The spatial structure of solar magnetoconvection at scales up to $60$~Mm

Abstract

While convective motions at the scale of granules on the solar surface are well understood, those of mesogranular and supergranulation are not. At still larger scales, the lack of giant cells is a major mystery. We aim to slightly improve understanding of the radial and horizontal flows associated at mesogranular scales and supergranulation. We perform a deep MURaM small-scale dynamo simulation, extending from $50$~Mm below the solar surface and with a horizontal size of 60~Mm and sufficient resolution to begin to properly resolve the magnetic bright points in intergranular lanes. We determine the structure of the convective modes from the simulations at different scales, and compare the power spectra to those which have been previously observed. At all scales which are resolved by the simulation the simulated flows agree with the amplitude implied by Doppler measurements and local correlation tracking (LCT) measurements. The power in the vertical Doppler velocities at supergranular and larger scales is shown to be influenced by density perturbations near the surface. The structure of the modes at depth is simple as expected from the previous study of \cite{LordCameron2014} except the horizontal forcing scale scales like $H_ρ^{2/3}$ instead of $Hρ$. The simulations reproduce the observations up to scales of $60$~Mm. Within the simulated range, $l>=70$, we do not see the excess power associated with the convective conundrum.