All Figures

$\begin{figure} \par\includegraphics[width=7cm,clip]{7418f1.ps}\end{figure}$ Figure 1: The ratio of the density to the density at the base of the convection zone ( $\rho / \rho _{0}$ - solid line) and the ratio of the turbulent dynamical viscosity to the turbulent viscosity at the base of the convection zone ( $\eta _{\rm t} /\eta _{0}$ - dotted) versus the fractionary radius $r/R_{\odot }$ in our solar interior model.
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In the text

$\begin{figure} \par\includegraphics[width=6.7cm,clip]{7418f2.ps}\end{figure}$ Figure 2: The modulus of the radial localization kernel versus the relative radius for the function (69), as obtained by truncating the series of the radial eigenfunctions at $K_{\rm m }= 19$ , for three different intervals centered at r=0.725 ( upper panel), 0.85 ( middle panel) and 0.965 $R_{\odot }$ ( lower panel), all with an amplitude of r₂ - r₁ = 0.05 $R_{\odot }$ . The modulus of the derivative has been normalized to its maximum value.
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In the text

$\begin{figure} \par\includegraphics[width=6.9cm,clip]{7418f3.ps}\end{figure}$ Figure 3: Upper panel: test case of the application of the inversion method from Sect. 2.4. An input profile with ${\vec \tau}_{1} = 1.0 \hat{\vec r}$ in nondimensional units between 0.80 and 0.85 $R_{\odot }$ (solid line) is used to simulate a noiseless profile of angular velocity perturbation. The reconstructed lower-limit profile according to Eq. (46) is plotted as a dotted line. Lower panel: same as in the upper panel, but with an input profile localized between 0.775 and 0.825 $R_{\odot }$ .
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In the text

$\begin{figure} \par\includegraphics[width=6.85cm,clip]{7418f4.ps}\end{figure}$ Figure 4: The modulus of the latitudinal localization kernel versus $\mu$ for the function (70), obtained by truncating the series of the Jacobian polynomials at $N_{\rm m }= 30$ , for three different intervals of $\mu$ in the Northern hemisphere, i.e., [0, 0.26] ( upper panel), [0.5, 0.7] ( middle panel) and [0.87, 0.99] ( lower panel). Note the symmetry of the modulus of the kernel with respect to the equator. The value of $\left\vert \frac{{\rm d}f}{{\rm d}\mu} \right\vert$ is normalized at its maximum at $\mu = \pm 1$ .
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In the text

$\begin{figure} \par\includegraphics[width=6.7cm,clip]{7418f5.ps}\end{figure}$ Figure 5: The isocontours of the function $A_{\tau } (r, \mu )$ as defined by Eq. (71) in the case of $\eta _{0}=2.56$ $\times$ 10¹² g cm^-1 s^-1. The scale on the left indicates the ranges corresponding to the different colors and is in units of 10⁵ g cm^-1 s^-2. The relative statistical uncertainty of $A_{\tau }$ is $\sim$ 30%, as it follows from the relative uncertainty of the data.
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In the text

$\begin{figure} \par\includegraphics[width=6.7cm,clip]{7418f6.ps}\end{figure}$ Figure 6: The isocontours of $\Phi _{\tau } (r, \mu )$ as defined by Eq. (72) in the case of $\eta _{0}=2.56$ $\times$ 10¹² g cm^-1 s^-1. The phase ranges from $-\frac{\pi}{2}$ to $\frac{\pi}{2}$ . The scale on the left indicates the phase ranges corresponding to the different colors and is in radians.
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In the text

$\begin{figure} \par\includegraphics[width=6.7cm,clip]{7418f7.ps}\end{figure}$ Figure 7: As for Fig. 5 in the case of $\eta _{0}=5.62$ $\times$ 10¹⁰ g cm^-1 s^-1. The scale on the left is in units of 10³ g cm^-1 s^-2. The relative statistical uncertainty of $A_{\tau }$ is about 30%.
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In the text

$\begin{figure} \par\includegraphics[width=6.7cm,clip]{7418f8.ps}\end{figure}$ Figure 8: As for Fig. 6 in the case of $\eta _{0}=5.62$ $\times$ 10¹⁰ g cm^-1 s^-1.
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In the text

$\begin{figure} \par\includegraphics[width=6.7cm,clip]{7418f9.ps}\end{figure}$ Figure 9: Upper panel: the lower limit of the amplitude of the perturbation term $\vert{\vec \tau}_{\rm 1r}\vert$ averaged over spherical shells of thickness 0.05 $R_{\odot }$ versus the relative radius; different linestyles and colors refer to the depth at which the torsional oscillations are assumed to vanish: black solid line - oscillations extending down to the base of the convection zone; green dotted line - oscillations extending down to 0.80 $R_{\odot }$ ; red dashed line - oscillations extending down to 0.90 $R_{\odot }$ . Results are obtained assuming a turbulent dynamical viscosity at the base of the convection zone $\eta _{0}=2.56$ $\times$ 10¹² g cm^-1 s^-1. Lower panel: as in the upper panel, but for $\eta _{0}=5.62$ $\times$ 10¹⁰ g cm^-1 s^-1. The relative statistical uncertainties are in all cases about 30%, as follows from the uncertainties of the data.
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In the text

