Poynting flux is the flux of magnetic energy, which is responsible for chromospheric and coronal heating in the solar atmosphere. It is defined as a cross product of electric and magnetic fields, and in ideal MHD conditions it can be expressed in terms of magnetic field and plasma velocity. Poynting flux has been computed for active regions and plages, but estimating it in the quiet Sun (QS) remains challenging due to resolution effects and polarimetric noise. However, with upcoming DKIST capabilities, these estimates will become more feasible than ever before. Here, we study QS Poynting flux in Sunrise/IMaX observations and MURaM simulations. We explore two methods for inferring transverse velocities from observations - FLCT and a neural network based method DeepVel - and show DeepVel to be the more suitable method in the context of small-scale QS flows. We investigate the effect of azimuthal ambiguity on Poynting flux estimates, and we describe a new method for azimuth disambiguation. Finally, we use two methods for obtaining the electric field. The first method relies on idealized Ohm's law, whereas the second is a state-of-the-art inductive electric field inversion method PDFI SS. We compare the resulting Poynting flux values with theoretical estimates for chromospheric and coronal energy losses and find that some of Poynting flux estimates are sufficient to match the losses. Using MURaM simulations, we show that photospheric Poynting fluxes vary significantly with optical depth, and that there is an observational bias that results in underestimated Poynting fluxes due to unaccounted shear term contribution.

Context: The paradigm of convection in solar-like stars is questioned based on recent solar observations. Aims: The primary aim is to study the effects of surface-driven entropy rain on convection zone structure and flows. Methods: Simulations of compressible convection in Cartesian geometry with non-uniform surface cooling are used. The cooling profile includes localized cool patches that drive deeply penetrating plumes. Results are compared with cases with uniform cooling. Results: Sufficiently strong surface driving leads to strong non-locality and a largely subadiabatic convectively mixed layer. In such cases the net convective energy transport is done almost solely by the downflows. The spatial scale of flows decreases with increasing number of cooling patches for the vertical flows whereas the horizontal flows still peak at large scales. Conclusions: To reach the plume-dominated regime with a predominantly subadiabatic bulk of the convection zone requires significantly more efficient entropy rain than what is realized in simulations with uniform cooling. It is plausible that this regime is realized in the Sun but that it occurs on scales smaller than those resolved currently. Current results show that entropy rain can lead to largely mildly subadiabatic convection zone, whereas its effects for the scale of convection are more subtle.