Spontaneous flux concentrations from the negative effective magnetic pressure instability beneath a radiative stellar surface

¹ DSM/IRFU/SAp, CEA-Saclay and UMR AIM, CEA-Université Paris 7, 91191 Gif-sur-Yvette, France
e-mail: barbara.perri@cea.fr
² JILA and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80303, USA
³ Department of Astronomy, AlbaNova University Center, Stockholm University, 10691 Stockholm, Sweden
⁴ Nordita, KTH Royal Institute of Technology and Stockholm University, 10691 Stockholm, Sweden
⁵ Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80303, USA

Received: 11 January 2017
Accepted: 19 October 2017

Abstract

Context. The formation of sunspots requires the concentration of magnetic flux near the surface. The negative effective magnetic pressure instability (NEMPI) might be a possible mechanism for accomplishing this, but it has mainly been studied in simple systems using an isothermal equation of state without a natural free surface.

Aims. We study NEMPI in a stratified Cartesian mean-field model where turbulence effects are parameterized. We use an ideal equation of state and include radiation transport, which establishes selfconsistently a free surface.

Methods. We use a Kramers-type opacity with adjustable exponents chosen such that the deeper layers are approximately isentropic. No convection is therefore possible in this model, allowing us to study NEMPI with radiation in isolation. We restrict ourselves to two-dimensional models. We use artificially enhanced mean-field coefficients to allow NEMPI to develop, thereby making it possible to study the reason why it is much harder to excite in the presence of radiation.

Results. NEMPI yields moderately strong magnetic flux concentrations a certain distance beneath the surface where the optical depth is unity. The instability is oscillatory and in the form of upward traveling waves. This seems to be a new effect that has not been found in earlier models without radiative transport. The horizontal wavelength is about ten times smaller than what has previously been found in more idealized isothermal models.

Conclusions. In our models, NEMPI saturates at field strengths too low to explain sunspots. Furthermore, the structures appear too narrow and too far beneath the surface to cause significant brightness variations at the radiative surface. We speculate that the failure to reproduce effects resembling sunspots may be related to the neglect of convection.