  We study the properties of slow magneto-acoustic waves that are naturally
excited due to turbulent convection and investigate their role in the energy
balance of a plage region using three dimensional (3D) radiation-MHD
simulations. We calculate 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. To compare our results
with the observations we degrade the simulation data with Gaussian kernels
having FWHM of 100 km and 200 km, and calculate horizontally averaged power
spectra for the vertical component of velocity. The power spectra of the
longitudinal component of velocity, averaged over field lines in the core of a
kG magnetic flux concentration, reveal that the dominant period of oscillations
shifts from around 6.5 minutes in the photosphere to around 4 minutes in the
chromosphere. At the same time, the velocity power spectra, averaged
horizontally over the whole domain, show that low frequency waves
(approximately 6.5 minute period) may reach well into the chromosphere.
Importantly, 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. Our results show that longitudinal waves carry (just) sufficient energy to
heat the chromosphere in solar plage. We conjecture that current observations
(with spatial resolution around 200 km) underestimate the energy flux by
roughly a factor of three, or more if the observations have lower spatial
resolution.
