Relative contributions to the total luminosity L over time for the water core simulation of GJ 436 b. The blue and black lines are from Baraffe (2015; priv. comm.), the red and brown lines are from this work and represent the following: solid blue/ brown line: energy release from the core, which is the sum of core cooling and core contraction; dashed blue/ brown line: core cooling; dash-dotted blue/ brown line: core contraction; dashed black/ red line: envelope cooling and contraction. A discussion can be found in Sect. 4.3.