All Figures

$\begin{figure} \par\includegraphics[width=12.6cm,clip]{3020fig1.eps} \end{figure}$ Figure 1: Schematic view of the physical processes and their interactions involved in momentum redistribution by IGW. Complete calculations take all processes enclosed in the dashed box into account.
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{3020fig2.eps} \end{figure}$ Figure 2: Penetration of IGW into the convection zone of a ZAMS $1~M_\odot$ model for various degrees $\ell$ . The arrows indicate the depth where the amplitude is reduced by a factor of 2. Also shown is the local convective flux given by the mixing length theory.
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In the text

$\begin{figure} \par\includegraphics[width=5.1cm,clip]{3020fig3a.eps}\hspace*{2mm... ...eps}\hspace*{2mm} \includegraphics[width=5.1cm,clip]{3020fig3c.eps} \end{figure}$ Figure 3: Behavior of the shear layer as a function of the diminishing viscosity for a $1.3~M_\odot$ model with a turbulent viscosity given by Eq. (4). From left to right, N=8, N=7.9 and N=7.85. ( Top) Time evolution of the rotation velocity at two different depths. ( Full line) $\Omega (r_1)$ ( dashed line) $\Omega (r_2)$ with $r_1=r_{{\rm cz}}-0.003H_{\rm P}$ and $r_2=r_{{\rm cz}}-0.015H_{\rm P}$ . ( Bottom) Phase space diagram.
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In the text

$\begin{figure} \par\includegraphics[width=7.7cm,clip]{3020fig4.eps} \end{figure}$ Figure 4: ( Left) Shear layer evolution (successive profiles are separated by 1 year) and ( right) average turbulent viscosity (as described in Sect. 3.1). The dashed line corresponds to an analytical fit (cf. Eq. (17)).
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In the text

$\begin{figure} \par\includegraphics[width=11cm,clip]{3020fig5.eps} \end{figure}$ Figure 5: Wave characteristics below the shear layer for a differential rotation of $\delta \Omega = 0.1~\mu {\rm Hz}$ over $5\%$ in radius in a 1.3 $M_\odot$ star. First and second row: wave amplitude for $m=\pm 1$ and $m=\pm \ell$ . Third row: amplitude difference between retrograde and prograde waves of the same azimuthal number. Fourth row: net luminosity for a given azimuthal number.
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In the text

$\begin{figure} \par\includegraphics[width=7.25cm,clip]{3020fig6.eps} \end{figure}$ Figure 6: ( Top) Instantaneous rotation profile. ( Middle, bottom) Instantaneous damping length (corresponding to a reduction of wave amplitude A=A₀/e) for wave frequencies of $\nu =0.5$ and $\nu=1~\mu{\rm Hz}$ in a 1.3 $M_\odot$ star. The m=0 mode (open dots) is not affected by rotation, the $m=\pm \ell$ (squares and triangles) modes are the most affected. Below the shear layer, the radiative region is rotating more rapidly; it is the retrograde modes of low order that penetrate deeper, leading to a net deposition of negative momentum in the interior. The low ( $\ell =1$ and 2) modes have to travel back and forth a few times before they are damped, and are not shown in the bottom graph.
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In the text

$\begin{figure} \par\includegraphics[width=7.25cm,clip]{3020fig7.eps} \end{figure}$ Figure 7: Local deposition of angular momentum for various values of differential rotation. The rotation profile rises linearly between the base of the convection zone and (1-m/M)=-2.85 by a value of $\delta \Omega$ , which varies logarithmically from 10^-5 to 10^-1 $\mu {\rm Hz}$ . This is illustrated for a $1.3~M_\odot$ model. For moderate amounts of differential rotation (below $\sim$ $10^{-2}~\mu{\rm Hz}$ ), the net momentum flux at a given point is a linear function of differential rotation.
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In the text

