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 2

System parameters as derived from the joint LC and RV analysis accounting for TTVs.

Parameter	Symbol	TOI-396 b	TOI-396 c ^(c)	TOI-396 d
Orbital period	P ^(a) (d)	${3.585287}_{- 0.000012}^{+ 0.000009}$ $3.585287_{ - 0.000012}^{ + 0.000009}$	${5.973865}_{- 0.000016}^{+ 0.000015}$ $5.973865_{ - 0.000016}^{ + 0.000015}$	${11.230511}_{- 0.000045}^{+ 0.000043}$ $11.230511_{ - 0.000045}^{ + 0.000043}$
Transit timing	T₀ ^(a) (BJD)	${8409.1900}_{- 0.0012}^{+ 0.0011}$ $8409.1900_{ - 0.0012}^{ + 0.0011}$	${8415.63344}_{- 0.00093}^{+ 0.00099}$ $8415.63344_{ - 0.00093}^{ + 0.00099}$	${8409.7324}_{- 0.0025}^{+ 0.0028}$ $8409.7324_{ - 0.0025}^{ + 0.0028}$
Transit depth	dF (ppm)	${213.7}_{- 6.4}^{+ 6.5}$ $213.7_{ - 6.4}^{ + 6.5}$	${208.7}_{- 8.3}^{+ 8.5}$ $208.7_{ - 8.3}^{ + 8.5}$	$213_{- 11}^{+ 12}$ $213_{ - 11}^{ + 12}$
Impact parameter	b	${0.587}_{- 0.028}^{- 0.025}$ $0.587_{ - 0.028}^{ - 0.025}$	${0.701}_{- 0.019}^{+ 0.017}$ $0.701_{ - 0.019}^{ + 0.017}$	${0.712}_{- 0.023}^{+ 0.026}$ $0.712_{ - 0.023}^{ + 0.026}$
RV semi-amplitude	K (m s⁻¹)	${1.30}_{- 0.35}^{+ 0.34}$ $1.30_{ - 0.35}^{ + 0.34}$	${0.28}_{- 0.19}^{+ 0.29}$ $0.28_{ - 0.19}^{ + 0.29}$	1.78 ± 0.40
Transit duration	W (h)	${2.705}_{- 0.034}^{+ 0.038}$ $2.705_{ - 0.034}^{ + 0.038}$	${2.843}_{- 0.043}^{+ 0.046}$ $2.843_{ - 0.043}^{ + 0.046}$	${3.47}_{- 0.13}^{+ 0.08}$ $3.47_{ - 0.13}^{ + 0.08}$
Semi-major axis	a (AU)	0.04888 ± 0.00066	0.06870 ± 0.00092	0.1046 ± 0.0014
Orbital inclination	i (º)	${85.98}_{- 0.25}^{+ 0.26}$ $85.98_{ - 0.25}^{ + 0.26}$	${86.59}_{- 0.14}^{+ 0.15}$ $86.59_{ - 0.14}^{ + 0.15}$	${87.72}_{- 0.11}^{+ 0.10}$ $87.72_{ - 0.11}^{ + 0.10}$
Scaled semi-major axis	a/R_⋆	${8.37}_{- 0.16}^{+ 0.17}$ $8.37_{ - 0.16}^{ + 0.17}$	${11.77}_{- 0.22}^{+ 0.24}$ $11.77_{ - 0.22}^{ + 0.24}$	${17.93}_{- 0.34}^{+ 0.37}$ $17.93_{ - 0.34}^{ + 0.37}$
Equilibrium temperature	T_eq ^(b) (K)	$1552_{- 23}^{+ 22}$ $1552_{ - 23}^{ + 22}$	1309 ± 19	$1061_{- 16}^{+ 15}$ $1061_{ - 16}^{ + 15}$
Eccentricity	e	0 (fixed)	0 (fixed)	0 (fixed)
Argument of pericentre	ω (º)	90 (fixed)	90 (fixed)	90 (fixed)
Planet radius	R_p (R_⊕)	${2.004}_{- 0.047}^{+ 0.045}$ $2.004_{ - 0.047}^{ + 0.045}$	${1.979}_{- 0.051}^{+ 0.054}$ $1.979_{ - 0.051}^{ + 0.054}$	${2.001}_{- 0.064}^{+ 0.063}$ $2.001_{ - 0.064}^{ + 0.063}$
Planet mass	Mp (M_⊕)	${3.55}_{- 0.96}^{+ 0.94}$ $3.55_{ - 0.96}^{ + 0.94}$	${0.90}_{- 0.63}^{+ 0.94}$ $0.90_{ - 0.63}^{ + 0.94}$	7.1 ± 1.6
Planet density	ρ_p (g cm⁻³)	${2.44}_{- 0.68}^{+ 0.69}$ ${2.44_{ - 0.68}^{ + 0.69}}$	${0.65}_{- 0.45}^{+ 0.67}$ ${0.65_{ - 0.45}^{ + 0.67}}$	${4.9}_{- 1.1}^{+ 1.2}$ ${4.9_{ - 1.1}^{ + 1.2}}$

LD coefficient 1	u_1,TESS	${0.2318}_{- 0.0064}^{+ 0.0066}$ $0.2318_{ - 0.0064}^{ + 0.0066}$
LD coefficient 2	u_2,TESS	${0.3084}_{- 0.0029}^{+ 0.0030}$ $0.3084_{ - 0.0029}^{ + 0.0030}$
RV jitter	σ_HARPS (m s⁻¹)	${1.490}_{- 0.022}^{+ 0.041}$ $1.490_{ - 0.022}^{ + 0.041}$

Notes. All jump parameters, but the LD coefficients, were subject to unbounded uniform priors following the parameterisations specified in Bonfanti & Gillon (2020); see text for further details. ^(a)Uncertainties from the run assuming linear ephemerides (no TTVs). T₀ values are shifted by −2 450 000. ^(b) Assuming zero albedo and full recirculation. ^(c)The 3σ upper limits on the RV semi-amplitude, the planet mass, and the mean planet density of TOI-396 c are $K_{c}^{u p} = 1.2 m s^{- 1}, M_{c}^{u p} = 3.8 M_{\oplus}, and ρ_{c}^{u p} = 2.9 g {cm}^{- 3}$ $K_c^{up} = 1.2{\rm{m}}{{\rm{s}}^{ - 1}},M_c^{up} = 3.8{M_ \oplus }{\rm{, and }}\rho _c^{up} = 2.9{\rm{g}}{\rm{c}}{{\rm{m}}^{ - 3}}$ , respectively.

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