All Figures

$\begin{figure} \par {\includegraphics[width=8.4cm,clip]{0678fg01} } \end{figure}$ Figure 1: The intrinsic flux $f_{\rm {int}}$ as function of metallicity Z for a star with $T_{0}=4500~ \rm {K}$ and an effective gravity $\log g=4.5$ that is irradiated by $f_{\rm {irr}}\approx 1.006$ with an angle of incidence $\beta =47.9\hbox {$^\circ $ }$ , i.e., effectively by $f_{\rm {irr}}\approx 0.674$ . The star is irradiated by its companion with $T_{1}=6 000~ \rm {K}$ and a relative radius of $\frac{R_{1}}{A}=\frac{1}{\sqrt{\pi }}$ . The data shown are taken from Hameury & Ritter (1997) (asterisk) and Nordlund & Vaz (1990, Table 1): grey atmospheres (crosses), and non-grey atmospheres irradiated by a Planck spectrum (triangles) and a real stellar spectrum (diamonds).
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In the text

$\begin{figure} \par {\includegraphics[width=8.4cm,clip]{0678fg02} } \end{figure}$ Figure 2: The intrinsic flux $f_{\rm {int}}$ as function of the mixing length l in units of the pressure scale height $H_{\rm {P}}$ . Otherwise see Fig. 1.
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In the text

$\begin{figure} \par {\includegraphics[width=8.4cm,clip]{0678fg03} } \end{figure}$ Figure 3: The intrinsic flux $f_{\rm {int}}$ as function of the angle of incidence $\beta$ . Otherwise see Fig. 1.
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In the text

$\begin{figure} \par {\includegraphics[width=8.4cm,clip]{0678fg04} } \end{figure}$ Figure 4: $f_{\rm {int}}$ for models Nos. 1-4 and 6 of Table 1 (solid, long-dashed, short-dashed, dash-dotted and dot-dash-dotted line, respectively).
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In the text

$\begin{figure} \par {\includegraphics[width=8.8cm,clip]{0678fg05} } \end{figure}$ Figure 5: Irradiation geometry. A surface element E is irradiated by the source with an angle of incidence $\beta$ to the surface normal.
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In the text

$\begin{figure} \begin{displaymath} \begin{CD} \hspace{1.5cm}-\dot{M}_2 @>{\quad{... ...d{}\rm {decreases}\quad{}}<< F_{\rm {irr}} \end{CD}\end{displaymath}\end{figure}$ Figure 6: Schematic diagram of the irradiation feedback mechanism at turn on of mass transfer.
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In the text

$\begin{figure} \par {\includegraphics[width=8.5cm,clip]{0678fg06} } \end{figure}$ Figure 7: $s'_{\rm {cf}}$ (Eq. (58)) for stellar models Nos. 1-4 and 6 of Table 1 (solid, long-dashed, short-dashed, dash-dotted and dot-dash-dotted line, respectively) and also s'_k for k=1 (Eq. (60), dotted line).
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In the text

$\begin{figure} \par {\includegraphics[width=8.5cm,clip]{0678fg07} } \end{figure}$ Figure 8: $s'_{\rm {ps}}$ (Eq. (57)) for the same stellar models as in Fig. 7. For comparison of the point source with the constant flux model also s'_kfor k=1 (Eq. (60)) is shown.
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In the text

$\begin{figure} \par {\includegraphics[width=8.6cm,clip]{0678fg08} } \end{figure}$ Figure 9: s' for a CV with an unevolved $0.5~ M_{\hbox{$\odot$ }}$ MS star (No. 2 of Table 1) and an $0.8~ M_{\hbox{$\odot$ }}$ white dwarf for the point source and the constant flux model (solid and dotted line). s' is compared to f for models 1-4listed in Table 2 (dot-dash-dotted, long-dashed, dash-dotted and short-dashed line, respectively). The mass transfer is unstable and undergoes cycles if s'>f which is only the case in a certain interval $\left[ \left\langle f_{\rm {irr,min}}\right\rangle\!, \left\langle f_{\rm {irr,max}}\right\rangle \right]$ whose limits depend on $\alpha$ . Otherwise, the system is stable.
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In the text

