOI-396

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Volume 693 (January 2025)

A&A, 693 (2025) A90

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Table 5

Best-fit parameters (MAP and HDI at 68.27%) along with their respective priors, as inferred from the dynamical joint modelling of RVs and TTVs with TRADES.

	TOI-396 b		TOI-396 c		TOI-396 d
	MAP (HDI)	Prior	MAP (HDI)	Prior	MAP (HDI)	Prior
M_p/M_⋆ (10⁻⁶)	${8.62}_{- 2.26}^{+ 0.76}$ $8.62_{ - 2.26}^{ + 0.76}$	𝒰(0.02, 52.0)	${5.59}_{- 1.69}^{+ 0.25}$ $5.59_{ - 1.69}^{ + 0.25}$	𝒰(0.02, 52.0)	$17_{- 1}^{+ 3}$ $17_{ - 1}^{ + 3}$	𝒰(0.02, 52.0)
P (d)	${3.585535}_{- 0.000171}^{+ 0.000092}$ $3.585535_{ - 0.000171}^{ + 0.000092}$	𝒰(3, 4)	${5.97291}_{- 0.00031}^{+ 0.00058}$ $5.97291_{ - 0.00031}^{ + 0.00058}$	𝒰(5, 7)	${11.230355}_{- 0.000016}^{+ 0.000173}$ $11.230355_{ - 0.000016}^{ + 0.000173}$	𝒰(10, 12)
$\sqrt{e} \cos ω$ $\sqrt e \cos \omega$	$- {0.099}_{- 0.014}^{+ 0.155}$ $- 0.099_{ - 0.014}^{ + 0.155}$	$U (- \sqrt{0.5}, \sqrt{0.5})$ ${\cal U}( - \sqrt {0.5} ,\sqrt {0.5} )$	$- {0.264}_{- 0.017}^{+ 0.060}$ $- 0.264_{ - 0.017}^{ + 0.060}$	$U (- \sqrt{0.5}, \sqrt{0.5})$ ${\cal U}( - \sqrt {0.5} ,\sqrt {0.5} )$	$- {0.168}_{- 0.035}^{+ 0.069}$ $- 0.168_{ - 0.035}^{ + 0.069}$	$U (- \sqrt{0.5}, \sqrt{0.5})$ ${\cal U}( - \sqrt {0.5} ,\sqrt {0.5} )$
$\sqrt{e} \sin ω$ $\sqrt e \sin \omega$	$- {0.268}_{- 0.031}^{+ 0.038}$ $- 0.268_{ - 0.031}^{ + 0.038}$	$U (- \sqrt{0.5}, \sqrt{0.5})$ ${\cal U}( - \sqrt {0.5} ,\sqrt {0.5} )$	$- {0.066}_{- 0.042}^{+ 0.062}$ $- 0.066_{ - 0.042}^{ + 0.062}$	$U (- \sqrt{0.5}, \sqrt{0.5})$ ${\cal U}( - \sqrt {0.5} ,\sqrt {0.5} )$	${0.220}_{- 0.071}^{+ 0.062}$ $0.220_{ - 0.071}^{ + 0.062}$	$U (- \sqrt{0.5}, \sqrt{0.5})$ ${\cal U}( - \sqrt {0.5} ,\sqrt {0.5} )$
λ(°)	${122.53}_{- 5.50}^{+ 0.21}$ $122.53_{ - 5.50}^{ + 0.21}$	𝒰(0, 360)	${230.04}_{- 3.53}^{+ 0.61}$ $230.04_{ - 3.53}^{ + 0.61}$	𝒰(0, 360)	${9.93}_{- 2.99}^{+ 0.55}$ $9.93_{ - 2.99}^{ + 0.55}$	𝒰(0, 360)
M_p (M_⊕)	${3.46}_{- 0.97}^{+ 0.27}$ $3.46_{ - 0.97}^{ + 0.27}$	(derived)	${2.24}_{- 0.67}^{+ 0.13}$ $2.24_{ - 0.67}^{ + 0.13}$	(derived)	${6.89}_{- 0.60}^{+ 1.41}$ $6.89_{ - 0.60}^{ + 1.41}$	(derived)
e	${0.082}_{- 0.020}^{+ 0.011}$ $0.082_{ - 0.020}^{ + 0.011}$	ℋ_𝒢(0, 0.083)	${0.0741}_{- 0.0275}^{+ 0.0071}$ $0.0741_{ - 0.0275}^{ + 0.0071}$	ℋ_𝒢(0, 0.083)	${0.077}_{- 0.031}^{+ 0.013}$ $0.077_{ - 0.031}^{ + 0.013}$	ℋ_𝒢(0, 0.083)
ω(°)	$250_{- 5}^{+ 31}$ $250_{ - 5}^{ + 31}$	(derived)	$194_{- 13}^{+ 12}$ $194_{ - 13}^{ + 12}$	(derived)	$127_{- 18}^{+ 16}$ $127_{ - 18}^{ + 16}$	(derived)
ℳ (°)	$53_{- 37}^{+ 5}$ $53_{ - 37}^{ + 5}$	(derived)	$216_{- 14}^{+ 12}$ $216_{ - 14}^{ + 12}$	(derived)	$63_{- 15}^{+ 16}$ $63_{ - 15}^{ + 16}$	(derived)
ρ_p (ρ_⊕)	${0.426}_{- 0.136}^{+ 0.013}$ $0.426_{ - 0.136}^{ + 0.013}$	(derived)	${0.288}_{- 0.096}^{+ 0.003}$ $0.288_{ - 0.096}^{ + 0.003}$	(derived)	${0.842}_{- 0.123}^{+ 0.12}$ $0.842_{ - 0.123}^{ + 0.12}$	(derived)
ρ_p (g cm⁻³)	${2.339}_{- 0.750}^{+ 0.073}$ $2.339_{ - 0.750}^{ + 0.073}$	(derived)	${1.582}_{- 0.528}^{+ 0.019}$ $1.582_{ - 0.528}^{ + 0.019}$	(derived)	${4.624}_{- 0.676}^{+ 0.704}$ $4.624_{ - 0.676}^{ + 0.704}$	(derived)

	MAP (HDI)	Prior
γ_RV (m s⁻¹)	${0.059}_{- 0.234}^{+ 0.095}$ $0.059_{ - 0.234}^{ + 0.095}$	𝒰(−5005, +5005)
log₂ σ_jitter	$- 32_{- 11}^{+ 19}$ $- 32_{ - 11}^{ + 19}$	(−49.83, 6.65)
σ_jitter (m s⁻¹)	≪10⁻⁵	(derived)

Notes. All parameters have been defined at the reference time T_ref = BJD_TDB − 2 450 000 = 8379. 𝒰(X, Y) means uniform distribution between X and Y values; ℋ(µ, σ) means half-normal distribution with mean µ and standard deviation σ.

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