Table C.1

Prior parameter distribution for the calculation of the internal compositions of TOI-5789 c, where M_atm is the atmosphere mass, Z_env the envelope water mass fraction, M_core+mantle the mass of the deep interior including core and mantle, for which we assume an Earth-like core-to-mantle ratio of 0.325:0.675. The prior on M_atm is equivalent to mass fractions between 0.5 - 15%.

Parameter	Prior range	Distribution
Matm/M⊕	0.025 − 0.75	log-uniform
Mcore+mantle	$\mathcal{N}\left(M_{\text{p}},{\sigma }_{M_{\text{p}}}^2\right)$	gaussian
Zenv (envelope water mass fraction)	0.02 − 1.0	uniform