Net circular polarization of sunspot penumbrae

The net circular polarization, N, is used as a measure for the asymmetry of Stokes-V profiles: $N\equiv\int V(\lambda)\,{\rm d} \lambda$, integrated over an absorption line. Exemplary for Fe I 630.2 nm and Fe I 1564.8 nm, we synthesize penumbral V-profiles that stem from a model atmosphere in which the Evershed flow is confined to horizontal flux tubes which are embedded in a magnetic field that has the same magnetic field strength as the flow channel, but is less inclined w.r.t. the surface normal. At the two points where a line-of-sight enters and leaves the flow channel, discontinuities in the inclination, γ, the velocity v, and the azimuth, ϕ, of the magnetic field vector w.r.t. the plane perpendicular to the line-of-sight produce V-asymmetries. Assuming an axially symmetric penumbra, we investigate the azimuthal dependence $N(\psi)$ for a mid-penumbral radius. We find: (1) Without including anomalous dispersion, $N(\psi)$ is symmetric w.r.t. the line that connects disk center to the center of the spot. (2) Including anomalous dispersion, this symmetry is broken. We demonstrate that this is due to the difference in azimuth, $\triangle\phi(\psi)$, between the flow channel and the background that varies along the penumbral circle. For Fe I 630.2 nm this effect is found to be of minor relevance leading to essentially symmetric N-maps, whereas strong asymmetries are predicted for Fe I 1564.8 nm. Our results provide an explanation for recent observational findings