Transit timing variations in HIP 41378: CHEOPS and TESS confirm a non-transiting sixth planet in the system

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Table A.2

Posteriors and derived orbital parameters for HIP 41378 b & c from the global photometric analysis with PYORBIT, presented in Section 4.2

Parameter	Unit	Prior	Posterior value
HIP 41378 b
FITTED PARAMETERS
Orbital Period (P)	[days]	(fixed)	${15.571893}_{- 0.000053}^{+ 0.000068}$ $\[15.571893_{-0.000053}^{+0.000068}\]$
Impact Parameter (b)	−	𝒰(0, 1 + (R_⋆/R_p)/2)	${0.445}_{- 0.023}^{+ 0.020}$ $\[0.445_{-0.023}^{+0.020}\]$
Planet-star radius ratio (R_p/R_⋆)	−	𝒰(0, 0.5)	${0.01705}_{- 0.00015}^{+ 0.00015}$ $\[0.01705_{-0.00015}^{+0.00015}\]$
DERIVED PARAMETERS
Semimajor axis (a)	[au]	−	${0.1303}_{- 0.0013}^{+ 0.0013}$ $\[0.1303_{-0.0013}^{+0.0013}\]$
Scaled semimajor axis (a/R_s)	−	−	${21.54}_{- 0.16}^{+ 0.16}$ $\[21.54_{-0.16}^{+0.16}\]$
Inclination (i)	[deg]	−	${88.816}_{- 0.061}^{+ 0.065}$ $\[88.816_{-0.061}^{+0.065}\]$
Planet Radius (R_p)	[R_⊕]	−	${2.419}_{- 0.027}^{+ 0.027}$ $\[2.419_{-0.027}^{+0.027}\]$
Transit duration (T₁₄)	[days]	−	${0.2099}_{- 0.0012}^{+ 0.0014}$ $\[0.2099_{-0.0012}^{+0.0014}\]$
Equilibrium temperature (T_eq)	[K]	−	${970.67}_{- 10.54}^{+ 10.54}$ $\[970.67_{-10.54}^{+10.54}\]$
Stellar Insolation Flux (S)	[S_⊕]	−	${148.50}_{- 7.12}^{+ 7.12}$ $\[148.50_{-7.12}^{+7.12}\]$
HIP 41378 c
FITTED PARAMETERS
Orbital Period (P)	[days]	(fixed)	${31.708380}_{- 0.00041}^{+ 0.00039}$ $\[31.708380_{-0.00041}^{+0.00039}\]$
Impact Parameter (b)	−	𝒰(0, 1 + (R_⋆/R_p)/2)	${0.9290}_{- 0.0044}^{+ 0.0041}$ $\[0.9290_{-0.0044}^{+0.0041}\]$
Planet-star radius ratio (R_p/R_⋆)	−	𝒰(0, 0.5)	${0.01766}_{- 0.00042}^{+ 0.00043}$ $\[0.01766_{-0.00042}^{+0.00043}\]$
DERIVED PARAMETERS
Semimajor axis (a)	[au]	−	${0.2093}_{- 0.0022}^{+ 0.0022}$ $\[0.2093_{-0.0022}^{+0.0022}\]$
Scaled semimajor axis (a/R_s)	−	−	${34.60}_{- 0.26}^{+ 0.26}$ $\[34.60_{-0.26}^{+0.26}\]$
Inclination (i)	[deg]	−	${88.462}_{- 0.015}^{+ 0.015}$ $\[88.462_{-0.015}^{+0.015}\]$
Planet Radius (R_p)	[R_⊕]	−	${2.505}_{- 0.056}^{+ 0.057}$ $\[2.505_{-0.056}^{+0.057}\]$
Transit duration (T₁₄)	[days]	−	${0.1212}_{- 0.0025}^{0.0027}$ $\[0.1212_{-0.0025}^{0.0027}\]$
Equilibrium temperature (T_eq)	[K]	−	${765.87}_{- 8.33}^{+ 8.33}$ $\[765.87_{-8.33}^{+8.33}\]$
Stellar Insolation Flux (S)	[S_⊕]	−	${57.55}_{- 2.79}^{+ 2.79}$ $\[57.55_{-2.79}^{+2.79}\]$
HOST STAR HIP 41378
Stellar density	[ρ_⊙]	𝒢(0.5539, 0.0126)	${0.554}_{- 0.013}^{+ 0.013}$ $\[0.554_{-0.013}^{+0.013}\]$
Limb Darkening Coefficients
Quadratic Limb Darkening term c₁ (K2)	−	𝒢(0.4834, 0.05)	${0.447}_{- 0.043}^{+ 0.043}$ $\[0.447_{-0.043}^{+0.043}\]$
Quadratic Limb Darkening term c₂ (K2)	−	𝒢(0.1535, 0.05)	${0.157}_{- 0.046}^{+ 0.046}$ $\[0.157_{-0.046}^{+0.046}\]$
Quadratic Limb Darkening term c₁ (TESS)	−	𝒢(0.3822, 0.05)	${0.401}_{- 0.047}^{+ 0.047}$ $\[0.401_{-0.047}^{+0.047}\]$
Quadratic Limb Darkening term c₂ (TESS)	−	𝒢(0.1429, 0.05)	${0.171}_{- 0.048}^{+ 0.048}$ $\[0.171_{-0.048}^{+0.048}\]$
Quadratic Limb Darkening term c₁ (HST)	−	𝒢(0.228, 0.05)	${0.183}_{- 0.042}^{+ 0.041}$ $\[0.183_{-0.042}^{+0.041}\]$
Quadratic Limb Darkening term c₂ (HST)	−	𝒢(0.1398, 0.05)	${0.127}_{- 0.045}^{+ 0.046}$ $\[0.127_{-0.045}^{+0.046}\]$
Quadratic Limb Darkening term c₁ (Spitzer)	−	𝒢(0.0969, 0.05)	${0.108}_{- 0.047}^{+ 0.049}$ $\[0.108_{-0.047}^{+0.049}\]$
Quadratic Limb Darkening term c₂ (Spitzer)	−	𝒢(0.0508, 0.05)	${0.058}_{- 0.047}^{+ 0.049}$ $\[0.058_{-0.047}^{+0.049}\]$
Quadratic Limb Darkening term c₁ (CHEOPS)	−	𝒢(0.4947, 0.05)	${0.463}_{- 0.041}^{+ 0.040}$ $\[0.463_{-0.041}^{+0.040}\]$
Quadratic Limb Darkening term c₂ (CHEOPS)	−	𝒢(0.1519, 0.05)	${0.150}_{- 0.045}^{+ 0.045}$ $\[0.150_{-0.045}^{+0.045}\]$

Notes. The listed best-fit values and uncertainties are the medians and 15.865th-84.135th percentiles of the posterior distributions, respectively.

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