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Hydraulic effects in a radiative atmosphere with ionization

In a paper of 1978, Eugene Parker postulated the need for hydraulic downward motion to explain magnetic flux concentrations at the solar surface. A similar process has recently also been seen in simplified (e.g., isothermal) models of flux concentrations from the negative effective magnetic pressure instability. We study the effects of partial ionization near the radiative surface on the formation of such magnetic flux concentrations. We first obtain one-dimensional (1D) equilibrium solutions using either a Kramers-like opacity or the ${\rm H}^{-}$ opacity. The resulting atmospheres are then used as initial conditions in two-dimensional (2D) models where flows are driven by an imposed gradient force resembling a localized negative pressure in the form of a blob. To isolate the effects of partial ionization and radiation, we ignore turbulence and convection. In 1D models, due to partial ionization, an unstable stratification forms always near the surface. We show that the extrema in the specific entropy profiles correspond to the extrema in degree of ionization. In the 2D models without partial ionization, flux concentrations form close to the height where the blob is placed. In models with partial ionization, such flux concentrations form at the surface much above the blob. This is due to the corresponding unstable layer in specific entropy. With ${\rm H}^{-}$ opacity, flux concentrations are weaker due to the stably stratified deeper parts. We demonstrate that, together with density stratification, the imposed source of negative pressure drives the formation of flux concentrations. We find that the inclusion of partial ionization affects entropy profiles causing the strong flux concentrations to form closer to the surface. We speculate that turbulence is needed to limit the strength of flux concentrations and homogenize the specific entropy to a more nearly marginal stratification.