All Figures

$\begin{figure} \par\includegraphics[width=5.5cm,clip]{8678fig1.eps} \end{figure}$ Figure 1: The two coordinate systems used in this paper: l,b in the sky plane and s along the line of sight, and x,y,z in the model galaxy plane and perpendicular to it. The dashed lines indicate the thickness of the disk.
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In the text

$\begin{figure} \par\includegraphics[width=14cm,clip]{8678fig2.eps} \end{figure}$ Figure 2: Modeled strength of the regular magnetic field multiplied by the thermal electron density in the galactic midplane (i.e. in the plane x,y) for the field modes m=0 (ASS), m=1 (BSS), and m=2 (QSS) for B=1.
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In the text

$\begin{figure} \par\includegraphics[width=5.5cm,clip]{8678fig3.eps} \end{figure}$ Figure 3: Orientation of the halo magnetic field. The box sketches the region of ionized gas r <r₀, -h <z <h.
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In the text

$\begin{figure} \par\includegraphics[width=14cm,clip]{8678fig4.eps}\end{figure}$ Figure 4: Modeled $~{\rm RM}$ maps (in $~{\rm rad~m^{-2}}$ ) for an inclination angle of $i=10^\circ$ generated for a pure BSS field pattern, for $B=5~\mu$ G and n₀ =0.03 cm^-3 ( left), a random turbulent field $~{\rm RM}_{\rm turb}$ for $\Delta\!~{\rm RM}_{\rm turb}=30~~{\rm rad~m^{-2}}$ ( middle), and their superposition ( right).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.8cm,clip]{8678fig5.ps} \end{figure}$ Figure 5: The dotted line shows the cumulative count N of polarized sources brighter than the polarized flux density P at $\lambda =21$ cm, taken from Taylor et al. (2007), extrapolated to 0.01 mJy polarized flux density and normalized to source numbers per 1 deg² solid angle on sky. The possible range of extrapolated number counts per galaxy solid angles of 1 deg² are shown as thick solid lines, 0.013 deg² as dashed lines, and 0.00013 deg² as dot-dashed lines. These solid angles correspond to distances of a galaxy (with r₀=10 kpc) at 1.15 Mpc, 10 Mpc, and 100 Mpc. The two different lines at each distance refer to slopes $\gamma$ of the extrapolated source numbers of 0.7 ( lower line) and 1.1 ( upper line). The two thin vertical lines represent the $5\sigma _{\rm p}$ detection limit for sources observed at $\lambda =21$ cm with the SKA within 100 h ( left) and 1 h ( right) observation time.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.8cm,clip]{8678fig6.ps} \end{figure}$ Figure 6: Relation between instrumental noise and distance to the galaxy (see Eq. (18)) for different values of the ``observation parameter'' Q=0.001, 0.01, 0.1, 1, 10 rad m^-2 ( from left to right) drawn for pessimistic and optimistic slopes, $\gamma =0.7$ (dashed line) and $\gamma =1.1$ (solid line) for $\lambda =21$ cm, $\delta \lambda /\lambda = 0.25$ . The dotted line corresponds to the observed slope $\gamma \approx 1$ (see Fig. 5). The numbers of sources per solid angle of the galaxy corresponding to the above Q values are $N_{\rm max}=462, 92, 18, 4, 1$ for $\gamma =0.7$ and $N_{\rm max}=15~411, 1224, 97, 8, 1$ for $\gamma =1.1$ (Eq. (19)).
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In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{8678fig7.eps} \end{figure}$ Figure 7: Factor of effective points vs. inclination angle i due to geometry of the disk of thermal electrons.
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In the text

$\begin{figure} {\includegraphics[width=8.8cm,clip]{8678fig8.eps} } \end{figure}$ Figure 8: ASS field model: mean values (figures in left column) and standard deviations (figures in right column) of pitch angles $\bar{p}'$ and amplitudes $\bar{B'}$ (given in $\mu$ G) for fixed values of $h=1~{\rm kpc}$ , $p=20^{\circ }$ , $B=5~\mu$ G, $i=45^{\circ }$ and assuming the pessimistic case of number counts ( $\gamma =0.7$ ). N is the real number of points observed within the solid angle of the galaxy and Q is the observation parameter (Eq. (18)).
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In the text

$\begin{figure} {\includegraphics[width=7cm,clip]{8678fig9.eps} } \end{figure}$ Figure 9: Required asymptotic values N^* and Q^* to recognize an ASS-type field. The points correspond to $\delta p'=3^{\circ }$ for three different levels of turbulence (from bottom to top in each triplet: 10 $~{\rm rad~m^{-2}}$ , 30 $~{\rm rad~m^{-2}}$ and 50 $~{\rm rad~m^{-2}}$ ) and for different inclination angles ( $15^{\circ }$ , $45^{\circ }$ , $75^{\circ }$ ) for fixed $h=1~{\rm kpc}$ , $p=20^{\circ }$ . Filled symbols correspond to the optimistic case ( $\gamma =1.1$ ), open symbols to the pessimistic one ( $\gamma =0.7$ ).
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In the text

