Kernel density estimation (KDE) of the distribution of the vertical component of the Poynting flux vector associated with Alfvénic swirls, $S_z^{\text{swirl }}$ (green). For each entry into the distribution, the corresponding quantity is the mean over the area of those swirls that are compatible with torsional Alfvénic waves in the middle photosphere of the four stellar models. The KDEs of the horizontal and vertical terms of $S_z^{\text{swirl }},S_z^{\mathrm{h}}$ and $S_z^{\mathrm{v}}$, are shown in orange and blue, respectively. The red vertical dashed lines represent the mean vertical component of the Poynting flux vector computed over the entire domain at the middle photosphere, $S_z^{\text{tot }}$, while the green vertical dashed lines represent the mean values of $S_z^{\text{swirl }}$.