Astronomy & Astrophysics

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$\begin{figure} \par\includegraphics[width=6.5cm,clip]{2553f1.eps} \end{figure}$ Figure 1: Example of the geometrical scheme used in the inversion. The radiative transfer equation is solved along the 2 rays (dashed and dot-dashed lines) representing the embedded flux tube and surrounding atmosphere respectively. $\gamma _{\rm s}$ and $\gamma _{\rm t}$ refer to the inclination of the magnetic field vector with respect to the observer. In this picture for simplicity the heliocentric angle is $\theta =0$ and $\gamma _{\rm t}=90^{\circ }$ .
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In the text

$\begin{figure} \par\includegraphics[width=6.2cm,clip]{2553f2a.ps}\hspace*{4mm} \... ...f2c.ps}\hspace*{4mm} \includegraphics[width=6.2cm,clip]{2553f2d.ps} \end{figure}$ Figure 2: Top panels: NOAA 8706 observed in 21 September 1999 at a heliocentric angle $\mu =0.51$ ( left: continuum intensity map at 1.56 $\mu$ m; right: total circular polarization map for Fe I 15 648.5 Å). Bottom panels: NOAA 8706 observed in 27 September 1999 at a heliocentric angle $\mu =0.91$ ( left: continuum intensity map at 1.56 $\mu$ m; right: total circular polarization map for Fe I 15 648.5 Å). The arrows point towards the direction of the solar disk center. The two inner-most contours enclose the umbral-penumbral boundary. The external contour defines the sunspot radius r=R, at each position angle. These three contours have been defined as $0.45I_{\rm c}$ , $0.65 I_{\rm c}$ and $0.85 I_{\rm c}$ , where $I_{\rm c}$ represents the average continuum intensity of the quiet Sun. The radial cuts selected for our analysis are also shown.
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In the text

$\begin{figure} \par\includegraphics[width=6.7cm,clip]{2553f3a.ps}\hspace*{4mm} \includegraphics[width=6.7cm,clip]{2553f3b.ps} \end{figure}$ Figure 3: Example of the observed (dots) and fitted (solid lines) Stokes V profiles ( left: 15 648.5 Å; right: 15 652.5 Å) for a penumbral point. The fitted profile is obtained by linearly combining the profile emerging from the surrounding component (dot-dashed line) and the profile emerging from the ray piercing the flux tube (dashed line). The employed filling factors, $\alpha _{\rm t}$ and $\alpha _{\rm q}$ , as well as the area asymmetry of the observed and fitted profiles are also given.
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In the text

$\begin{figure} \par\includegraphics[width=12.3cm,clip]{2553f4.ps} %\end{figure}$ Figure 4: Temperature ( top-left panel), magnetic field strength ( top-right panel), magnetic field inclination ( bottom-left) and line-of-sight velocity ( bottom-right) for the flux tube atmosphere (dashed lines) and its surroundings (dot-dashed lines) as a function of the geometrical depth, obtained from the inversion of the profiles in Fig. 3. The flux tube's radius returned by the inversion is 125 km and its central position is z₀=150 km.
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In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{2553f5a.ps}\hspace*{4mm} \... ...5e.ps}\hspace*{4mm} \includegraphics[width=6.5cm,clip]{2553f5f.ps} \end{figure}$ Figure 5: Top panels: temperature difference between the flux tube atmosphere and its surroundings as a function of radial distance from the spot center. Middle panels: radial variation of the line-of-sight velocities inside (dashed lines) and outside the flux tubes (dashed-dotted lines). Bottom panels: radial variation of the flux tube's filling factor, $\alpha _{\rm t}$ . Left panels: sunspot at $\mu =0.91$ . Right Panels: sunspot at $\mu =0.51$ . All quantities refer to the central position of the tube, z=z₀. Shaded areas denote the maximum deviations from the average at each radial position, obtained from the individual inversions of all the radial cuts. The arrow indicates the approximate radial position where the flux tube experiences a final temperature enhancement (see Sect. 6.4).
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In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{2553f6a.ps}\hspace*{4mm} ... ...6c.ps}\hspace*{4mm} \includegraphics[width=6.5cm,clip]{2553f6d.ps} \end{figure}$ Figure 6: The same as Fig. 5, but now for the radial variation of the magnetic field zenith angle ( top panels) and magnetic field strength ( bottom panels).
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In the text

$\begin{figure} \par\hspace*{2mm}\includegraphics[width=6.5cm,clip]{2553f7a.ps}\p... ...ps}\par\vspace*{2mm} \includegraphics[width=6.5cm,clip]{2553f7c.ps} \end{figure}$ Figure 7: Top panel: area asymmetry from the best-fit Stokes V profiles, $\delta A_{\rm FIT}$ , versus area asymmetry of the observed Stokes V, $\delta A_{\rm OBS}$ , for both Fe I lines for the case $\mu =0.91$ . For $\mu =0.51$ (not shown) the result is very similar. Filled circles are for Fe I 15 648.5 Å, open circles for 15 652.8 Å. Middle panel: average position, in the optical depth scale, of the lower boundary of the flux tube (solid line). The $\log\tau_{1.56}=0$ level is indicated by the dashed line. Maximum and minimum individual deviations of the 10 radial cuts considered are indicated by the shaded area. Bottom panel: radial variation of the fitted (dashed line) and observed area asymmetry (solid line) of Fe I 15 648.5 Å.
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In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{2553f8a.ps}\par\vspace*{2mm} \includegraphics[width=6cm,clip]{2553f8b.ps} \end{figure}$ Figure 8: Radial variation of the gas pressure difference, $\Delta P_{\rm gas}$ , between the flux tube and its surrounding atmosphere at z=z₀. Top panel: for NOAA 8706 at an heliocentric angle of $\mu =0.91$ . Bottom panel: the same for $\mu =0.51$ .
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In the text

$\begin{figure} \par\hspace*{1mm} \includegraphics[width=7cm]{2553f9a.ps}\hspace*... ...2553f9c.ps}\hspace*{2mm} \includegraphics[width=7.5cm]{2553f9d.ps} \end{figure}$ Figure 9: Top left panel: radial variation of the flow velocity inside the flux tube (solid line). Local sound speed and tube's critical speed are also plotted (dashed and dashed-dotted lines respectively). The vertical arrow marks the position where the flow speed becomes supercritical, $r/R \simeq 0.78$ . Top right panel: radial variation of the equivalent width for Fe I 15 648.5 Å line. The open circles are three selected radial positions before, during and after the shock occurs. Bottom left panels: intensity profiles corresponding to the 3 selected radial positions ( top right panel in this figure) before (dashed line), during (solid line) and after the shock (dotted line). Bottom right panels: radial variation of $\sqrt {v_{\rm mic,t}^2+v_{\rm mac,t}^2}$ .
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In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{2553f6a.ps}\hspace{4mm} ... ...6c.ps}\hspace{4mm} \includegraphics[width=6.5cm,clip]{2553f6d.ps} \end{figure}$	Figure 6: The same as Fig. 5, but now for the radial variation of the magnetic field zenith angle ( top panels) and magnetic field strength ( bottom panels).
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$\begin{figure} \par\includegraphics[width=6cm,clip]{2553f8a.ps}\par\vspace*{2mm} \includegraphics[width=6cm,clip]{2553f8b.ps} \end{figure}$	Figure 8: Radial variation of the gas pressure difference, $\Delta P_{\rm gas}$ , between the flux tube and its surrounding atmosphere at z=z₀. Top panel: for NOAA 8706 at an heliocentric angle of $\mu =0.91$ . Bottom panel: the same for $\mu =0.51$ .
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