$\begin{figure} \par\includegraphics[width=16.8cm,clip]{3020fig8.eps} \end{figure}$ Figure 8: Filtered momentum luminosity spectrum for the $m=\ell$ mode (that is ${\cal L}_{\rm net} = {\cal L}_{m=-\ell } - {\cal L}_{m=\ell }$ ) below the shear layer for various masses. Differential rotation is $\delta \Omega = 10^{-4}~\mu {\rm Hz}$ over $5\%$ in radius.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8cm,clip]{3020fig9.eps} \end{figure}$ Figure 9: Evolution of the rotation profile in the case of very strong and moderate initial differential rotation in a $1~M_\odot$ star.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8cm,clip]{3020fig10.eps} \end{figure}$ Figure 10: Evolution of the rotation profile with moderate initial differential rotation for a wave spectrum derived from GMK spectrum (cf. Eq. (1)) and for a flat spectrum with the same total energy flux. Calculations are made in a $1~M_\odot$ star
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In the text

$\begin{figure} \par\includegraphics[width=7.3cm,clip]{3020fig11.eps} \end{figure}$ Figure 11: Evolution of the rotation profile in a complete model where the transport of angular momentum is due to internal gravity waves, meridional circulation and turbulence. The model shown is for a $1.2~M_\odot$ Z=0.02, star with an initial rotation velocity of $50~{\rm km~s^{-1}}$ . The curves are labeled according to the corresponding ages in Gyr.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.5cm,clip]{3020fig12.eps} \end{figure}$ Figure 12: Same as Fig. 11 for 0.2, 0.5, and 0.7 Gyr in a case without ( left) and with ( right) internal gravity waves included. The time sequence goes from the highest to the smallest surface velocity
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In the text

$\begin{figure} \par\includegraphics[width=7.25cm,clip]{3020fig13.eps} \end{figure}$ Figure 13: Profiles of the vertical component of the meridional velocity in a $1.2~M_\odot$ star at 0.5 Gyr in a simple rotating model (dotted line) and in a rotating model including gravity waves (full line). The bold lines indicate positive values of U.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.35cm,clip]{3020fig14.eps} \end{figure}$ Figure 14: Comparison of the transport coefficients in a $1.2~M_\odot$ star at 0.5 Gyr in a simple rotating model ( left) and in a rotating model including IGW ( right). Coefficients are identified in the figure. D_v is the dashed line and $D_{\rm eff}$ a full line.
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In the text

$\begin{figure} \par\includegraphics[width=7.1cm,clip]{3020fig15.eps} \end{figure}$ Figure 15: Total diffusion coefficient in a $1.2~M_\odot$ star at 0.5 Gyr in a simple rotating model (dotted line) and in a rotating model including IGW (full line). The dashed-dotted line gives $D_{\rm waves}$ .
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In the text

$\begin{figure} \par\includegraphics[width=7.3cm,clip]{3020fig16.eps} \end{figure}$ Figure 16: ⁴He profile at the age of the Hyades in the complete model (full line) and in the model without the IGW (dashed line) for a $1.2~M_\odot$ star.
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In the text

$\begin{figure} \par\includegraphics[width=7.3cm,clip]{3020fig17.eps} \end{figure}$ Figure 17: ⁷Li profile at the age of the Hyades in the complete model (full line) and in the model without the IGW (dashed line) for a $1.2~M_\odot$ star. The box indicates the observed Li abundances in Hyades stars with an effective temperature ( $\pm$ 100 K) corresponding to that of the model at 0.7 Gyr (data by Boesgaard & King 2002).
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In the text

