TOI-837 b: Characterisation, formation, and evolutionary history of an infant warm Saturn-mass planet

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Volume 688 (August 2024)

A&A, 688 (2024) A15

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Table 2

Priors and best-fit values of the free and derived parameters related to the joint RV+light curve modelling.

Parameter	Priors	Best-fit value^(a)
		GP + 1 sinusoid	Two GPs + 2 sinusoids
		(base model)	(adopted model)
Free parameters
h₁ (m s⁻¹)	𝒰(0,300)	$138_{- 32}^{+ 56}$ $138_{ - 32}^{ + 56}$	$181_{- 58}^{+ 68}$ $181_{ - 58}^{ + 68}$
λ₁ (days)	𝒰(0,1000)	$32_{- 10}^{+ 12}$ $32_{ - 10}^{ + 12}$	$400_{- 207}^{+ 334}$ $400_{ - 207}^{ + 334}$
w₁	𝒰(0,1)	${0.33}_{- 0.11}^{+ 0.17}$ $0.33_{ - 0.11}^{ + 0.17}$	${0.46}_{- 0.14}^{+ 0.16}$ $0.46_{ - 0.14}^{ + 0.16}$
θ₁ (days)	𝒰(0,5)	3.01 ± 0.02	${3.000}_{- 0.004}^{+ 0.003}$ $3.000_{ - 0.004}^{ + 0.003}$
h₂ (m s⁻¹)	𝒰(0,300)	–	$36_{- 7}^{+ 10}$ $36_{ - 7}^{ + 10}$
λ₂ (days)	𝒰(0,1000)	–	$6_{- 3}^{+ 16}$ $6_{ - 3}^{ + 16}$
w₂	𝒰(0,1)	–	${0.39}_{- 0.13}^{+ 0.18}$ $0.39_{ - 0.13}^{ + 0.18}$
θ₂ (days)	𝒰(0,5)	–	${3.06}_{- 0.28}^{+ 0.25}$ $3.06_{ - 0.28}^{ + 0.25}$
K_b (m s⁻¹)	𝒰(0,100)	${32.9}_{- 5.9}^{+ 5.8}$ $32.9_{ - 5.9}^{ + 5.8}$	${34.2}_{- 5.3}^{+ 4.9}$ $34.2_{ - 5.3}^{ + 4.9}$
orbital period, P_b (days)	𝒰(8.31,8.32)	8.3249104 ± 0.0000040	8.3249102 ± 0.0000037
time of inferior conjunction, T_conj,b (BJD-2 450 000)	𝒰(9290.2,9290.3)	9290.2151 ± 0.00030	9290.2151 ± 0.00027
K_{long period} (m s⁻¹)	𝒰(0,100)	–	${42.6}_{- 12.2}^{+ 11.2}$ $42.6_{ - 12.2}^{ + 11.2}$
period, P_{long period} (d)	𝒰(10,100)	–	${74.8}_{- 9.1}^{+ 13.4}$ $74.8_{ - 9.1}^{ + 13.4}$
T_{RV=0, long period} (BJD-2 450 000)	𝒰(9860,9970)	–	${9906.4}_{- 3.0}^{+ 3.4}$ $9906.4_{ - 3.0}^{ + 3.4}$
acceleration, $\dot{γ} (m s^{- 1} {day}^{- 1})$ $\dot \gamma \left( {{\rm{m}}\,{{\rm{s}}^{ - 1}}{\rm{ da}}{{\rm{y}}^{ - 1}}} \right)$	𝒰(−1, 1)	$- {0.22}_{- 0.53}^{+ 0.68}$ $- 0.22_{ - 0.53}^{ + 0.68}$	−0.11 ±± 0.47
R_b/R_⋆	𝒰(0.0, 0.3)	${0.086}_{- 0.006}^{+ 0.008}$ $0.086_{ - 0.006}^{ + 0.008}$	${0.079}_{- 0.005}^{+ 0.008}$ $0.079_{ - 0.005}^{ + 0.008}$
