Simulations Show that Vortex Flows Could Heat the Chromosphere in Solar Plage

The relationship between vortex flows at different spatial scales and their contribution to the energy balance in the chromosphere is not yet fully understood. We perform three-dimensional (3D) radiation-magnetohydrodynamic (MHD) simulations of a unipolar solar plage region at a spatial resolution of 10 km using the MURaM code. We use the swirling-strength criterion that mainly detects the smallest vortices present in the simulation data. We additionally degrade our simulation data to smooth-out the smaller vortices, so that also the vortices at larger spatial scales can be detected. Vortex flows at various spatial scales are found in our simulation data for different effective spatial resolutions. We conclude that the observed large vortices are likely clusters of much smaller ones that are not yet resolved by observations. We show that the vertical Poynting flux decreases rapidly with reduced effective spatial resolutions and is predominantly carried by the horizontal plasma motions rather than vertical flows. Since the small-scale horizontal motions or the smaller vortices carry most of the energy, the energy transported by vortices deduced from low resolution data is grossly underestimated. In full resolution simulation data, the Poynting flux contribution due to vortices is more than adequate to compensate for the radiative losses in plage, indicating their importance for chromospheric heating.