All Figures

$\begin{figure} \par\includegraphics[width=8.7cm,clip]{0822fig1.eps}\end{figure}$ Figure 1: Threshold values of the shear factor $\sigma =(\partial \omega/\partial \ln r)$ for the dynamical (solid line) and the secular (dashed line) shear instability. Constant gravity and temperature, i.e., g=10⁹ ${\rm cm/s^2}$ , $T = 5\times 10^7$ K, are assumed. The chemical composition is also assumed to be constant, with $X_{\rm C}=0.43$ and $X_{\rm O}=0.54$ . For the critical Richardson number, $R_{\rm i,c} = 1/4$ is employed. $R_{\rm e,c} = 2500$ is used for the critical Reynolds number.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0822fig2.eps}\end{figure}$ Figure 2: The critical density $\rho _{\rm SSI, crit}$ , above which the secular shear instability cannot occur, as function of temperature (solid line). The region where the thermal diffusion time scale exceeds the turbulent viscous time scale is hatched. Abundances of $X_{\rm C}=0.43$ and $X_{\rm O}=0.54$ are assumed. $R_{\rm e,c} = 2500$ is used for the critical Reynolds number.
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In the text

$\begin{figure} \par\includegraphics[width=8.6cm,clip]{0822fig3.eps}\end{figure}$ Figure 3: Evolution of central density and temperature in non-rotating accreting CO white dwarfs. The initial mass is 1.0 $\ensuremath {{M}_\odot }$ and the accretion rate is $\ensuremath {10^{-6}}$ ${M}_{\odot }/{\rm yr}$ . The dotted line denotes the case of helium accretion, and the dashed line the case of carbon-oxygen accretion. The initial central temperature was $T_{\rm c, init} = 2.29 \times 10^8$ K for thehelium-accreting white dwarf and and $T_{\rm c, init} = 1.69 \times 10^8$ K forthe CO-accreting one. The numbers next to the filled circles denote the white dwarf mass in solar masses.
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In the text

$\begin{figure} \par\includegraphics[width=8.35cm,clip]{0822fg4a.eps}\hspace*{3mm... ....eps}\hspace*{3mm} \includegraphics[width=8.35cm,clip]{0822fg4d.eps}\end{figure}$ Figure 4: Temperature as a function of the mass coordinate in white dwarf models when $M_{\rm {WD}}$ = 0.96, 1.22 and 1.37 $\ensuremath {{M}_\odot }$ . a) non-rotating case with $M_{\rm init}$ = 0.9 $\ensuremath {{M}_\odot }$ and $\ensuremath{\dot{M}}$ = $\ensuremath {5\times 10^{-7}}$ ; b) model sequence T6; c) model sequence A6; d) model sequence A6.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{0822fig5.eps}\end{figure}$ Figure 5: Rotational energy dissipation rate (see Eq. (16)) as function of the mass coordinate, when $M_{\rm {WD}}$ = 0.98, 1.22 and 1.37 $\ensuremath {{M}_\odot }$ in model sequence A6.
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0822fg6a.eps}\hspace*{3mm}... ...c.eps}\hspace*{3mm} \includegraphics[width=8.3cm,clip]{0822fg6d.eps}\end{figure}$ Figure 6: Angular velocity as a function of the mass coordinate at different white dwarf masses. Panels a), b), c) and d) give results for model sequences A2, A6, A10 and D6, respectively (see Table 2).
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0822fig7.eps}\end{figure}$ Figure 7: Shear factor $\sigma~({=} \partial \omega/\partial \ln r)$ as a function of the mass coordinate in two different white dwarf models at $M_{\rm {WD}}$ = 1.26 $\ensuremath {{M}_\odot }$ and 1.37 $\ensuremath {{M}_\odot }$ from model sequence A6. The dashed lines denote the threshold value of $\sigma$ for the dynamical shear instability (i.e., $\sigma _{\rm DSI, crit} = (N^2/R_{\rm i, c})^{1/2}$ ; see Eq. (7)).
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In the text

