Astronomy & Astrophysics

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$\begin{figure}\par\includegraphics[width=8.8cm,clip=TRUE]{13may01.014_HeI10830.eps} \end{figure}$ Figure 1: Stokes I, Q, U and V maps of the observed region (NOAA 9451, solar position 33 $^{\circ }$ W, 22 $^{\circ }$ S). Plotted are the absolute values of the wavelength integrated Stokes parameters of the strongest He I lines normalized to the continuum intensity. The size of the region is $46 \times 30$ Mm. The white / black circles indicate the positions where a detailed analysis of spectra is discussed in this paper. The reference direction for Stokes Q is along the +y-axis of the maps.
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In the text

$\begin{figure}\par\includegraphics[width=8.8cm,clip=TRUE]{all_spectra.eps} \end{figure}$ Figure 2: Average Stokes I, Q, U and V spectrum at position x=108, y=71). For later reference the weighting scheme is indicated by the dashed lines (see Sect. 4). The reference direction for Stokes Q is along the +y-axis of the maps in Fig. 1.
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In the text

$\begin{figure}\par\includegraphics[width=8.8cm,clip=TRUE]{hanle_profile.eps} \end{figure}$ Figure 3: Typical profile in the region dominated by scattering-polarization (pixel x=72, y=43). The shape of the absorption signal of the He I lines in Stokes U is similar to their I profiles justifying the simplifying assumption made for the implementation of the Hanle effect. The horizontal dashed line represents U=0. The reference direction for Stokes Q is along the +y-axis of the maps in Fig. 8.
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In the text

$\begin{figure}\par\includegraphics[width=8.8cm,clip=TRUE]{gauss_vs_voigt.eps} \end{figure}$ Figure 4: Effect of a fixed or free damping constant on the profile shape. The reference direction for Q is along the +y-axis of the maps in Fig. 1. The observed profile (solid line, pixel x=26, y=11) is from the center of the small pore, where He I absorption and the magnetic field are strong. The profile with the damping constant as a free parameter (diamonds) is almost indistinguishable from the one where the damping is fixed at a small value (plus signs). The relevant atmospheric parameters retrieved by the fits are very similar (see Table 2).
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In the text

$\begin{figure}\par\includegraphics[width=8.8cm,clip=TRUE]{hanle_zeeman.eps} \end{figure}$ Figure 5: Combined Hanle and Zeeman diagnostics. The synthetic Q and U profiles obtained using the combination of Zeeman-diagnostics and the special case of the Hanle effect valid close to disk center (diamonds) agree very well with the observed profile at x=58, y=28 (solid line). For the case where the Hanle effect is not included (plus signs), the fit to the observed U profile is unsatisfactory. The reference direction for Stokes Q is along the +y-axis of the maps in Fig. 8.
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In the text

$\begin{figure}\par\includegraphics[width=8.8cm,clip=TRUE]{fit_accuracy.eps} \end{figure}$ Figure 6: Convergence and noise analysis of synthesized spectra for the parameters magnetic field strength (B) and direction ( $\chi$ and $\gamma$ ). Every polar plot is divided in two regions: the upper half shows as radial coordinate the magnetic field strength B (in Gauss) with the inclination $\gamma$ as polar angle (diamonds). The lower half is similar but with the azimuthal angle $\chi$ as polar angle (plus signs). The gray shaded areas indicate the magnetic field vector used for the synthesis with a deviation of $\pm$ 15 $^{\circ }$ for the angles and $\pm$ 30 G in strength around the initial values in Table 3. The three rows stand for synthetic profiles calculated for different magnetic field strengths of 80 G, 300 G and 600 G. Random noise with an amplitude of 10 $^{-4}~I_{\rm c}$ (left column) and $5\times 10^{-4}~I_{\rm c}$ (middle and right column) was added to the synthesized profiles. The right column displays the results using, in addition to the Zeeman effect, the simple implementation of the Hanle effect leading to a very reliable determination of the magnetic field direction.
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In the text

$\begin{figure}\par\includegraphics[width=8.8cm,clip=TRUE]{chimap_pikaia_powell.eps} \end{figure}$ Figure 7: Inversion results for the azimuthal angle ( $\chi$ , reference direction +y-axis) using the genetic algorithm PIKAIA (top panel) and UOBYQA (bottom panel). Large pixel to pixel variation using UOBYQA indicate that the optimization routine got stuck in a local minimum of the parameter space.
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In the text

$\begin{figure}\par\includegraphics[width=6cm,clip=TRUE]{1comp_maps.eps} \end{figure}$ Figure 8: Atmospheric parameters returned by a 1-component inversion. The reference direction for the azimuth (2nd panel) is the +y-axis.
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In the text

$\begin{figure}\par\includegraphics[width=8.8cm,clip=TRUE]{comp12.eps} \end{figure}$ Figure 9: Comparison of 1-component (plus signs) and 2-component (diamonds) fits to the I and V profiles at pixel x=40, y=25 (solid line). Clearly the 1-component fit is not able to reproduce the data reasonably, whereas the synthetic profiles resulting from a 2-component fit very nicely match the observations.
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In the text

$\begin{figure}\par\includegraphics[width=8.8cm,clip=TRUE]{all_spectra.eps} \end{figure}$	Figure 2: Average Stokes I, Q, U and V spectrum at position x=108, y=71). For later reference the weighting scheme is indicated by the dashed lines (see Sect. 4). The reference direction for Stokes Q is along the +y-axis of the maps in Fig. 1.
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$\begin{figure}\par\includegraphics[width=8.8cm,clip=TRUE]{chimap_pikaia_powell.eps} \end{figure}$	Figure 7: Inversion results for the azimuthal angle ( $\chi$ , reference direction +y-axis) using the genetic algorithm PIKAIA (top panel) and UOBYQA (bottom panel). Large pixel to pixel variation using UOBYQA indicate that the optimization routine got stuck in a local minimum of the parameter space.
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$\begin{figure}\par\includegraphics[width=6cm,clip=TRUE]{1comp_maps.eps} \end{figure}$	Figure 8: Atmospheric parameters returned by a 1-component inversion. The reference direction for the azimuth (2nd panel) is the +y-axis.
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$\begin{figure}\par\includegraphics[width=8.8cm,clip=TRUE]{comp12.eps} \end{figure}$	Figure 9: Comparison of 1-component (plus signs) and 2-component (diamonds) fits to the I and V profiles at pixel x=40, y=25 (solid line). Clearly the 1-component fit is not able to reproduce the data reasonably, whereas the synthetic profiles resulting from a 2-component fit very nicely match the observations.
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