All Figures

$\begin{figure} \par\includegraphics[width=12cm,clip]{H3916F11.PS}\par\vspace*{3mm} \includegraphics[width=12cm,clip]{H3916F12.PS} \end{figure}$ Figure 1: Evolution in the H-R diagram of a system with initial component masses $7+1.5 ~ {M_{\hbox{$\odot$ }}}$ and initial orbital period (at ZAMS) of 350 d. Case 2a (upper panel) has two phases of Roche lobe overflow while case 2b (lower panel) has one. In case 2a, after the second Roche lobe overflow the secondary mass has reached $2.1 ~ {M_{\hbox{$\odot$ }}}$ . In case 2b the secondary does not accrete any mass because the post-CE remnant does not fill its Roche lobe again. Symbols, defined in the left-hand side of the figures, represent time intervals on the evolutionary tracks. The crosses correspond to the evolutionary phases A₁ through A₈ described in the text. Note the non-solar chemical composition of the secondary star owing to thermohaline-mixing.
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{H3916F21.PS}\par\vspace*{3mm}% \includegraphics[]{h3916f2b.eps} %\par\end{figure}$ Figure 2: Case 2a evolution of the primary for a system of initially $7+1.5 ~ {M_{\hbox{$\odot$ }}}$ stars and initial orbital period 350 d (see also Fig. 1). Upper panel: the time-variation of mass-loss rate $\dot{M}$ is indicated by the full line from ZAMS until $t=4.88 \times 10^{7}$ yr (point A₅). The evolution in this time interval is the same for both cases 2a and 2b of evolution. The total mass of the primary versus time is denoted by the dot-dashed line while the mass of the CO core $M_{{\rm CO}}$ is shown with the dotted line. Points $\rm A_{1}{-}A_{5}$ are defined in Table 1. Lower panel: Continued detailed diagram for the time evolution of $\dot{M}$ , $M_{{\rm d}}$ and $M_{{\rm CO}}$ after $t=4.88 \times 10^{7}$ yr for the time interval $\rm A_{5}{-}A_{6}$ . During this phase, He burns at a shell and if no enhanced winds play important role, He-rich mass is accreted to the secondary. As a result the secondary is enriched with helium under the thermohaline mixing effect. At a suitable time point A₆ a tidally enhanced wind as described in the text was assumed to overcome the surface shell flashes on the surface of the post-CE remnant of the primary which cause convergence problems to the code and allow the cooling of the star to the WD branch. This artificial wind does not change the long term evolution of the primary.
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In the text

$\begin{figure} \includegraphics[width=12cm,clip]{H3916F3.PS} \end{figure}$ Figure 3: Case 2a evolution of the primary for a system of initially $7+1.5 ~ {M_{\hbox{$\odot$ }}}$ , the time variation of the binary separation (full line) and the corresponding orbital period changes (dot-dashed line).
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In the text

