The multi-planet system TOI-5624: four transiting sub-Neptunes with an outer companion revealed by transit-timing variations

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Table C.5

Posteriors of the TOI-5624 system from the two tested dynamical scenarios.

Configurations		4 Planets	5 Planets
Parameter	Prior	MAP (HDI±1σ)		Unit
TOI-5624 d

FITTED PARAMETERS
M_p/M_⋆	U(0.30, 954.7)	$44_{- 13}^{+ 4}$ $Mathematical equation: $44_{-13}^{+4}$$	$17_{- 5}^{+ 8}$ $Mathematical equation: $17_{-5}^{+8}$$	$(\frac{M_{⊙}}{M_{⋆}}) \times 10^{- 6}$ $Mathematical equation: $\left(\frac{M_\odot}{M_\star}\right) \times 10^{-6}$$
Orbital Period (P)	U(13.6, 13.8)	${13.72796}_{- 0.00087}^{+ 0.00079}$ $Mathematical equation: $13.72796_{-0.00087}^{+0.00079}$$	${13.72930}_{- 0.00109}^{+ 0.00018}$ $Mathematical equation: $13.72930_{-0.00109}^{+0.00018}$$	days
$\sqrt{e} \cos ω$ $Mathematical equation: $\sqrt{e} \cos \omega$$	U( $- \sqrt{0.5}, \sqrt{0.5}$ $Mathematical equation: $-\sqrt{0.5}, \sqrt{0.5}$$ )	${0.117}_{- 0.069}^{+ 0.040}$ $Mathematical equation: $0.117_{-0.069}^{+0.040}$$	$- {0.078}_{- 0.047}^{+ 0.098}$ $Mathematical equation: $-0.078_{-0.047}^{+0.098}$$
$\sqrt{e} \sin ω$ $Mathematical equation: $\sqrt{e} \sin \omega$$	U( $- \sqrt{0.5}, \sqrt{0.5}$ $Mathematical equation: $-\sqrt{0.5}, \sqrt{0.5}$$ )	$- {0.137}_{- 0.028}^{+ 0.094}$ $Mathematical equation: $-0.137_{-0.028}^{+0.094}$$	$- {0.004}_{- 0.111}^{+ 0.068}$ $Mathematical equation: $-0.004_{-0.111}^{+0.068}$$
Mean Longitude (λ)	U(0, 360)	${315.66}_{- 0.43}^{+ 1.98}$ $Mathematical equation: $315.66_{-0.43}^{+1.98}$$	${318.54}_{- 0.96}^{+ 1.04}$ $Mathematical equation: $318.54_{-0.96}^{+1.04}$$	deg
DERIVED PARAMETERS
Mass (M_p)	–	$13_{- 4}^{+ 1}$ $Mathematical equation: $13_{-4}^{+1}$$	$5_{- 1}^{+ 3}$ $Mathematical equation: $5_{-1}^{+3}$$	M_⊕
Eccentricity (e)	U(0, 0.5)	${0.0325}_{- 0.0230}^{+ 0.0031}$ $Mathematical equation: $0.0325_{-0.0230}^{+0.0031}$$	${0.0061}_{- 0.0060}^{+ 0.0109}$ $Mathematical equation: $0.0061_{-0.0060}^{+0.0109}$$
Argument of Periastron (ω)	–	$- 50_{- 31}^{+ 24}$ $Mathematical equation: $-50_{-31}^{+24}$$	$183_{- 70}^{+ 113}$ $Mathematical equation: $183_{-70}^{+113}$$	deg
Mean Anomaly (M)	–	$185_{- 26}^{+ 31}$ $Mathematical equation: $185_{-26}^{+31}$$	$- 44_{- 115}^{+ 70}$ $Mathematical equation: $-44_{-115}^{+70}$$	deg

