Hydraulic effects in a radiative atmosphere with ionization

¹ Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
e-mail: palvi@iucaa.ernet.in
² Inter University Centre for Astronomy and Astrophysics, Post Bag 4, Pune University Campus, Ganeshkhind, 411 007 Pune, India
³ Department of Astrophysical Sciences and Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08540, USA
⁴ Department of Astronomy, AlbaNova University Center, Stockholm University, 10691 Stockholm, Sweden
⁵ JILA and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80303, USA
⁶ Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80303, USA

Received: 24 November 2014
Accepted: 14 September 2015

Abstract

Context. In his 1978 paper, Eugene Parker postulated the need for hydraulic downward motion to explain magnetic flux concentrations at the solar surface. A similar process has also recently been seen in simplified (e.g., isothermal) models of flux concentrations from the negative effective magnetic pressure instability (NEMPI).

Aims. We study the effects of partial ionization near the radiative surface on the formation of these magnetic flux concentrations.

Methods. We first obtain one-dimensional (1D) equilibrium solutions using either a Kramers-like opacity or the 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 that resembles a localized negative pressure in the form of a blob. To isolate the effects of partial ionization and radiation, we ignore turbulence and convection.

Results. Because of partial ionization, an unstable stratification always forms near the surface. We show that the extrema in the specific entropy profiles correspond to the extrema in the degree of ionization. In the 2D models without partial ionization, strong flux concentrations form just above the height where the blob is placed. Interestingly, in models with partial ionization, such flux concentrations always form at the surface well above the blob. This is due to the corresponding negative gradient in specific entropy. Owing to the absence of turbulence, the downflows reach transonic speeds.

Conclusions. 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 the entropy profile dramatically, causing strong flux concentrations to form closer to the surface. We speculate that turbulence effects are needed to limit the strength of flux concentrations and homogenize the specific entropy to a stratification that is close to marginal.