Magnetostatic penumbra models with field-free gaps

¹ Institute for Solar Physics, Royal Swedish Academy of Sciences, Alba Nova University Center, 10691 Stockholm, Sweden e-mail: scharmer@astro.su.se
² Max Planck Institute for Astrophysics, Box 1317, 85741 Garching, Germany e-mail: henk@mpa-Garching.mpg.de

Received: 12 July 2006
Accepted: 5 September 2006

Abstract

We present numerical 2D magnetostatic models for sunspot penumbrae consisting of radially aligned field-free gaps in a potential magnetic field, as proposed by Spruit & Scharmer (2006, A&A, 447, 343). The shape of the gaps and the field configurations around them are computed consistently from the condition of magnetostatic pressure balance between the gap and the magnetic field. The results show that field-free gaps in the inner penumbra are cusp-shaped and bounded by a magnetic field inclined by about from the vertical. Here, the magnetic component has a Wilson depression on the order 200–300 km relative to the top of the field-free gap; the gaps should thus appear as noticeably elevated features. This structure explains the large variations in field strength in the inner penumbra inferred from magnetograms and two-component inversions, and the varying appearance of the inner penumbra with viewing angle. In the outer penumbra, on the other hand, the gaps are flat-topped with a horizontal magnetic field above the middle of the gap. The magnetic field has large inclination variations horizontally, but only small fluctuations in field strength, in agreement with observations.