$\begin{figure} \par\includegraphics[width=6.8cm,clip]{7418f10.ps}\end{figure}$ Figure 10: Upper panel: the lower limit of the amplitude of the perturbation term $\vert{\vec \tau}_{1\theta}\vert$ averaged over different latitude zones versus their average value of $\mu$ . Different linestyles and colors are used to indicate the results for different penetration depths of the torsional oscillations, as in Fig. 9. Results are obtained assuming a turbulent dynamical viscosity at the base of the convection zone $\eta _{0}=2.56$ $\times$ 10¹² g cm^-1 s^-1. Lower panel: as in the upper panel, but for $\eta _{0}=5.62$ $\times$ 10¹⁰ g cm^-1 s^-1. The relative statistical uncertainties are in all cases about 30%, as follows from the uncertainties of the data.
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In the text

$\begin{figure} \par\includegraphics[width=6.7cm,clip]{7418f11.ps}\end{figure}$ Figure 11: Upper panel: the phase lag $\Pi _{\rm r}$ between $B_{\rm r}$ and $B_{\phi }$ as derived by Eqs. (54) averaged over spherical shells of thickness 0.05 $R_{\odot }$ versus the relative radius. Different linestyles are used to indicate the results for different penetration depths of the torsional oscillations, as in Fig. 9. Results are obtained assuming a turbulent dynamical viscosity at the base of the convection zone $\eta _{0}=2.56$ $\times$ 10¹² g cm^-1 s^-1. Lower panel: as in the upper panel, but for $\eta _{0}=5.62$ $\times$ 10¹⁰ g cm^-1 s^-1.
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In the text

$\begin{figure} \par\includegraphics[width=6.8cm,clip]{7418f12.ps}\end{figure}$ Figure 12: Upper panel: the phase lag $\Pi _{\theta }$ between $B_{\theta }$ and $B_{\phi }$ , as derived by equations analogous to (54), averaged over different latitude zones versus their average value of $\mu$ . Different linestyles are used to indicate the results for different penetration depths of the torsional oscillations, as in Fig. 9. Results are obtained assuming a turbulent dynamical viscosity at the base of the convection zone $\eta _{0}=2.56$ $\times$ 10¹² g cm^-1 s^-1. Lower panel: as in the upper panel, but for $\eta _{0}=5.62$ $\times$ 10¹⁰ g cm^-1 s^-1.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{7418f1.ps}\end{figure}$	Figure 1: The ratio of the density to the density at the base of the convection zone ( $\rho / \rho _{0}$ - solid line) and the ratio of the turbulent dynamical viscosity to the turbulent viscosity at the base of the convection zone ( $\eta _{\rm t} /\eta _{0}$ - dotted) versus the fractionary radius $r/R_{\odot }$ in our solar interior model.
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$\begin{figure} \par\includegraphics[width=6.7cm,clip]{7418f5.ps}\end{figure}$	Figure 5: The isocontours of the function $A_{\tau } (r, \mu )$ as defined by Eq. (71) in the case of $\eta _{0}=2.56$ $\times$ 10¹² g cm^-1 s^-1. The scale on the left indicates the ranges corresponding to the different colors and is in units of 10⁵ g cm^-1 s^-2. The relative statistical uncertainty of $A_{\tau }$ is $\sim$ 30%, as it follows from the relative uncertainty of the data.
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$\begin{figure} \par\includegraphics[width=6.7cm,clip]{7418f6.ps}\end{figure}$	Figure 6: The isocontours of $\Phi _{\tau } (r, \mu )$ as defined by Eq. (72) in the case of $\eta _{0}=2.56$ $\times$ 10¹² g cm^-1 s^-1. The phase ranges from $-\frac{\pi}{2}$ to $\frac{\pi}{2}$ . The scale on the left indicates the phase ranges corresponding to the different colors and is in radians.
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$\begin{figure} \par\includegraphics[width=6.7cm,clip]{7418f7.ps}\end{figure}$	Figure 7: As for Fig. 5 in the case of $\eta _{0}=5.62$ $\times$ 10¹⁰ g cm^-1 s^-1. The scale on the left is in units of 10³ g cm^-1 s^-2. The relative statistical uncertainty of $A_{\tau }$ is about 30%.
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$\begin{figure} \par\includegraphics[width=6.7cm,clip]{7418f8.ps}\end{figure}$	Figure 8: As for Fig. 6 in the case of $\eta _{0}=5.62$ $\times$ 10¹⁰ g cm^-1 s^-1.
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