Top: normalized cumulated work integral versus logarithm of temperature for five values of eigenfrequencies. These modes are emphasized in Fig. A.1. Middle: imaginary part of the Lagrangian perturbation of entropy versus logarithm of temperature. Bottom: normalized convective and radiative fluxes versus logarithm of temperature. The difference between the real and adiabatic gradient (∇) is also plotted and normalized to its maximum.