$\begin{figure} \par {\includegraphics[width=8.5cm,clip]{0678fg09} } \end{figure}$ Figure 10: Mass transfer rate $-\dot{M}_{2}~ \left[ M_{\hbox{$\odot$ }}/\rm {yr}\right]$ from a slightly evolved $0.5~ M_{\hbox{$\odot$ }}$ MS star with an age of ${\sim} 10^{10}~ \rm {yr}$ and $X_{\rm {c}}\approx 0.62$ onto an $0.8~ M_{\hbox{$\odot$ }}$ white dwarf for the point source model as function of orbital period $P~ \left[ \rm {h}\right]$ . System parameters: $\bar{\eta }=0$ , $\nu =q$ , $\alpha =0.3$ , and $\dot{J}=5\dot{J}_{\rm {grav}}$ (solid line). The dotted line shows the mass transfer rate for the same system without irradiation feedback. Both computations have been stopped beyond the minimum period at $M_{2}=0.04~ M_{\hbox{$\odot$ }}$ .
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In the text

$\begin{figure} \par {\includegraphics[width=8.5cm,clip]{0678fg10} } \end{figure}$ Figure 11: Same as Fig. 10 but for gravitational braking only.
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In the text

$\begin{figure} \par {\includegraphics[width=8.7cm,clip]{0678fg11} } \end{figure}$ Figure 12: Mass transfer rate $-\dot{M}_{2}~ \left[ M_{\hbox{$\odot$ }}/\rm {yr}\right]$ as function of time $t~ \left[ \rm {yr}\right]$ for the same system as in Fig. 10. The computation stops at $M_{2}\approx 0.34~ M_{\hbox{$\odot$ }}$ .
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In the text

$\begin{figure} \par {\includegraphics[width=8.6cm,clip]{0678fg12} } \end{figure}$ Figure 13: Mass transfer rate $-\dot{M}_{2}~ \left[ M_{\hbox{$\odot$ }}/\rm {yr}\right]$ from a slightly evolved $1~ M_{\hbox{$\odot$ }}$ MS star ( $X_{\rm {c}}\approx 0.62$ ) onto a $0.8~ M_{\hbox{$\odot$ }}$ white dwarf for the point source model as function of orbital period $P~ \left[ \rm {h}\right]$ . System parameters: $\bar{\eta }=0$ , $\nu =q$ , $\alpha =0.3$ , and strong braking according to Verbunt & Zwaan (1981). The dotted line shows the evolution without irradiationfeedback.
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In the text

$\begin{figure} \par {\includegraphics[width=8.8cm,clip]{0678fg13} } \end{figure}$ Figure 14: Mass transfer rate $-\dot{M}_{2}~ \left[ M_{\hbox{$\odot$ }}/\rm {yr}\right]$ from an unevolved $0.5~ M_{\hbox{$\odot$ }}$ MS star onto an $0.8~ M_{\hbox{$\odot$ }}$ white dwarf for conservative mass transfer $\left( \bar{\eta }=1\right)$ , $\dot{J}=\dot{J}_{\rm {grav}}$ , and the constant flux model for $\alpha =0.02$ , 0.04, 0.1, 0.2, 0.4, and 1.0 (dotted, dot-dash-dotted, dash-dotted, short-dashed, long-dashed, and solid line, respectively) as function of time $t~ \left[ \rm {yr}\right]$ .
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In the text

$\begin{figure} \par {\includegraphics[width=8.6cm,clip]{0678fg14} } \end{figure}$ Figure 15: s' for a CV with an highly evolved $0.45~ M_{\hbox{$\odot$ }}$ remnant of thermal timescale mass transfer (No. 4 of Table 1) and an $0.86~ M_{\hbox{$\odot$ }}$ white dwarf for the point source and constant flux model (solid and dotted line). s' is compared to f for $\bar{\eta }=0.25$ and $\alpha =0.1$ , 0.3, and 1.0 (short-dashed, dash-dotted, and dot-dash-dotted line, respectively).
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In the text