$\begin{figure} \par\includegraphics[width=12.6cm,clip]{3020fig1.eps} \end{figure}$	Figure 1: Schematic view of the physical processes and their interactions involved in momentum redistribution by IGW. Complete calculations take all processes enclosed in the dashed box into account.
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$\begin{figure} \par\includegraphics[width=7.9cm,clip]{3020fig2.eps} \end{figure}$	Figure 2: Penetration of IGW into the convection zone of a ZAMS $1~M_\odot$ model for various degrees $\ell$ . The arrows indicate the depth where the amplitude is reduced by a factor of 2. Also shown is the local convective flux given by the mixing length theory.
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$\begin{figure} \par\includegraphics[width=7.7cm,clip]{3020fig4.eps} \end{figure}$	Figure 4: ( Left) Shear layer evolution (successive profiles are separated by 1 year) and ( right) average turbulent viscosity (as described in Sect. 3.1). The dashed line corresponds to an analytical fit (cf. Eq. (17)).
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$\begin{figure} \par\includegraphics[width=16.8cm,clip]{3020fig8.eps} \end{figure}$	Figure 8: Filtered momentum luminosity spectrum for the $m=\ell$ mode (that is ${\cal L}_{\rm net} = {\cal L}_{m=-\ell } - {\cal L}_{m=\ell }$ ) below the shear layer for various masses. Differential rotation is $\delta \Omega = 10^{-4}~\mu {\rm Hz}$ over $5\%$ in radius.
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$\begin{figure} \par\includegraphics[angle=270,width=8cm,clip]{3020fig9.eps} \end{figure}$	Figure 9: Evolution of the rotation profile in the case of very strong and moderate initial differential rotation in a $1~M_\odot$ star.
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$\begin{figure} \par\includegraphics[angle=270,width=8cm,clip]{3020fig10.eps} \end{figure}$	Figure 10: Evolution of the rotation profile with moderate initial differential rotation for a wave spectrum derived from GMK spectrum (cf. Eq. (1)) and for a flat spectrum with the same total energy flux. Calculations are made in a $1~M_\odot$ star
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$\begin{figure} \par\includegraphics[width=7.3cm,clip]{3020fig11.eps} \end{figure}$	Figure 11: Evolution of the rotation profile in a complete model where the transport of angular momentum is due to internal gravity waves, meridional circulation and turbulence. The model shown is for a $1.2~M_\odot$ Z=0.02, star with an initial rotation velocity of $50~{\rm km~s^{-1}}$ . The curves are labeled according to the corresponding ages in Gyr.
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$\begin{figure} \par\includegraphics[angle=270,width=8.5cm,clip]{3020fig12.eps} \end{figure}$	Figure 12: Same as Fig. 11 for 0.2, 0.5, and 0.7 Gyr in a case without ( left) and with ( right) internal gravity waves included. The time sequence goes from the highest to the smallest surface velocity
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$\begin{figure} \par\includegraphics[width=7.25cm,clip]{3020fig13.eps} \end{figure}$	Figure 13: Profiles of the vertical component of the meridional velocity in a $1.2~M_\odot$ star at 0.5 Gyr in a simple rotating model (dotted line) and in a rotating model including gravity waves (full line). The bold lines indicate positive values of U.
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$\begin{figure} \par\includegraphics[angle=270,width=8.35cm,clip]{3020fig14.eps} \end{figure}$	Figure 14: Comparison of the transport coefficients in a $1.2~M_\odot$ star at 0.5 Gyr in a simple rotating model ( left) and in a rotating model including IGW ( right). Coefficients are identified in the figure. D_v is the dashed line and $D_{\rm eff}$ a full line.
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$\begin{figure} \par\includegraphics[width=7.1cm,clip]{3020fig15.eps} \end{figure}$	Figure 15: Total diffusion coefficient in a $1.2~M_\odot$ star at 0.5 Gyr in a simple rotating model (dotted line) and in a rotating model including IGW (full line). The dashed-dotted line gives $D_{\rm waves}$ .
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$\begin{figure} \par\includegraphics[width=7.3cm,clip]{3020fig16.eps} \end{figure}$	Figure 16: ⁴He profile at the age of the Hyades in the complete model (full line) and in the model without the IGW (dashed line) for a $1.2~M_\odot$ star.
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$\begin{figure} \par\includegraphics[width=7.3cm,clip]{3020fig17.eps} \end{figure}$	Figure 17: ⁷Li profile at the age of the Hyades in the complete model (full line) and in the model without the IGW (dashed line) for a $1.2~M_\odot$ star. The box indicates the observed Li abundances in Hyades stars with an effective temperature ( $\pm$ 100 K) corresponding to that of the model at 0.7 Gyr (data by Boesgaard & King 2002).
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