Slow magneto-acoustic waves in simulations of a solar plage region carry enough energy to heat the chromosphere

Aims. We study the properties of slow magneto-acoustic waves that are naturally excited as a result of turbulent convection and we investigate their role in the energy balance of a plage region using three dimensional radiation magnetohydrodynamic simulations. Methods. To follow slow magneto-acoustic waves traveling along the magnetic field lines, we selected 25 seed locations inside a strong magnetic element and tracked the associated magnetic field lines both in space and time. We calculate the longitudinal component (i.e., parallel to the field) of velocity at each grid point along the field line and compute the temporal power spectra at various heights above the mean solar surface. Additionally, the horizontally-averaged (over the whole domain) frequency power spectra for both longitudinal and vertical (i.e., the component perpendicular to the surface) components of velocity are calculated using time series at fixed locations. To compare our results with the observations, we degrade the simulation data with Gaussian kernels having a full width at half maxium of 100 km and 200 km and calculate the horizontally-averaged power spectra for the vertical component of velocity using time series at fixed locations. Results. The power spectra of the longitudinal component of velocity, averaged over 25 field lines in the core of a kG magnetic flux concentration reveal that the dominant period of oscillations shifts from ∼6.5 min in the photosphere to ∼4 min in the chromosphere. This behavior is consistent with earlier studies that were restricted to vertically propagating waves. At the same time, the velocity power spectra, averaged horizontally over the whole domain, show that low frequency waves (∼6.5 min period) may reach well into the chromosphere. In addition, the power spectra at high frequencies follow a power law with an exponent close to −5/3, suggestive of turbulent excitation. Moreover, waves with frequencies above 5 mHz propagating along different field lines are found to be out of phase with each other, even within a single magnetic concentration. The horizontally-averaged power spectra of the vertical component of velocity at various effective resolutions show that the observed acoustic wave energy fluxes are underestimated by a factor of three, even if determined from observations carried out at a high spatial resolution of 200 km. Since the waves propagate along the non-vertical field lines, measuring the velocity component along the line-of-sight, rather than along the field, contributes significantly to this underestimation. Moreover, this underestimation of the energy flux indirectly indicates the importance of high-frequency waves that are shown to have a smaller spatial coherence and are thus more strongly influenced by the spatial averaging effect compared to low-frequency waves. Conclusions. Inside a plage region, there is on average a significant fraction of low frequency waves leaking into the chromosphere due to inclined magnetic field lines. Our results show that longitudinal waves carry (just) enough energy to heat the chromosphere in the solar plage. However, phase differences between waves traveling along different field lines within a single magnetic concentration can lead to underestimations of the wave energy flux due to averaging effects in degraded simulation data and, similarly, in observations with lower spatial resolution. We find that current observations (with spatial resolution around 200 km) underestimate the energy flux by roughly a factor of three – or more if the observations are carried out at a lower spatial resolution. We expect that even at a very high resolution, which is expected with the next generation of telescopes such as DKIST and the EST, less than half, on average, of the energy flux carried by such waves will be detected if only the line-of-sight component of the velocity is measured