All Figures

$\begin{figure} \par\resizebox{7.8cm}{!}{\includegraphics[clip]{0327fg1a.ps}}\par... ...pace*{-2mm}\resizebox{7.5cm}{!}{\includegraphics[clip]{0327fg1c.ps}}\end{figure}$ Figure 1: Evolution of nuclear luminosity due to helium burning in the helium-accreting white dwarf models with $\ensuremath{\dot{M}}$ = $2\times 10^{-7}$ ${M}_{\odot }/\rm {yr}$ . The box in panel a) gives the result from the non-rotating case (NR1) while the results from the rotating models with $f_{\rm c} = 1/30$ (R1) and $f_{\rm c}=1/3$ (RT1) are shown in panels b) and c). The abscissa denotes the total mass of the white dwarf, which serves as a measure of time.
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In the text

$\begin{figure} \par\resizebox{7.8cm}{!}{\includegraphics[clip]{0327fg2a.ps}}\par\vspace*{3mm} \resizebox{7.8cm}{!}{\includegraphics[clip]{0327fg2b.ps}}\end{figure}$ Figure 2: Evolution of the white dwarf in the sequences NR1 a) and R1 b) in the Hertzprung-Russell diagram. The starting point is marked by a filled circle. The endapoint, where the surface luminosity reaches the Eddington limit, is marked by an asterisk for each case. The raggedness which appears in some parts of the evolutionary tracks is due to the limited number of digits in the numerical outputs.
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In the text

$\begin{figure} \par\resizebox{7.6cm}{!}{\includegraphics[clip]{0327fg3a.ps}}\par... ...pace*{3mm} \resizebox{7.6cm}{!}{\includegraphics[clip]{0327fg3c.ps}}\end{figure}$ Figure 3: Same as in Fig. 1 but with $\ensuremath{\dot{M}}$ = $3\times 10^{-7}$ ${M}_{\odot }/\rm {yr}$ (NR2 a), R2 b) and RT2 c)).
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In the text

$\begin{figure} \par\resizebox{7.8cm}{!}{\includegraphics[clip]{0327fg4a.ps}}\hsp... ...pace*{7mm} \resizebox{7.9cm}{!}{\includegraphics[clip]{0327fg4d.ps}}\end{figure}$ Figure 4: Evolution of nuclear luminosity due to helium burning in the helium-accreting white dwarf models for $\ensuremath{\dot{M}}$ = $5\times 10^{-7}$ ${M}_{\odot }/\rm {yr}$ (NR3 a) and R3 b)) and $\ensuremath{\dot{M}}$ = 10^-6 ${M}_{\odot }/\rm {yr}$ (NR4 c) and R4 d)). The abscissa denotes the total mass of the white dwarf, which serves as a measure of time. Note that what appears to look like noise in the plots for R3 and NR4 corresponds to many successive thermal pulses, each as well resolved in time (i.e., by roughly 10³ time steps) as those in the plots in Figs. 1 and 3.
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In the text

$\begin{figure} \par\resizebox{7.8cm}{!}{\includegraphics[clip]{0327fg5.ps}}\end{figure}$ Figure 5: Evolution of the white dwarf in sequence R4 in the Hertzsprung-Russell diagram. The region with $\log L_{\rm s}/L_{\odot} = 3.4\dots4.2$ and $\log T = 5.46\dots5.48$ represents the epoch from the onset of helium accretion to the first mild helium shell flash (cf. Fig. 4d).
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In the text

$\begin{figure} \par\resizebox{8cm}{!}{\includegraphics[clip]{0327fg6a.ps}}\par\v... ...vspace*{2mm} \resizebox{8cm}{!}{\includegraphics[clip]{0327fg6c.ps}}\end{figure}$ Figure 6: Spin velocity at different white dwarf masses, normalized to the local Keplerian value, as a function of the mass coordinate for RT1, R3 and R4.
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In the text

