Convergence behavior during the MCMC run with (blue) and without (red) the constraint. The dotted line shows the median of the relative luminosity deviation (|L_X−L_acc|/L_X) for the walkers of each MCMC step. The solid line indicates, for both runs, the convergence of the regular, unmodified χ² median of each step. We note that the convergence of the unmodified fit-statistic does not deteriorate while only with our constraint the criterion of energy conservation is quickly reached.