All Figures

$\begin{figure} \par\includegraphics[width=18cm,clip]{0455fig1.eps} \end{figure}$ Figure 1: Thermal conductivity $\kappa _0$ , in cgs units, versus density $\rho$ and temperature T. The left panel shows the phonon-only contribution $\kappa_{0 \; \rm ph}$ , the right one the impurity-only contribution $\kappa_{0 \; \rm imp}$ , and the central panel the complete $\kappa _0$ (with an impurity concentration $Q_{\rm imp} = 0.1$ ).
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0455fig2.eps} \end{figure}$ Figure 2: Magnetization parameter $\omega _{\scriptscriptstyle B} \tau$ vs. density at six different temperatures (as labeled on the curves) assuming a uniform magnetic field of strength B =10¹² G. Its value for different field strengths scales linearly in B.
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0455fig3.eps} %\end{figure}$ Figure 3: Thermal conductivity, in cgs units, perpendicular to the magnetic field, $\kappa _\perp$ , vs. density $\rho$ and temperature T for a uniform magnetic field of strength $3\times 10^{12}$ G. For field strengths $\gg$ 10¹² G, i.e., for $\omega _{\scriptscriptstyle B} \tau \gg 1$ , $\kappa _\perp$ scales as B^-2. The impurity parameter Q is assumed to be 0.1.
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In the text

$\begin{figure} \par\includegraphics[width=3.5cm,clip]{0455fig4.ps}\hspace*{3mm} \includegraphics[width=3.5cm,clip]{0455fig5.ps} \end{figure}$ Figure 4: Magnetic field lines of the core field ( left panel) and of the crustal field as applied in our calculations. Both field configurations match for $r \ge R_{\rm NS}$ with a dipolar poloidal vacuum field. They are presented in a meridional plane, of the crust for $\rho _n \ge \rho \ge \rho _{\rm b}$ (see Sects. 2.4 and 2.5). The polar surface value B₀ is identical for both field types.
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In the text

$\begin{figure} \par\includegraphics[width=18cm,clip]{0455fig6.eps} \end{figure}$ Figure 5: The crustal temperature T (normalized on $T_{\rm core}$ ) as a function of the density within the crust at 4 different polar angles: $\theta =0$ : dotted-dashed line (almost coincident with the upper limit of the figure), $\theta =30$ : dashed line, $\theta =60\hbox {$^\circ $ }$ : dotted line, and $\theta =90\hbox {$^\circ $ }$ : full line, for a crustal field of strength $B_0=3\times 10^{12}$ G. The three panels correspond, from left to right, to $T_{\rm core}=10^8$ K, 10⁷ K, and 10⁶ K, respectively.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{0455fig7.ps} \end{figure}$ Figure 6: Same as Fig. 5 but for a dipolar core field with $T_{\rm core}=10^7$ K.
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In the text

$\begin{figure} \par\includegraphics[width=4cm,clip]{0455fig8.ps}\hspace*{3mm} \includegraphics[width=4cm,clip]{0455fig9.ps} \end{figure}$ Figure 7: Representation of both field lines and temperature distribution in the crust whose radial scale ( $r(\rho _n) \le r \le r(\rho _{\rm b})$ ) is stretched by a factor of 5, assuming $B_0=3\times 10^{12}$ G and $T_{\rm core}=10^6$ K. Left panel corresponds to a crustal field, right panel to a star-centered core field. Bars show the temperature scales in units of $T_{\rm core}$ .
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{0455fig10.eps} \end{figure}$ Figure 8: 3-D presentation of the temperature distribution in the crust for $T_{\rm core}=10^6$ K and a crustal field with strength $B_0=3\times 10^{12}$ G. (corresponding to the right panel of Fig. 5).
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0455fig11.eps} %\end{figure}$ Figure 9: Illustration of the magnetic-field-induced anisotropy (see text for details).
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=4cm,height=9.4cm,clip]{0455fig12... ...} \includegraphics[width=4cm,height=9.4cm,clip]{0455fig14.eps} } \end{figure}$ Figure 10: The surface temperature $T_{\rm s}$ as a function of the polar angle $\theta$ and for $T_{\rm core}=10^6$ K ( left panels), $T_{\rm core}=10^7$ K ( mid panels), or $T_{\rm core}=10^8$ K ( right panels) The dashed lines show the surface temperature distribution when an isothermal crust is assumed. The full lines represent the surface temperatures when the crust temperature distributions take into account the anisotropy of heat transport induced by a crustal magnetic field (the temperature at the crust-core interface being fixed at the $T_{\rm core}$ ). Almost indistinguishable from the isothermal crust model is the $T_{\rm s}$ -distribution for a star-centered core field. It is shown by dot-dashed lines for $T_{\rm core}=10^8$ K; for lower $T_{\rm core}$ the differences are even smaller. The assumed polar surface field strengths B₀ are 10¹² G ( upper panels), $3\times 10^{12}$ G ( mid panels) and 10¹³ G ( lower panels).
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In the text

$\begin{figure} \par\includegraphics[width=18cm,clip]{0455fig1.eps} \end{figure}$	Figure 1: Thermal conductivity $\kappa _0$ , in cgs units, versus density $\rho$ and temperature T. The left panel shows the phonon-only contribution $\kappa_{0 \; \rm ph}$ , the right one the impurity-only contribution $\kappa_{0 \; \rm imp}$ , and the central panel the complete $\kappa _0$ (with an impurity concentration $Q_{\rm imp} = 0.1$ ).
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0455fig2.eps} \end{figure}$	Figure 2: Magnetization parameter $\omega _{\scriptscriptstyle B} \tau$ vs. density at six different temperatures (as labeled on the curves) assuming a uniform magnetic field of strength B =10¹² G. Its value for different field strengths scales linearly in B.
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0455fig3.eps} %\end{figure}$	Figure 3: Thermal conductivity, in cgs units, perpendicular to the magnetic field, $\kappa _\perp$ , vs. density $\rho$ and temperature T for a uniform magnetic field of strength $3\times 10^{12}$ G. For field strengths $\gg$ 10¹² G, i.e., for $\omega _{\scriptscriptstyle B} \tau \gg 1$ , $\kappa _\perp$ scales as B^-2. The impurity parameter Q is assumed to be 0.1.
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$\begin{figure} \par\includegraphics[width=7cm,clip]{0455fig7.ps} \end{figure}$	Figure 6: Same as Fig. 5 but for a dipolar core field with $T_{\rm core}=10^7$ K.
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$\begin{figure} \par\includegraphics[width=4cm,clip]{0455fig8.ps}\hspace*{3mm} \includegraphics[width=4cm,clip]{0455fig9.ps} \end{figure}$	Figure 7: Representation of both field lines and temperature distribution in the crust whose radial scale ( $r(\rho _n) \le r \le r(\rho _{\rm b})$ ) is stretched by a factor of 5, assuming $B_0=3\times 10^{12}$ G and $T_{\rm core}=10^6$ K. Left panel corresponds to a crustal field, right panel to a star-centered core field. Bars show the temperature scales in units of $T_{\rm core}$ .
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$\begin{figure} \par\includegraphics[width=7.5cm,clip]{0455fig10.eps} \end{figure}$	Figure 8: 3-D presentation of the temperature distribution in the crust for $T_{\rm core}=10^6$ K and a crustal field with strength $B_0=3\times 10^{12}$ G. (corresponding to the right panel of Fig. 5).
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0455fig11.eps} %\end{figure}$	Figure 9: Illustration of the magnetic-field-induced anisotropy (see text for details).
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