Hot Rocks Survey - III. A deep eclipse for LHS 1140c and a new Gaussian process method to account for correlated noise in individual pixels

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Table D.2

Priors used for the secondary analysis fit.

Parameter	Distribution	Prior
f_p/f_*	Uniform	[-0.01, 0.01]
T₀	Normal	(2460304.70775, 0.00004)
P	Fixed	3.777940
a/R_*	Normal	(27.1, 0.1)
R_p/R_*	Fixed	0.05312
b	Trunc. Normal	(0.09, 0.1) & b > 0
$\sqrt{e} \cos ω$ $\[\sqrt{e} ~\cos~ \omega\]$	Normal	(-0.14, 0.1)
$\sqrt{e} \sin ω$ $\[\sqrt{e}~\sin~ \omega\]$	Normal	(-0.04, 0.1)
m_flux ^a	Normal	(0.0, 0.1)
σ^b	LogUniform	(10, 10000)
Linear (L)
θ	Uniform	[-100,100]
Exponential (E)
A	Uniform	[-1,1]
τ	Uniform	[-1,1]
Gaussian Process (GP)
GP_ξ	LogUniform	(10⁻⁸, 10⁻²)
GP_ρ	LogUniform	(10⁻⁸, 10²)

a Out-of-transit flux.

b White noise (ppm).

Notes. Values taken from Cadieux et al. (2024b) for T₀, a/R_*, R_p/R_*, b and Cadieux et al. (2024a) for $P, \sqrt{e} \cos ω$ $\[P, \sqrt{e} ~\cos~ \omega\]$ and $\sqrt{e} \sin ω$ $\[\sqrt{e}~\sin~ \omega\]$ . We indicate the priors and distributions for the parameters of the detrending methods. Each parameter is fitted independently for each observation.

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