$\begin{figure} {\includegraphics[width=8.8cm,clip]{8678fig10.eps} } \end{figure}$ Figure 10: BSS field model: mean values (figures in left column) and standard deviations (figures in right column) of fitted pitch angles $\bar{p}'$ , amplitudes $\bar{B'}$ , and azimuthal phases $\bar{\phi_0}'$ for fixed $h=1~{\rm kpc}$ , $p=20^{\circ }$ , $\phi _0=0^\circ$ , and $i=45^{\circ }$ , and assuming the pessimistic case of number counts ( $\gamma =0.7$ ). N is the real number of points observed within the solid angle of the galaxy and Q the observation parameter.
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In the text

$\begin{figure} {\includegraphics[width=7cm,clip]{8678fig11.eps} } \end{figure}$ Figure 11: Required asymptotical values N^* and Q^* to recognize a BSS-type field. The points correspond to $\delta p'=3^{\circ }$ for three different levels of turbulence (from bottom to top in each triplet: 10 $~{\rm rad~m^{-2}}$ , 30 $~{\rm rad~m^{-2}}$ and 50 $~{\rm rad~m^{-2}}$ ) and different inclination angles ( $15^{\circ }$ , $45^{\circ }$ , $75^{\circ }$ ) for fixed $h=1~{\rm kpc}$ , $p=20^{\circ }$ . Filled symbols correspond to optimistic case ( $\gamma =1.1$ ), open symbols to the pessimistic one ( $\gamma =0.7$ ).
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In the text

$\begin{figure} {\includegraphics[width=8.8cm,clip]{8678fig12.eps} } \end{figure}$ Figure 12: Probabilities calculated from $\chi ^2$ for ASS ( left) and BSS ( right).
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In the text

$\begin{figure} {\includegraphics[width=7cm,clip]{8678fig13a.eps} } \par\vspace*{2mm} {\includegraphics[width=7cm,clip]{8678fig13b.eps} } \end{figure}$ Figure 13: Accuracy (standard deviation) of the fitted pitch angle ( upper panel) and the magnetic field amplitude ( lower panel) for the ASS model (open circles, black lines) and the BSS model (triangles, red lines) vs. inclination angle i. Weak turbulence - dashed lines, strong turbulence - solid lines. Fixed parameters of the model are the pitch angle $p=20^{\circ }$ and the field amplitude $B=5~\mu$ G. Each template is based on 35 $~{\rm RM}$ points.
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In the text

$\begin{figure} {\includegraphics[width=7cm,clip]{8678fig14a.eps} } \par\vspace*{2mm} {\includegraphics[width=7cm,clip]{8678fig14b.eps} } \end{figure}$ Figure 14: Fitted pitch angle ( upper panel) and the magnetic field amplitude ( lower panel) for the ASS model (open circles, black lines) and the BSS model (triangles, red lines), both including a vertical field, recognized with templates without a vertical field, plotted vs. inclination angle i. Weak turbulence - dashed lines, strong turbulence - solid lines. Fixed parameters of the model are the pitch angle $p=20^{\circ }$ and the field amplitude $B=5~\mu$ G. Each template is based on 35 $~{\rm RM}$ points.
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In the text

$\begin{figure} {\includegraphics[width=8.5cm,clip]{8678fig15.eps} } \end{figure}$ Figure 15: $~{\rm RM}$ source sample of M 31 (from Han et al. 1998). Numbers give $~{\rm RM}$ (in $~{\rm rad~m^{-2}}$ ), after subtraction of the mean $~{\rm RM}$ from the Galactic foreground. Isolines show the weight function used for $\chi ^2$ . Coordinates are given in kpc.
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In the text

$\begin{figure} \par\includegraphics[width=4cm,clip]{8678fig16a.eps}\hspace*{2mm} \includegraphics[width=4cm,clip]{8678fig16b.eps} \end{figure}$ Figure 16: The function f(x,y) ( left) and the $~{\rm RM}$ grid ( right) for a BSS galaxy model (pitch angle $p=20^{\circ }$ ) inclined at $i=70^{\circ }$ .
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In the text

$\begin{figure} \par\includegraphics[width=70mm,clip]{8678fig17a.eps}\par\vspace*{2mm} \includegraphics[width=70mm,clip]{8678fig17b.eps} \end{figure}$ Figure 17: The profiles f(y) along or parallel to the minor axis of the projected galaxy disk in the sky plane and the corresponding profiles of $~{\rm RM}(b)$ for a BSS-type galaxy, inclined at $i=70^{\circ }$ : x=0 (thick curve), x=3 kpc (dashed), and x=7.5 kpc (thin).
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In the text