$\begin{figure} \par {\includegraphics[width=8.5cm,clip]{0678fg15} } \end{figure}$ Figure 16: Mass transfer rate $-\dot{M}_{2}~ \left[ M_{\hbox{$\odot$ }}/\rm {yr}\right]$ from an evolved initially $1.6~ M_{\hbox{$\odot$ }}$ MS star (No. 4 of Table 1) onto an initially $0.6~ M_{\hbox{$\odot$ }}$ white dwarf for the point source model as function of orbital period $P~ \left[ \rm {h}\right]$ . System parameters: $\bar{\eta }=0.25$ , $\nu =q$ , $\alpha =0.3$ , and strong braking according to Verbunt & Zwaan (1981). The dotted line shows the evolution without irradiation feedback. The onset of mass transfer cycles occurs at $M_{1}\approx 0.91~ M_{\hbox{$\odot$ }}$ and $M_{2}\approx 0.26~ M_{\hbox{$\odot$ }}$ .
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In the text

$\begin{figure} \par {\includegraphics[width=8.6cm,clip]{0678fg16} } \end{figure}$ Figure 17: s' for a CV with an $0.8~ M_{\hbox{$\odot$ }}$ giant (No. 6 of Table 1) and an $1.2~ M_{\hbox{$\odot$ }}$ white dwarf for the point source and the constant flux model (solid and dotted line). s' is compared to f for $\bar{\eta }=0$ and $\alpha =0.1$ , 0.3, and 1.0 (short-dashed, dash-dotted, and dot-dash-dotted line,respectively).
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In the text

$\begin{figure} \par {\includegraphics[width=8.6cm,clip]{0678fg17} } \end{figure}$ Figure 18: s' for an LMXB with an unevolved $0.8~ M_{\hbox{$\odot$ }}$ MS star (No. 3 of Table 1) and an initially $1.4~ M_{\hbox{$\odot$ }}$ NS for the point source and the constant flux model (solid and dotted line). s' is compared to ffor $\bar{\eta }=1$ and $\alpha =0.01$ , 0.1, and 1.0 (short-dashed, dash-dotted, and dot-dash-dotted line, respectively).
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In the text

$\begin{figure} \par {\includegraphics[width=8.6cm,clip]{0678fg18} } \end{figure}$ Figure 19: s' for an LMXB with an $0.6~ M_{\hbox{$\odot$ }}$ remnant of thermal timescale mass transfer (No. 5 of Table 1) and an initially $1.4~ M_{\hbox{$\odot$ }}$ NS for the point source and the constant flux model (solid and dotted line). s' is compared to f for $\bar{\eta }=1$ and $\alpha =0.01$ , 0.1, and 1.0 (short-dashed, dash-dotted, and dot-dash-dotted line, respectively).
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In the text

$\begin{figure} \par {\includegraphics[width=8.6cm,clip]{0678fg19} } \end{figure}$ Figure 20: s' for an LMXB with an $0.8~ M_{\hbox{$\odot$ }}$ giant (No. 6 of Table 1) and an initially $1.4~ M_{\hbox{$\odot$ }}$ NS for the point source and the constant flux model (solid and dotted line). s' is compared to f for $\bar{\eta }=1$ and $\alpha =0.01$ , 0.1, and 1.0(short-dashed, dash-dotted, and dot-dash-dotted line,respectively).
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In the text

