EDP Sciences
Free Access
Volume 446, Number 1, January IV 2006
Page(s) 307 - 314
Section The Sun
DOI https://doi.org/10.1051/0004-6361:20053488
Published online 09 January 2006

A&A 446, 307-314 (2006)
DOI: 10.1051/0004-6361:20053488

A necessary extension of the surface flux transport model

I. Baumann, D. Schmitt and M. Schüssler

Max-Planck-Institut für Sonnensystemforschung, 37191 Katlenburg-Lindau, Germany
    e-mail: msch@linmpi.mpg.de

(Received 20 May 2005 / Accepted 14 September 2005 )

Customary two-dimensional flux transport models for the evolution of the magnetic field at the solar surface do not account for the radial structure and the volume diffusion of the magnetic field. When considering the long-term evolution of magnetic flux, this omission can lead to an unrealistic long-term memory of the system and to the suppression of polar field reversals. In order to avoid such effects, we propose an extension of the flux transport model by a linear decay term derived consistently on the basis of the eigenmodes of the diffusion operator in a spherical shell. A decay rate for each eigenmode of the system is determined and applied to the corresponding surface part of the mode evolved in the flux transport model. The value of the volume diffusivity associated with this decay term can be estimated to be in the range 50-100 $\,\,\rm km^2\, \rm s^{-1}$ by considering the reversals of the polar fields in comparison of flux transport simulations with observations. We show that the decay term prohibits a secular drift of the polar field in the case of cycles of varying strength, like those exhibited by the historical sunspot record.

Key words: Sun: magnetic fields -- magnetohydrodynamics (MHD) -- Sun: activity -- magnetic fields

© ESO 2006

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