$\begin{figure} \par\includegraphics[width=70mm,clip]{8678fig18a.eps}\par\vspace*... ...par\vspace*{2mm} \includegraphics[width=70mm,clip]{8678fig18c.eps} \end{figure}$ Figure 18: The profiles f(y) reconstructed using three different values of the supposed galactic thickness: h'=0.75 kpc ( top), h'=1 kpc ( middle), h'=1.25 kpc ( bottom). The correct value is h=1 kpc. The profiles are given for x=0 (thick curve), x=3 kpc (dashed), and x=7.5 kpc (thin).
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In the text

$\begin{figure} \par\includegraphics[width=5.5cm,clip]{8678fig1.eps} \end{figure}$	Figure 1: The two coordinate systems used in this paper: l,b in the sky plane and s along the line of sight, and x,y,z in the model galaxy plane and perpendicular to it. The dashed lines indicate the thickness of the disk.
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$\begin{figure} \par\includegraphics[width=14cm,clip]{8678fig2.eps} \end{figure}$	Figure 2: Modeled strength of the regular magnetic field multiplied by the thermal electron density in the galactic midplane (i.e. in the plane x,y) for the field modes m=0 (ASS), m=1 (BSS), and m=2 (QSS) for B=1.
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$\begin{figure} \par\includegraphics[width=5.5cm,clip]{8678fig3.eps} \end{figure}$	Figure 3: Orientation of the halo magnetic field. The box sketches the region of ionized gas r <r₀, -h <z <h.
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$\begin{figure} \par\includegraphics[width=14cm,clip]{8678fig4.eps}\end{figure}$	Figure 4: Modeled $~{\rm RM}$ maps (in $~{\rm rad~m^{-2}}$ ) for an inclination angle of $i=10^\circ$ generated for a pure BSS field pattern, for $B=5~\mu$ G and n₀ =0.03 cm^-3 ( left), a random turbulent field $~{\rm RM}_{\rm turb}$ for $\Delta\!~{\rm RM}_{\rm turb}=30~~{\rm rad~m^{-2}}$ ( middle), and their superposition ( right).
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$\begin{figure} \par\includegraphics[width=6.5cm,clip]{8678fig7.eps} \end{figure}$	Figure 7: Factor of effective points vs. inclination angle i due to geometry of the disk of thermal electrons.
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$\begin{figure} {\includegraphics[width=8.8cm,clip]{8678fig12.eps} } \end{figure}$	Figure 12: Probabilities calculated from $\chi ^2$ for ASS ( left) and BSS ( right).
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$\begin{figure} {\includegraphics[width=8.5cm,clip]{8678fig15.eps} } \end{figure}$	Figure 15: $~{\rm RM}$ source sample of M 31 (from Han et al. 1998). Numbers give $~{\rm RM}$ (in $~{\rm rad~m^{-2}}$ ), after subtraction of the mean $~{\rm RM}$ from the Galactic foreground. Isolines show the weight function used for $\chi ^2$ . Coordinates are given in kpc.
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$\begin{figure} \par\includegraphics[width=4cm,clip]{8678fig16a.eps}\hspace*{2mm} \includegraphics[width=4cm,clip]{8678fig16b.eps} \end{figure}$	Figure 16: The function f(x,y) ( left) and the $~{\rm RM}$ grid ( right) for a BSS galaxy model (pitch angle $p=20^{\circ }$ ) inclined at $i=70^{\circ }$ .
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$\begin{figure} \par\includegraphics[width=70mm,clip]{8678fig17a.eps}\par\vspace*{2mm} \includegraphics[width=70mm,clip]{8678fig17b.eps} \end{figure}$	Figure 17: The profiles f(y) along or parallel to the minor axis of the projected galaxy disk in the sky plane and the corresponding profiles of $~{\rm RM}(b)$ for a BSS-type galaxy, inclined at $i=70^{\circ }$ : x=0 (thick curve), x=3 kpc (dashed), and x=7.5 kpc (thin).
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$\begin{figure} \par\includegraphics[width=70mm,clip]{8678fig18a.eps}\par\vspace... ...par\vspace{2mm} \includegraphics[width=70mm,clip]{8678fig18c.eps} \end{figure}$	Figure 18: The profiles f(y) reconstructed using three different values of the supposed galactic thickness: h'=0.75 kpc ( top), h'=1 kpc ( middle), h'=1.25 kpc ( bottom). The correct value is h=1 kpc. The profiles are given for x=0 (thick curve), x=3 kpc (dashed), and x=7.5 kpc (thin).
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