$\begin{figure} \par {\includegraphics[width=8.5cm,clip]{0678fg20} } \end{figure}$ Figure 21: Mass transfer rate $-\dot{M}_{2}~ \left[ M_{\hbox{$\odot$ }}/\rm {yr}\right]$ from an evolved ( $X_{\rm {c}}\approx 0.66$ ) initially $0.8~ M_{\hbox{$\odot$ }}$ MS star onto an initially $1.4~ M_{\hbox{$\odot$ }}$ neutron star for the point source model as function of orbital period $P~ \left[ \rm {h}\right]$ . System parameters: $\bar{\eta }=1$ , $\alpha =0.01$ , and strong braking according to Verbunt & Zwaan (1981). The dotted line shows the evolution without irradiation feedback.
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In the text

$\begin{figure} \par {\includegraphics[width=8.5cm,clip]{0678fg21} } \end{figure}$ Figure 22: Mass transfer rate $-\dot{M}_{2}~ \left[ M_{\hbox{$\odot$ }}/\rm {yr}\right]$ from an evolved, initially $3.0~ M_{\hbox{$\odot$ }}$ MS star (No. 5 of Table 1) onto an initially $1.4~ M_{\hbox{$\odot$ }}$ neutron star for the point source model and $\alpha =0.1$ as function of orbital period $P~ \left[ \rm {h}\right]$ . For this computation $\bar{\eta }=\eta =1$ has been used as long as the Eddington accretion rate of the neutron star $\left( 2\times 10^{-8}~ \dot{M}_{\hbox{$\odot$ }}/\rm {yr}\right)$ is not exceeded, otherwise $\bar{\eta }=\eta <1$ . The dotted line shows the evolution of the same system without irradiation feedback.
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In the text

$\begin{figure} \par {\includegraphics[width=8.6cm,clip]{0678fg22} } \end{figure}$ Figure 23: Mass transfer rate $-\dot{M}_{2}~ \left[ M_{\hbox{$\odot$ }}/\rm {yr}\right]$ from an $0.8~ M_{\hbox{$\odot$ }}$ giant (No. 6 of Table 1) onto an initially $1.4~ M_{\hbox{$\odot$ }}$ neutron star for the point source model, $\bar{\eta }=1$ , and $\alpha =0.1$ as function of orbital period $P~ \left[ \rm {d}\right]$ . The dotted line shows the evolution of the same system without irradiation feedback.
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In the text

$\begin{figure} \par {\includegraphics[width=8.4cm,clip]{0678fg23} } \end{figure}$ Figure 24: Same as Fig. 23 but $-\dot{M}_{2}$ as function of time $t~ \left[ \rm {yr}\right]$ .
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In the text