$\begin{figure} \par\mbox{\hspace*{2.2mm}\includegraphics[width=8.8cm,clip]{0822f... ...ip]{0822fg8c.eps}\includegraphics[width=8.8cm,clip]{0822fg8d.eps} } \end{figure}$ Figure 8: a) Thermodynamic quantities as a function of the mass coordinate, in the white dwarf model of sequence A6 when $M_{\rm {WD}}$ = 1.26 $\ensuremath {{M}_\odot }$ : $\ensuremath {\nabla _{\rm ad}}$ (solid line), $\nabla$ (dot-dashed line), $f_{\mu }$ $\ensuremath {(\varphi _{\rm e}\nabla _{\mu _{\rm e}}+\varphi _{\rm I}\nabla _{\mu _{\rm I}})/\delta }$ where $f_{\mu }=0.05$ (dashed line) and temperature (dotted line). The region where the white dwarf is unstable to the dynamical shear instability is hatched. b) Diffusion coefficients for rotationally induced hydrodynamic instabilities, as a function of the mass coordinate, in the white dwarf model of sequence A6 at $M_{\rm {WD}}$ = 1.26 $\ensuremath {{M}_\odot }$ . The solid line denotes the diffusion coefficient for the dynamical shear instability, the dashed line, the dotted line and the dashed-dotted lines are for the secular shear instability, the Eddington-Sweet circulation, and the GSF instability respectively. c) Same as in a) but for $M_{\rm {WD}}$ = 1.27 $\ensuremath {{M}_\odot }$ . d) Same as in b) but for $M_{\rm {WD}}$ = 1.37 $\ensuremath {{M}_\odot }$ .
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In the text

$\begin{figure} \par\includegraphics[width=7.7cm,clip]{0822fig9.eps}\end{figure}$ Figure 9: Angular velocity profiles given as a function of the mass coordinate at 17 different evolutionary epochs of sequence A6: 1.26, 1.28, 1.30, 1.31, 1.33, 1.34, 1.36, 1.37, 1.38, 1.40, 1.42, 1.44, 1.45, 1.47, 1.48, 1.50, 1.52 $\ensuremath {{M}_\odot }$ , from the bottom to the top. The filled circles designate the mass coordinate $M_{\rm rm,DSI}$ below which the white dwarf interior is dynamical shear unstable.
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{0822fg10.eps}\end{figure}$ Figure 10: Integrated angular momentum $J(M_{\rm r}) = \int^{M_{\rm r}} _0 j(m) {\rm d}m$ divided by $M_{\rm r}^{5/3}$ , as a function of the mass coordinate at five different evolutionary epochs of sequence A6: $M_{\rm {WD}}$ = 1.21, 1.30, 1.37, 1.44 and 1.52 $\ensuremath {{M}_\odot }$ . The thin contour lines denote levels of constant J in logarithmic scale, labeled with $\log (J/10^{50}~ {\rm erg s})$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.7cm,clip]{0822fg11.eps}\end{figure}$ Figure 11: The evolution of the accumulated angular momentum in model sequences A5, A6 and A10, given as a function of the white dwarf mass. The thin lines denote the accumulated total angular momentum in the white dwarf models. The thick lines give the accumulated rejected angular momentum by Eq. (18).
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In the text

$\begin{figure} \par\hspace*{-2mm}\includegraphics[width=8.7cm,clip]{0822f12a.eps}\vspace*{2mm} \includegraphics[width=8.7cm,clip]{0822f12b.eps}\end{figure}$ Figure 12: a) Mass fraction of carbon as a function of the mass coordinate in two white dwarf models of sequence D6, at $M_{\rm {WD}}$ = 0.9 $\ensuremath {{M}_\odot }$ (initial model, dashed line) and 1.37 $\ensuremath {{M}_\odot }$ (solid line). b) Thermodynamic quantities as a function of the mass coordinate for the same models: $\ensuremath {\nabla _{\rm ad}}$ (solid line), $\nabla$ (dot-dashed line), $\ensuremath {(\varphi _{\rm e}\nabla _{\mu _{\rm e}}+\varphi _{\rm I}\nabla _{\mu _{\rm I}})/\delta }$ (dashed line) and temperature (dotted line). The region where the white dwarf is unstable to the dynamical shear instability is hatched.
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In the text

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{0822fg13.eps}\end{figure}$ Figure 13: Angular velocity normalized to the local Keplerian value, as a function of the mass coordinate in white dwarf models of sequence A6, when $\ensuremath {E_{\rm rot}/\vert W\vert}$ = 0.04, 0.07, 0.10 and 0.14.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0822fg14.eps}\end{figure}$ Figure 14: Growth time scales for the bar-mode instability ( $\tau _{\rm bar}$ ; Eq. (20)) as well as for the r-mode instability ( $\tau _{\rm r}$ ; Eq. (21)). $\tau _{\rm bar}$ is plotted as a function of $\ensuremath {E_{\rm rot}/\vert W\vert}$ , with thin lines for 3 different masses: 1.4 $\ensuremath {{M}_\odot }$ (solid line), 1.5 $\ensuremath {{M}_\odot }$ (dotted line) and 1.6 $\ensuremath {{M}_\odot }$ (dashed-dotted line). Two different values of $\ensuremath{(E_{\rm rot}/\vert W\vert)_{\rm bar,~crit}}$ (0.1 and 0.14) for the bar-mode instability are considered, as indicated in the figure. The thick dashed line denotes $\tau _{\rm r}$ in the models of sequence A6, while the thick solid line is for sequence A12. The thick dashed-dotted and dotted lines give the viscous time scale for sequences A6 and A12 respectively.
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In the text

