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.4

HARPS-N derived parameters of TOI-5624, as inferred using the multi-dimensional GP approach implemented in pyaneti.

Parameter	Prior^(a)	Derived value
TOI-5624 b
Orbital period, P_orb,b (d)	N [3.390364,0.000011]	3.390364 ± 0.000011
Transit epoch, T_0,b (BJD_TDB - 2 400 000)	N [59649.1245,0.0011]	59649.1244 ± 0.0011
Radial velocity semi-amplitude variation, K_b (ms⁻¹)	U[0,20]	${4.54}_{- 0.78}^{+ 0.77}$ $Mathematical equation: $4.54_{-0.78}^{+0.77}$$
Planet mass, M_b (M_⊕)		9.6 ± 1.7

TOI-5624 c
Orbital period, P_orb,c (d)	N [7.885393,0.000038]	7.885393 ± 0.000039
Transit epoch, T_0,c (BJD_TDB — 2 400 000)	N [59650.9224,0.0010]	59650.9224 ± 0.0010
Radial velocity semi-amplitude variation, K_c (m s⁻¹)	U[0,20]	${2.50}_{- 0.82}^{+ 0.84}$ $Mathematical equation: $2.50_{-0.82}^{+0.84}$$
Planet mass, M_c (M_⊕)		${7.0}_{- 2.3}^{+ 2.4}$ $Mathematical equation: $7.0_{-2.3}^{+2.4}$$

TOI-5624 d
Orbital period, P_orb,d (d)	N [13.73151,0.00014]	13.73151 ± 0.00014
Transit epoch, T_0,d (BJD_TDB - 2 400 000)	N [59655.2043,0.0020]	59655.2044 ± 0.0020
Radial velocity semi-amplitude variation, K_d (ms⁻¹)	U[0,20]	${2.13}_{- 0.81}^{+ 0.80}$ $Mathematical equation: $2.13_{-0.81}^{+0.80}$$
Planet mass, M_d (M_⊕)		7.2 ± 2.7

TOI-5624 e
Orbital period, P_orb,e (d)	N [21.49031,0.00012]	21.49030 ± 0.00012
Transit epoch, T_0,e (BJD_TDB - 2 400 000)	N [60687.1358,0.0019]	60687.1358 ± 0.0019
Radial velocity semi-amplitude variation, K_e (m s⁻¹)	U[0,20]	${1.74}_{- 0.85}^{+ 0.88}$ $Mathematical equation: $1.74_{-0.85}^{+0.88}$$
Planet mass, M_e (M_⊕)		${6.8}_{- 3.3}^{+ 3.5}$ $Mathematical equation: $6.8_{-3.3}^{+3.5}$$

TOI-5624 f
Orbital period, P_orb,f (d)	U[38.0,50.0]	${44.41}_{- 0.82}^{+ 0.85}$ $Mathematical equation: $44.41_{-0.82}^{+0.85}$$
Inferior conjunction epoch, T_0,f (BJD_TDB - 2 400 000)	U[60355.0,60414.0]	60384.4 ± 3.2
Radial velocity semi-amplitude variation, K_f (ms⁻¹)	U[0,20]	${2.46}_{- 0.83}^{+ 0.78}$ $Mathematical equation: $2.46_{-0.83}^{+0.78}$$
Planet minimum mass, M_f sin i_f (M_⊕)		${12.3}_{- 4.2}^{+ 4.0}$ $Mathematical equation: $12.3_{-4.2}^{+4.0}$$

Additional model parameters
RV offset, A_RV (ms⁻¹)	U[–100,100]	1.1 ± 1.7
RV amplitude of GP, B_RV (m s⁻¹)	U[0,100]	${5.6}_{- 1.1}^{+ 1.3}$ $Mathematical equation: $5.6 _{-1.1}^{+1.3}$$
RV amplitude of GP time derivative, C_RV (m s⁻¹ d)	U[0,100]	${19.3}_{- 3.2}^{+ 4.2}$ $Mathematical equation: $19.3_{-3.2}^{+4.2}$$
RV jitter term (m s⁻¹ )	U[0,100]	${4.06}_{- 0.49}^{+ 0.52}$ $Mathematical equation: $4.06_{-0.49}^{+0.52}$$
FWHM offset, A_FWHM (ms⁻¹)	U[0,15000]	7125.2 ± 8.3
FWHM amplitude of GP, B_FWHM (ms⁻¹)	U[0,100]	${28.8}_{- 3.9}^{+ 5.3}$ $Mathematical equation: $28.8_{-3.9}^{+5.3}$$
FWHM jitter term (m s⁻¹ )	U[0,100]	${4.00}_{- 0.64}^{+ 0.74}$ $Mathematical equation: $4.00_{-0.64}^{+0.74}$$
Long-term evolution timescale of active regions, λ_e (d)	U[5,100]	${30.2}_{- 3.9}^{+ 4.1}$ $Mathematical equation: $30.2 _{-3.9 }^{+4.1}$$
Inverse of the harmonic complexity, λ_p	U[0.0,2.0]	${0.459}_{- 0.056}^{+ 0.064}$ $Mathematical equation: $0.459_{-0.056}^{+0.064}$$
GP characteristic period, P_GP (d)	U[15,25]	19.47 ± 0.25

Notes. ^(a) U[a, b] refers to uniform priors between a and b, whereas N[μ, σ] refers to Gaussian priors with mean μ and standard deviation σ.

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