$\begin{figure} \par\resizebox{7.8cm}{!}{\includegraphics[clip]{0327fg7a.ps}}\par\vspace*{2mm} \resizebox{7.8cm}{!}{\includegraphics[clip]{0327fg7b.ps}}\end{figure}$ Figure 7: Logarithm of the mass fractions of helium and carbon as a function of the mass coordinate (solid line), in the white dwarf models of sequences NR4 ( upper panel) and R4 ( lower panel) at a time when $M_{\rm WD}$ = 1.0305 $\ensuremath {{M}_\odot }$ . The dotted and dashed lines denote the corresponding energy generation rate (right scale) for the $3\alpha$ and $^{12}{\rm C}(\alpha ,\gamma )$ reactions respectively.
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In the text

$\begin{figure} \par\resizebox{8cm}{!}{\includegraphics[clip]{0327fg8.ps}}\end{figure}$ Figure 8: Carbon mass fraction as a function of the mass coordinate for the last computed models of sequences R4 (dashed line) and NR4 (dotted line). The thin solid line corresponds to the initial model. Note that the mass of the helium envelope is only of the order of 10^-4 $\ensuremath {{M}_\odot }$ , which is not resolved in this figure. The sharp peak in the carbon abundance near the surface in each white dwarf model is due to the active $3\alpha$ reaction at the bottom of the helium envelope (cf. Fig. 7).
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In the text

$\begin{figure} \par\resizebox{11.8cm}{!}{\includegraphics[clip]{0327fg9.ps}}\end{figure}$ Figure 9: Evolution of the helium shell source in the sequences NR4 and R4 during the stable shell burning phase, in the plane spanned by the degeneracy parameter $\eta$ and the relative thickness of the shell source $D/r_{\rm s}$ . Here D denotes the thickness of the shell source and $r_{\rm s}$ its radius. Each asterisk and black dot represents one selected stellar model in sequences NR4 and R4, respectively. The white dwarf mass in solar masses and the temperature of the shell source in units of 10⁸ K are indicated for various models. The thin lines separate the stable and unstable regimes, for $T/(10^8~{\rm K}) =$ 2.0 (dotted line), 2.2 (short dashed line), 2.4 (dotted-dashed line), 2.6 (three dotted - dashed line) and 2.8 (long dashed line) according to the analytic stability criterion of Yoon et al. (2004). I.e., helium shell burning is predicted to be stable (unstable) above (below) the lines, while thermal pulses become significant from $M_{\rm WD}\simeq 1.03$ $\ensuremath {{M}_\odot }$ in sequence NR4, and weak thermal pulses appear from $M_{\rm WD} \simeq 1.41$ $\ensuremath {{M}_\odot }$ in sequence R4.
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In the text

$\begin{figure} \par\resizebox{7.6cm}{!}{\includegraphics[clip]{0327fg3a.ps}}\par... ...pace*{3mm} \resizebox{7.6cm}{!}{\includegraphics[clip]{0327fg3c.ps}}\end{figure}$	Figure 3: Same as in Fig. 1 but with $\ensuremath{\dot{M}}$ = $3\times 10^{-7}$ ${M}_{\odot }/\rm {yr}$ (NR2 a), R2 b) and RT2 c)).
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$\begin{figure} \par\resizebox{7.8cm}{!}{\includegraphics[clip]{0327fg5.ps}}\end{figure}$	Figure 5: Evolution of the white dwarf in sequence R4 in the Hertzsprung-Russell diagram. The region with $\log L_{\rm s}/L_{\odot} = 3.4\dots4.2$ and $\log T = 5.46\dots5.48$ represents the epoch from the onset of helium accretion to the first mild helium shell flash (cf. Fig. 4d).
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$\begin{figure} \par\resizebox{8cm}{!}{\includegraphics[clip]{0327fg6a.ps}}\par\v... ...vspace*{2mm} \resizebox{8cm}{!}{\includegraphics[clip]{0327fg6c.ps}}\end{figure}$	Figure 6: Spin velocity at different white dwarf masses, normalized to the local Keplerian value, as a function of the mass coordinate for RT1, R3 and R4.
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