$\begin{figure} \par\hspace*{-1mm}\includegraphics[width=8.6cm,clip]{0822f15a.eps}\par\hspace*{-1mm}\includegraphics[width=8.6cm,clip]{0822f15b.eps}\end{figure}$ Figure 15: Evolution of the angular velocity in a), and temperature in b), of a rapidly rotating 1.50 $\ensuremath {{M}_\odot }$ white dwarf after the mass accretion stops. The initial model at t=0 has been taken from model sequence A12.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0822f16a.eps}\par\includegraphics[width=8.5cm,clip]{0822f16b.eps}\end{figure}$ Figure 16: a) Temperature (solid line) and angular velocity (dashed line) as a function of the mass coordinate in the last computed model of sequence C9. b) Equatorial rotational velocity (solid line) for the same model as in a) as a function of the mass coordinate. The dashed line denotes the sound speed as a function of the mass coordinate.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0822fig2.eps}\end{figure}$	Figure 2: The critical density $\rho _{\rm SSI, crit}$ , above which the secular shear instability cannot occur, as function of temperature (solid line). The region where the thermal diffusion time scale exceeds the turbulent viscous time scale is hatched. Abundances of $X_{\rm C}=0.43$ and $X_{\rm O}=0.54$ are assumed. $R_{\rm e,c} = 2500$ is used for the critical Reynolds number.
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$\begin{figure} \par\includegraphics[width=8.35cm,clip]{0822fg4a.eps}\hspace{3mm... ....eps}\hspace{3mm} \includegraphics[width=8.35cm,clip]{0822fg4d.eps}\end{figure}$	Figure 4: Temperature as a function of the mass coordinate in white dwarf models when $M_{\rm {WD}}$ = 0.96, 1.22 and 1.37 $\ensuremath {{M}_\odot }$ . a) non-rotating case with $M_{\rm init}$ = 0.9 $\ensuremath {{M}_\odot }$ and $\ensuremath{\dot{M}}$ = $\ensuremath {5\times 10^{-7}}$ ; b) model sequence T6; c) model sequence A6; d) model sequence A6.
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$\begin{figure} \par\includegraphics[width=8.2cm,clip]{0822fig5.eps}\end{figure}$	Figure 5: Rotational energy dissipation rate (see Eq. (16)) as function of the mass coordinate, when $M_{\rm {WD}}$ = 0.98, 1.22 and 1.37 $\ensuremath {{M}_\odot }$ in model sequence A6.
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$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0822fg6a.eps}\hspace{3mm}... ...c.eps}\hspace{3mm} \includegraphics[width=8.3cm,clip]{0822fg6d.eps}\end{figure}$	Figure 6: Angular velocity as a function of the mass coordinate at different white dwarf masses. Panels a), b), c) and d) give results for model sequences A2, A6, A10 and D6, respectively (see Table 2).
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$\begin{figure} \par\includegraphics[width=8.7cm,clip]{0822fg11.eps}\end{figure}$	Figure 11: The evolution of the accumulated angular momentum in model sequences A5, A6 and A10, given as a function of the white dwarf mass. The thin lines denote the accumulated total angular momentum in the white dwarf models. The thick lines give the accumulated rejected angular momentum by Eq. (18).
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$\begin{figure} \par\includegraphics[width=8.4cm,clip]{0822fg13.eps}\end{figure}$	Figure 13: Angular velocity normalized to the local Keplerian value, as a function of the mass coordinate in white dwarf models of sequence A6, when $\ensuremath {E_{\rm rot}/\vert W\vert}$ = 0.04, 0.07, 0.10 and 0.14.
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$\begin{figure} \par\hspace{-1mm}\includegraphics[width=8.6cm,clip]{0822f15a.eps}\par\hspace{-1mm}\includegraphics[width=8.6cm,clip]{0822f15b.eps}\end{figure}$	Figure 15: Evolution of the angular velocity in a), and temperature in b), of a rapidly rotating 1.50 $\ensuremath {{M}_\odot }$ white dwarf after the mass accretion stops. The initial model at t=0 has been taken from model sequence A12.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0822f16a.eps}\par\includegraphics[width=8.5cm,clip]{0822f16b.eps}\end{figure}$	Figure 16: a) Temperature (solid line) and angular velocity (dashed line) as a function of the mass coordinate in the last computed model of sequence C9. b) Equatorial rotational velocity (solid line) for the same model as in a) as a function of the mass coordinate. The dashed line denotes the sound speed as a function of the mass coordinate.
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