$\begin{figure} \includegraphics[]{h3916f4.eps} %\end{figure}$ Figure 4: As Fig. 2 (lower) but for case 2b. Here the time variation of $\dot{M}$ up to point A₅ is the same as in the upper panel of Fig. 2, for case 2a. However, in this case of evolution we assume tidally enhanced winds to dominate at A₅ so that they prevent the post-CE primary to overfill its Roche lobe after CE evolution. As a result, matter can not be accreted on the secondary, which now retains its solar composition.
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{H3916F5.PS} \end{figure}$ Figure 5: As Fig. 3 but for case 2b.
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{H3916F61.PS}\par\vspace*{3mm} \includegraphics[width=12cm,clip]{H3916F62.PS} \end{figure}$ Figure 6: Case-2a evolution for a post-CE binary with an He enriched donor of 2.1 ${M_{\hbox {$\odot $ }}}$ . The companion is a $0.98~{M_{\hbox{$\odot$ }}}$ CO white dwarf at an orbital period $P_{\rm orb}\approx 1.4~$ d. Upper panel: variation of $P_{{\rm orb}}$ (thick solid line) and $M_{{\rm WD}}$ (thick dashed line) as a function of the secondary mass $M_{{\rm s}}$ . Lower panel: evolution of $\dot{M}$ (thick solid line) and $M_{{\rm WD}}$ (thick dashed line) versus secondary mass. The system is a candidate luminous SSS and possibly a SN Ia. For comparison the evolution of a $2.1 ~ {M_{\hbox{$\odot$ }}}$ solar composition donor is shown with thin lines. In this case the WD does not grow sufficiently to become a SN Ia. The nearly horizontal dotted lines define the region of steady H burning, thick for our case 2a and thin for solar composition.
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{H3916F71.PS}\par\vspace*{3mm} \includegraphics[width=12cm,clip]{H3916F72.PS} \end{figure}$ Figure 7: As Fig. 6 but for case 2b. The post-CE companion maintains its solar composition and mass of $1.5~{M_{\hbox{$\odot$ }}}$ with a $0.94~{M_{\hbox{$\odot$ }}}$ CO white dwarf. Initially $P_{\rm orb}\approx 1.4~$ d. This system does not evolve as a SSS and is not a potential candidate for a SN Ia.
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{H3916F8.PS} \end{figure}$ Figure 8: $E_{{\rm bind}}$ (left axis) and donor's mass (right hand axis) versus time. Indices 1 and 2 denote the two core definitions inside the H-shell ( $M=M_{{\rm H}})$ and inside He-shell burning ( $M=M_{{\rm He}})$ . Note that the time axis is different for the pre-AGB, EAGB and TPAGB.
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In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{H3916F9.PS} \end{figure}$ Figure 9: Final orbital separation after the CE phase (dotted line) as a function of the separation at the onset of the CE phase (left and lower axes). Solid lines are orbital periods (right and upper axes). Results are for five different values of $\alpha _{{\rm CE}}$ from 0.5-4.0. Vertical dashed lines show the boundaries of EAGB evolution. The core mass is the mass inside the H-burning shell $M_{{\rm H}}$ . The critical orbital separation $a_{{\rm cr}}$ and period $P_{{\rm cr}}$ at which the companion star fills its Roche lobe at the end of the CE phase are also given. Systems within the grey area satisfy our criterion for survival of the binary system as described in Sect. 3.1.2.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3916F01.PS}\par\includegraphics[width=8.8cm,clip]{H3916F02.PS} \end{figure}$ Figure 10: Upper panel: minimum CE efficiency parameters $\alpha _{{\rm CE}}$ when the core is just inside the H-burning shell $M_{\rm c} = M_{\rm H}$ . Dashed vertical lines indicate the boundaries of EAGB evolution. Lower panel: minimum $\alpha _{{\rm CE}}$ when the core boundary lies just inside He-burning shell $M_{\rm c} = M_{\rm He}$ .
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In the text

$\begin{figure} \includegraphics[width=12cm,clip]{H3916F3.PS} \end{figure}$	Figure 3: Case 2a evolution of the primary for a system of initially $7+1.5 ~ {M_{\hbox{$\odot$ }}}$ , the time variation of the binary separation (full line) and the corresponding orbital period changes (dot-dashed line).
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$\begin{figure} \par\includegraphics[width=12cm,clip]{H3916F5.PS} \end{figure}$	Figure 5: As Fig. 3 but for case 2b.
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$\begin{figure} \par\includegraphics[width=12cm,clip]{H3916F71.PS}\par\vspace*{3mm} \includegraphics[width=12cm,clip]{H3916F72.PS} \end{figure}$	Figure 7: As Fig. 6 but for case 2b. The post-CE companion maintains its solar composition and mass of $1.5~{M_{\hbox{$\odot$ }}}$ with a $0.94~{M_{\hbox{$\odot$ }}}$ CO white dwarf. Initially $P_{\rm orb}\approx 1.4~$ d. This system does not evolve as a SSS and is not a potential candidate for a SN Ia.
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$\begin{figure} \par\includegraphics[width=12cm,clip]{H3916F8.PS} \end{figure}$	Figure 8: $E_{{\rm bind}}$ (left axis) and donor's mass (right hand axis) versus time. Indices 1 and 2 denote the two core definitions inside the H-shell ( $M=M_{{\rm H}})$ and inside He-shell burning ( $M=M_{{\rm He}})$ . Note that the time axis is different for the pre-AGB, EAGB and TPAGB.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H3916F01.PS}\par\includegraphics[width=8.8cm,clip]{H3916F02.PS} \end{figure}$	Figure 10: Upper panel: minimum CE efficiency parameters $\alpha _{{\rm CE}}$ when the core is just inside the H-burning shell $M_{\rm c} = M_{\rm H}$ . Dashed vertical lines indicate the boundaries of EAGB evolution. Lower panel: minimum $\alpha _{{\rm CE}}$ when the core boundary lies just inside He-burning shell $M_{\rm c} = M_{\rm He}$ .
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