$\begin{figure} \par {\includegraphics[width=8.4cm,clip]{0678fg02} } \end{figure}$	Figure 2: The intrinsic flux $f_{\rm {int}}$ as function of the mixing length l in units of the pressure scale height $H_{\rm {P}}$ . Otherwise see Fig. 1.
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$\begin{figure} \par {\includegraphics[width=8.4cm,clip]{0678fg03} } \end{figure}$	Figure 3: The intrinsic flux $f_{\rm {int}}$ as function of the angle of incidence $\beta$ . Otherwise see Fig. 1.
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$\begin{figure} \par {\includegraphics[width=8.4cm,clip]{0678fg04} } \end{figure}$	Figure 4: $f_{\rm {int}}$ for models Nos. 1-4 and 6 of Table 1 (solid, long-dashed, short-dashed, dash-dotted and dot-dash-dotted line, respectively).
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$\begin{figure} \par {\includegraphics[width=8.8cm,clip]{0678fg05} } \end{figure}$	Figure 5: Irradiation geometry. A surface element E is irradiated by the source with an angle of incidence $\beta$ to the surface normal.
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$\begin{figure} \begin{displaymath} \begin{CD} \hspace{1.5cm}-\dot{M}_2 @>{\quad{... ...d{}\rm {decreases}\quad{}}<< F_{\rm {irr}} \end{CD}\end{displaymath}\end{figure}$	Figure 6: Schematic diagram of the irradiation feedback mechanism at turn on of mass transfer.
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$\begin{figure} \par {\includegraphics[width=8.5cm,clip]{0678fg06} } \end{figure}$	Figure 7: $s'_{\rm {cf}}$ (Eq. (58)) for stellar models Nos. 1-4 and 6 of Table 1 (solid, long-dashed, short-dashed, dash-dotted and dot-dash-dotted line, respectively) and also s'_k for k=1 (Eq. (60), dotted line).
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$\begin{figure} \par {\includegraphics[width=8.5cm,clip]{0678fg07} } \end{figure}$	Figure 8: $s'_{\rm {ps}}$ (Eq. (57)) for the same stellar models as in Fig. 7. For comparison of the point source with the constant flux model also s'_kfor k=1 (Eq. (60)) is shown.
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$\begin{figure} \par {\includegraphics[width=8.5cm,clip]{0678fg10} } \end{figure}$	Figure 11: Same as Fig. 10 but for gravitational braking only.
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$\begin{figure} \par {\includegraphics[width=8.7cm,clip]{0678fg11} } \end{figure}$	Figure 12: Mass transfer rate $-\dot{M}_{2}~ \left[ M_{\hbox{$\odot$ }}/\rm {yr}\right]$ as function of time $t~ \left[ \rm {yr}\right]$ for the same system as in Fig. 10. The computation stops at $M_{2}\approx 0.34~ M_{\hbox{$\odot$ }}$ .
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$\begin{figure} \par {\includegraphics[width=8.6cm,clip]{0678fg16} } \end{figure}$	Figure 17: s' for a CV with an $0.8~ M_{\hbox{$\odot$ }}$ giant (No. 6 of Table 1) and an $1.2~ M_{\hbox{$\odot$ }}$ white dwarf for the point source and the constant flux model (solid and dotted line). s' is compared to f for $\bar{\eta }=0$ and $\alpha =0.1$ , 0.3, and 1.0 (short-dashed, dash-dotted, and dot-dash-dotted line,respectively).
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$\begin{figure} \par {\includegraphics[width=8.6cm,clip]{0678fg17} } \end{figure}$	Figure 18: s' for an LMXB with an unevolved $0.8~ M_{\hbox{$\odot$ }}$ MS star (No. 3 of Table 1) and an initially $1.4~ M_{\hbox{$\odot$ }}$ NS for the point source and the constant flux model (solid and dotted line). s' is compared to ffor $\bar{\eta }=1$ and $\alpha =0.01$ , 0.1, and 1.0 (short-dashed, dash-dotted, and dot-dash-dotted line, respectively).
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$\begin{figure} \par {\includegraphics[width=8.6cm,clip]{0678fg18} } \end{figure}$	Figure 19: s' for an LMXB with an $0.6~ M_{\hbox{$\odot$ }}$ remnant of thermal timescale mass transfer (No. 5 of Table 1) and an initially $1.4~ M_{\hbox{$\odot$ }}$ NS for the point source and the constant flux model (solid and dotted line). s' is compared to f for $\bar{\eta }=1$ and $\alpha =0.01$ , 0.1, and 1.0 (short-dashed, dash-dotted, and dot-dash-dotted line, respectively).
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$\begin{figure} \par {\includegraphics[width=8.6cm,clip]{0678fg19} } \end{figure}$	Figure 20: s' for an LMXB with an $0.8~ M_{\hbox{$\odot$ }}$ giant (No. 6 of Table 1) and an initially $1.4~ M_{\hbox{$\odot$ }}$ NS for the point source and the constant flux model (solid and dotted line). s' is compared to f for $\bar{\eta }=1$ and $\alpha =0.01$ , 0.1, and 1.0(short-dashed, dash-dotted, and dot-dash-dotted line,respectively).
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$\begin{figure} \par {\includegraphics[width=8.4cm,clip]{0678fg23} } \end{figure}$	Figure 24: Same as Fig. 23 but $-\dot{M}_{2}$ as function of time $t~ \left[ \rm {yr}\right]$ .
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