1 Introduction

In order to disentangle the physics of the fine structure in sunspot penumbrae, spectropolarimetry with high spatial and spectral resolution in absorption lines of diverse magnetic sensitivities, heights of formation, and wavelengths plays a crucial role. Two approaches are promising: (1) Inverting the measured Stokes vector to obtain a model atmosphere (e.g., del Toro Iniesta et al. 2001; Westendorp Plaza et al. 2001a,b), or (2) comparing specific properties of the measured Stokes vector with synthetic profiles that stem from model atmospheres (e.g., Maltby 1964; Landman & Finn 1979; Skumanich & Lites 1987; Solanki & Montavon 1993; Sanchez Almeida et al. 1996; Martínez Pillet 2000; Schlichenmaier & Collados 2001). In this contribution we have chosen the latter method.

The penumbral fine structure gives rise to asymmetries in spectral profiles of the Stokes parameters. In general, a velocity gradient or discontinuity along the line-of-sight (LOS) is necessary to generate Stokes asymmetries, while a gradient or discontinuity in the magnetic field can significantly alter and enhance the asymmetries (see, e.g., Auer & Heasley 1978; Sanchez Almeida & Lites 1992). Here, we restrict ourselves to asymmetry properties of Stokes-V profiles. One way to quantify the asymmetry is the net circular polarization, $N\equiv\int V(\lambda)\,{\rm d} \lambda$, where the integration ranges over a full absorption line.

First measurements of a non-zero net circular polarization in sunspot penumbrae have been performed by Illing et al. (1974a,b) in a broad band filter (10 nm around 530 nm). In order to compare measurements with synthetic lines, however, it is more appropriate to concentrate on the circular polarization of single absorption lines. Measurements of the net circular polarization of sunspot penumbrae in single absorption lines have been presented by Westendorp Plaza et al. (2001b) in FeI630.2 nm and by Schlichenmaier & Collados (2001) in FeI1564.8 nm. Surprisingly, sunspot maps of N in FeI630.2 are symmetric w.r.t. the line that connects disk with spot center, while N-maps in FeI1564.8 do not show that symmetry. Quite contrarily, there is a trend that the latter maps are antisymmetric. To understand this puzzling finding, we investigate the azimuthal dependence of N-maps of corresponding synthetic lines that are calculated on the basis of the moving tube model as proposed by Schlichenmaier et al. (1998, herafter SJS98). We show that the effects of anomalous dispersion (see, e.g., Landolfi & Landi degl'Innocenti 1996, hereafter LL96, and references therein) play a crucial role for the creation of N.

In Sect. 2 we define the coordinate system of an axially symmetric sunspot and describe its transformation into a coordinate system that is relevant for the LOS and hence for the line-formation process. In Sect. 3 we describe the model atmosphere that is used to calculate synthetic lines. Section 4 presents our results and discusses the symmetry properties of N within the penumbra. In Sect. 5 we draw our conclusions.