TOI-5108 b and TOI 5786 b: Two transiting sub-Saturns detected and characterized with TESS, MaHPS, and SOPHIE

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Table 6

Priors and final parameter values from the juliet fit of TOI-5786.

Parameter name	Prior	Derived values	Description
Fitting parameters
P₁ (d)	$N [6.99, 0.01]$ ${\cal N}[6.99,0.01]$	${6.998405}_{- 0.000021}^{+ 0.000015}$ $6.998405_{ - 0.000021}^{ + 0.000015}$	Orbital Period of the inner planet
T_0,1 (BJD_TDB - 2457000)	$N [1685.29, 0.01]$ ${{\cal N}[1685.29,0.01]}$	1685.288 ± 0.001	Time of Mid-Transit of the inner planet
R_p,1/R_⊕	$U [0.001, 1]$ ${{\cal U}[0.001,1]}$	0.0258 ± 0.0011	Planet-to-star radius ratio of the inner planet
b₁	$U [0, 1]$ ${\cal U}[0,1]$	${0.38}_{- 0.14}^{+ 0.11}$ $0.38_{ - 0.14}^{ + 0.11}$	Impact parameter of the inner planet
$\sqrt{e} sin ω_{1}$ ${\sqrt e \sin {\omega _1}}$	fixed	0	Parametrization of e and ω
$\sqrt{e} cos ω_{1}$ ${\sqrt e \cos {\omega _1}}$	fixed	0	Parametrization of e and ω
K₁ (m s⁻¹)	$U [0, 200]$ ${{\cal U}[0,200]}$	${4.1}_{- 19}^{+ 2.1}$ ${4.1_{ - 19}^{ + 2.1}}$	RV Amplitude of the inner planet
P₂ (d)	$U [12.7, 12.85]$ ${{\cal U}[12.7,12.85]}$	12.779107 ± 0.000015	Orbital Period of the outer planet
T_0,2 (BJD_TDB − 2457000)	$U [3140.5, 3140.7]$ ${\cal U}[3140.5,3140.7]$	3140.6139 ± 0.0004	Time of mid-transit of the outer planet
R_p,2/R_*	$U [0.001, 1]$ ${\cal U}[0.001,1]$	${0.0576}_{- 0.0008}^{+ 0.0009}$ $0.0576_{ - 0.0008}^{ + 0.0009}$	Planet-to-star radius ratio of the outer planet
b₂	$U [0, 1]$ ${\cal U}[0,1]$	${0.33}_{- 0.14}^{+ 0.09}$ $0.33_{ - 0.14}^{ + 0.09}$	Impact parameter of the outer planet
$\sqrt{e} sin ω_{2}$ $\sqrt e \sin {\omega _2}$	fixed	0	Parametrization of e and ω
$\sqrt{e} cos ω_{2}$ $\sqrt e \cos {\omega _2}$	fixed	0	Parametrization of e and ω
K₂ (m s⁻¹)	$U [0, 100]$ ${{\cal U}[0,100]}$	${17.4}_{- 2.0}^{+ 2.1}$ ${17.4_{ - 2.0}^{ + 2.1}}$	RV amplitude of the outer planet
ρ_* (kg/m³)	$N [690, 80]$ ${{\cal N}[690,80]}$	$682_{- 80}^{+ 90}$ ${682_{ - 80}^{ + 90}}$	Stellar Density
Instrumental parameters
q₁,TESS	$N [0.32, 0.1]$ ${{\cal N}[0.32,0.1]}$	${0.38}_{- 0.06}^{+ 0.07}$ ${0.38_{ - 0.06}^{ + 0.07}}$	limb-darkening parameter
q₂,TESS	$N [0.36, 0.1]$ ${{\cal N}[0.36,0.1]}$	0.31 ± 0.09	limb-darkening parameter
µ_MaHPS (m s⁻¹ )	$U [- 100, 100]$ ${{\cal U}[ - 100,100]}$	1.1 ±2.3	relative offset MaHPS
µ_SOPHIE (m s⁻¹ )	$U [- 29000, - 28000]$ ${{\cal U}[ - 29000, - 28000]}$	−28388 ± 2	relative offset SOPHIE
σ_MaHPS (m s⁻¹ )	$ℒ [0.001, 100]$ ${\cal L}[0.001,100]$	14.12 ± 3	MaHPS jitter term
σ_SOPHIE (m s⁻¹ )	$ℒ [0.001, 100]$ ${\cal L}[0.001,100]$	${2.3}_{- 20}^{+ 4.0}$ $2.3_{ - 20}^{ + 4.0}$	SOPHIE jitter term

TOI-5786 b parameters
a/R_*		18.0 ± 0.8	Scaled semi-major axis
a (au)		0.114 ± 0.007	Semi-major axis
T₁₄(h)		4.6 ± 0.3	Transit duration of TOI-5786 b
i (°)		88.9 ± 0.4	Orbital Inclination
R_p (R_⊕)		8.54 ± 0.13	Radius of TOI-5786 b
M_p (M_⊕)		73 ± 9	Mass of TOI-5786 b
ρ_p (kg/m³)		640 ± 80	Bulk density of TOI-5786 b
T_eq (K)		1040 ± 40	Equilibrium temperature of TOI-5786 b
Inner planet candidate parameters
a/R_*		12.1 ± 0.5	Scaled semi-major axis
a (au)		0.077 ± 0.004	Semi-major axis
T₁₄ (h)		4.0 ± 0.5	Transit duration of the inner planet candidate
i (°)		88.2 ± 0.7	Orbital Inclination
R_p (R_⊕)		3.83 ± 0.16	Radius of the inner planet candidate
M_p (M_⊕)		<36	3-σ upper limit for the mass
T_eq (K)		1260 ± 40	Equilibrium temperature of the inner planet candidate

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