i_b (degrees)	𝒰(80,90)	86.96 ± 0.06	86.96 ± 0.05
limb dark. parametrization, q_1,TESS	𝒰(0,1)	${0.57}_{- 0.21}^{+ 0.25}$ $0.57_{ - 0.21}^{ + 0.25}$	${0.55}_{- 0.20}^{+ 0.23}$ $0.55_{ - 0.20}^{ + 0.23}$
limb dark. parametrization, q_2,TESS	𝒰(0,1)	${0.45}_{- 0.28}^{+ 0.33}$ $0.45_{ - 0.28}^{ + 0.33}$	${0.46}_{- 0.29}^{+ 0.32}$ $0.46_{ - 0.29}^{ + 0.32}$
ρ_⋆ (ρ_⊙)	𝒢(1.08, 0.04)	1.08 ± 0.04	1.08 ± 0.03
σ_{jit RV,HARPS} (m s⁻¹)	𝒰(0,50)	25 ± 4	${10.5}_{- 6.7}^{+ 10.4}$ $10.5_{ - 6.7}^{ + 10.4}$
γ_RV,HARPS (m s⁻¹)	𝒰(−200, 200)	$53_{- 58}^{+ 51}$ $53_{ - 58}^{ + 51}$	$44_{- 94}^{+ 83}$ $44_{ - 94}^{ + 83}$
σjitTESS (ppm)	𝒰(0,0.1)	0.00030 ± 0.00003	0.00030 ± 0.00003
γ_TESS (ppm)	𝒰(−0.01, 0.01)	−0.00005 ± 0.00001	−0.00005 ± 0.00001
Derived parameters
eccentricity e_b	–	0 (fixed)	0 (fixed)
periastron argument, ω_⋆,b (rad)	–	π/2 (fixed)	π/2 (fixed)
limb dark. coeff., u_1,TESS	–	${0.66}_{- 0.41}^{+ 0.42}$ $0.66_{ - 0.41}^{ + 0.42}$	0.65 ± 0.40
limb dark. coeff., u_2,TESS	–	${0.07}_{- 0.45}^{+ 0.44}$ $0.07_{ - 0.45}^{ + 0.44}$	${0.06}_{- 0.42}^{+ 0.45}$ $0.06_{ - 0.42}^{ + 0.45}$
semi-major axis, a_b (au)	–	0.083 ± 0.001	0.083 ± 0.001
impact parameter, b	–	0.91 ± 0.03	0.91 ± 0.02
transit duration (days)	–	${0.0904}_{- 0.0076}^{+ 0.0072}$ $0.0904_{ - 0.0076}^{ + 0.0072}$	${0.0905}_{- 0.0068}^{+ 0.0075}$ $0.0905_{ - 0.0068}^{ + 0.0075}$
radius, r_b (R_⊕)	–	${9.74}_{- 0.67}^{+ 0.96}$ $9.74_{ - 0.67}^{ + 0.96}$	${9.71}_{- 0.60}^{+ 0.93}$ $9.71_{ - 0.60}^{ + 0.93}$
mass, m_b (M_⊕)	–	112 ± 20	$116_{- 18}^{+ 17}$ $116_{ - 18}^{ + 17}$
bulk density, ρ_b (g cm⁻³)	–	${0.64}_{- 0.19}^{+ 0.22}$ $0.64_{ - 0.19}^{ + 0.22}$	${0.68}_{- 0.18}^{+ 0.20}$ $0.68_{ - 0.18}^{ + 0.20}$
equilibrium temperature ^(b) ,T_eq,b (K)	–	1022±13
Bayesian evidence, ln 𝒵		34450.3	34456.3

Notes. ^(a)The best-fit values, with the lower and upper uncertainties given as the 50th, 16th, and 84th percentiles of the posterior distributions, respectively. ^(b)Assuming zero albedo.

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