Temperature–density relation snapshots of the three example cases shown in Figs. 4, E.1, and E.2. Solutions for t < 0 and t > 0 are presented with dashed and solid lines, respectively. The colored lines with increasing thickness correspond to increasing absolute time. The gray curves with increasing thickness trace the time evolution of fluid parcels at enclosed mass coordinate M = 1, 10, 100, 1000, 10 000 M_⊙.