Posterior distributions of Y_proto, Y_atm. T_1bar, J₄, and J₆ for four different MCMC runs using the MGF16+MH13 EOS. The blue histograms correspond to a run where the four parameters are free. In the orange run, Y_proto is fixed. In the green run, Y_proto and Y_atm are fixed. In the red run, Y_proto, Y_atm, and T_1bar are fixed. When histograms show a black vertical solid line, this indicates that a prior was set and was centred at the value from observations (Y_proto = 0.277 ± 0.006, Y_atm = 0.238 ± 0.005, T_1bar = 165 ± 4K, J₄.10⁶ = −586.53 ± 0.0836 and J₆.10⁶ = 34.18 ± 0.07682). The gray areas correspond to the standard deviation of the prior (1 sigma).