TOI-5624 e

FITTED PARAMETERS
M_p/M_⋆	U(0.30, 954.7)	$60_{- 12}^{+ 12}$ $Mathematical equation: $60_{-12}^{+12}$$	$25_{- 2}^{+ 13}$ $Mathematical equation: $25_{-2}^{+13}$$	$(\frac{M_{⊙}}{M_{⋆}}) \times 10^{- 6}$ $Mathematical equation: $\left(\frac{M_\odot}{M_\star}\right) \times 10^{-6}$$
Orbital Period (P)	U(21.4, 21.6)	${21.4979}_{- 0.0025}^{+ 0.0010}$ $Mathematical equation: $21.4979_{-0.0025}^{+0.0010}$$	${21.49253}_{- 0.00084}^{+ 0.00232}$ $Mathematical equation: $21.49253_{-0.00084}^{+0.00232}$$	days
$\sqrt{e} \cos ω$ $Mathematical equation: $\sqrt{e} \cos \omega$$	U( $- \sqrt{0.5}, \sqrt{0.5}$ $Mathematical equation: $-\sqrt{0.5}, \sqrt{0.5}$$ )	${0.010}_{- 0.094}^{+ 0.055}$ $Mathematical equation: $0.010_{-0.094}^{+0.055}$$	${0.049}_{- 0.091}^{+ 0.019}$ $Mathematical equation: $0.049_{-0.091}^{+0.019}$$
$\sqrt{e} \sin ω$ $Mathematical equation: $\sqrt{e} \sin \omega$$	U( $- \sqrt{0.5}, \sqrt{0.5}$ $Mathematical equation: $-\sqrt{0.5}, \sqrt{0.5}$$ )	$- {0.0905}_{- 0.0022}^{+ 0.1731}$ $Mathematical equation: $-0.0905_{-0.0022}^{+0.1731}$$	${0.119}_{- 0.037}^{+ 0.046}$ $Mathematical equation: $0.119_{-0.037}^{+0.046}$$
Mean Longitude (λ)	U(0, 360)	${241.73}_{- 0.72}^{+ 1.12}$ $Mathematical equation: $241.73_{-0.72}^{+1.12}$$	${241.45}_{- 0.40}^{+ 1.15}$ $Mathematical equation: $241.45_{-0.40}^{+1.15}$$	deg
DERIVED PARAMETERS
Mass (M_p)	–	$17_{- 4}^{+ 3}$ $Mathematical equation: $17_{-4}^{+3}$$	${7.01}_{- 0.66}^{+ 3.68}$ $Mathematical equation: $7.01_{-0.66}^{+3.68}$$	M_⊕
Eccentricity (e)	U(0, 0.5)	${0.0083}_{- 0.0083}^{+ 0.0060}$ $Mathematical equation: $0.0083_{-0.0083}^{+0.0060}$$	${0.0165}_{- 0.0062}^{+ 0.0110}$ $Mathematical equation: $0.0165_{-0.0062}^{+0.0110}$$
Argument of Periastron (ω)	–	$276_{- 149}^{+ 66}$ $Mathematical equation: $276_{-149}^{+66}$$	$67_{- 12}^{+ 44}$ $Mathematical equation: $67_{-12}^{+44}$$	deg
Mean Anomaly (M)	–	$145_{- 60}^{+ 156}$ $Mathematical equation: $145_{-60}^{+156}$$	$- 6_{- 43}^{+ 12}$ $Mathematical equation: $-6_{-43}^{+12}$$	deg

TOI-5624 f

FITTED PARAMETERS
Mp/M_⋆	U(0.30, 954.7)		$40_{- 6}^{+ 13}$ $Mathematical equation: $40_{-6}^{+13}$$	$(\frac{M_{⊙}}{M_{⋆}}) \times 10^{- 6}$ $Mathematical equation: $\left(\frac{M_\odot}{M_\star}\right) \times 10^{-6}$$
Orbital Period (P)	U(43, 48)		${44.092}_{- 0.057}^{+ 0.015}$ $Mathematical equation: $44.092_{-0.057}^{+0.015}$$	days
$\sqrt{e} \cos ω$ $Mathematical equation: $\sqrt{e} \cos \omega$$	U( $- \sqrt{0.5}, \sqrt{0.5}$ $Mathematical equation: $-\sqrt{0.5}, \sqrt{0.5}$$ )		${0.064}_{- 0.096}^{+ 0.143}$ $Mathematical equation: $0.064_{-0.096}^{+0.143}$$
$\sqrt{e} \sin ω$ $Mathematical equation: $\sqrt{e} \sin \omega$$	U( $- \sqrt{0.5}, \sqrt{0.5}$ $Mathematical equation: $-\sqrt{0.5}, \sqrt{0.5}$$ )		$- {0.143}_{- 0.035}^{+ 0.193}$ $Mathematical equation: $-0.143_{-0.035}^{+0.193}$$
Mean Longitude (λ)	U(0, 360)		$61_{- 11}^{+ 9}$ $Mathematical equation: $61_{-11}^{+9}$$	deg
Inclination (i)	U(0, 180.0)		$99_{- 29}^{+ 1}$ $Mathematical equation: $99_{-29}^{+1}$$	deg
DERIVED PARAMETERS
Mass (M_p)	–		$11_{- 2}^{+ 4}$ $Mathematical equation: $11_{-2}^{+4}$$	M_⊕
Eccentricity (e)	U(0, 0.5)		${0.025}_{- 0.024}^{+ 0.017}$ $Mathematical equation: $0.025_{-0.024}^{+0.017}$$
Argument of Periastron (ω)	–		$- 66_{- 45}^{+ 93}$ $Mathematical equation: $-66_{-45}^{+93}$$	deg
Mean Anomaly (M)	–		$- 53_{- 96}^{+ 36}$ $Mathematical equation: $-53_{-96}^{+36}$$	deg

Notes. Parameter estimates correspond to the maximum a posteriori (MAP) values, while the reported uncertainties represent the 68.3% highest density intervals (HDIs) of the marginalised posterior distributions.

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