All Figures

$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg01.eps}}} \end{figure}$ Figure 1: Evolution of the orbital periods of selected systems with Z = 0.01, an initial secondary mass of 1.0 $M_\odot$ and initial periods of 0.50, 0.75, 1.00, 1.25, 1.30, 1.35, 1.40, 1.45, 1.50, 1.55, 1.60, 1.65, 1.70, 1.75, 2.0, 2.25, 2.5 and 2.75 days. The symbols mark special points in the evolution: + marks the start of Roche-lobe overflow (RLOF), $\times$ the minimum period, $\bigtriangleup$ the end of RLOF and $\bigcirc$ marks the end of the calculation. The four dotted horizontal lines show the orbital periods of the closest observed LMXBs in globular clusters: 11.4 and 20.6, and in the galactic disk: 41 and 50 min.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg02.eps}}} \end{figure}$ Figure 2: Evolution of the orbital periods of selected systems with Z = 0.01, an initial secondary mass of 1.1 $M_\odot$ and initial periods of 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95, 1.00, 1.25, 1.50, 1.55, 1.60, 1.65, 1.70, 1.75, 2.0, 2.25, 2.5 and 2.75 days. See Fig. 1 for more details.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg03.eps}}} \end{figure}$ Figure 3: Mass fraction of the convective envelope ( $q_{\rm conv}$ ) as a function of the total mass of the donor, for the models with the shortest 9 initial orbital periods in Fig. 2. The numbers in the plot give the initial periods in days for that line. As evolution proceeds towards lower donor masses, the mass faction of the convective envelope increases. For the 5 models with initial periods between 0.5 and 0.7 d, the total mass at which the star becomes fully convective is anti-correlated with the initial period. At initial periods of 0.75 d and longer, the initial increase of the mass fraction of the convective envelope is followed by a decrease.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg04.eps}}} \end{figure}$ Figure 4: Timescales of the models that bracket the bifurcation period for 1.1 $M_\odot$ . Upper panel a): model with $P_{\rm i} = 0.85$ d. Lower panel b): model with $P_{\rm i}=0.90$ d. The line styles represent the different timescales: Solid line: nuclear evolution timescale $(M/M_\odot )/(L/L_\odot )\times 10^{10}$ yr, dashes: magnetic braking timescale $J_{\rm orb}/\dot{J}_{\rm MB}$ , dash-dot: gravitational radiation timescale $J_{\rm orb}/\dot{J}_{\rm GR}$ , dash-dot-dot-dot: mass transfer timescale $M/\dot{M}_{\rm tr}$ . See the text for a discussion.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg05.eps}}} \end{figure}$ Figure 5: Statistics results for the 1.1 $M_\odot$ models. Left panel a): results from the draw of one million random initial periods and times. Each dot represents the orbital period of the selected system at the selected time. Only models that were converging and transferring mass at that time were accepted, about 10.5% of the total number. The peaks at the higher orbital periods are artefacts, caused by interpolation between models with and without mass transfer. Dots below $P = 30~{\rm min}$ are plotted larger for clarity. Right panel b): a histogram displaying the fraction of systems found at a certain orbital period, at any time between 10 and 13 Gyr. The $\log P$ -axis was chosen to be vertical, to correspond to the vertical axis in the left panel. The thick line displays the data corresponding to the horizontal axis, the thin line is theshort-period tail of the same data, multiplied by a factor of 100 inthe horizontal (probability) direction. The dotted horizontal lines are the orbital periods of the four observed LMXBs mentioned in Fig. 1.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg06.eps}}} \end{figure}$ Figure 6: Probability distribution for all models with Z = 0.01. The solid line represents the sum of the distributions of the different masses weighed with the Salpeter birth function, the dash-dotted line assumes a flat distribution in mass. The thin lines below $\log P~(d) = -1.3$ and below $\log P~(d) = -1.7$ are the same data, multiplied with 100 and 1000 respectively. The four vertical, dotted lines show the orbital periods of the four observed LMXBs mentioned in Fig. 1.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg07.eps}}} \end{figure}$ Figure 7: Bifurcation periods and minimum periods as a function of the initial mass for the four metallicities. Upper panel a) the bifurcation period (in hours) between systems that converge and systems that do not converge within a Hubble time. Lower panel b) the minimum period (in minutes) that can be reached within a Hubble time as a function of the initial secondary mass. The different line styles display the different metallicities, as indicated in the upper panel. The data point for Z = 0.0001, $M_{\rm i} = 1.5~M_\odot$ is missing in both panels, because the bifurcation period for these systems is lower than the period at which such a donor fills its Roche lobe at ZAMS.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg08.eps}}} \end{figure}$ Figure 8: Probability distribution of the orbital periods for all models with Z = 0.0001. The characteristics of this plot are the same as in Fig. 6.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg09.eps}}} \end{figure}$ Figure 9: Probability distribution of the orbital periods for all models with Z = 0.002. The characteristics of this plot are the same as in Fig. 6.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg10.eps}}} \end{figure}$ Figure 10: Probability distribution of the orbital periods for all models with Z = 0.02. The characteristics of this plot are the same as in Fig. 6.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg11.eps}}} \end{figure}$ Figure 11: Cumulative plot for the distribution of the orbital periods for all models and all four metallicities. The different line styles represent the different metallicities as indicated in the lower right of the plot. The height of the lines shows the logarithm of the fraction of all probed systems that have an orbital period equal to or lower than the period on the horizontal axis. For all lines, a flat initial mass distribution is used. The dotted vertical lines show the observed orbital periods mentioned in Fig. 1.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg12.eps}}} \end{figure}$ Figure 12: Comparison of our models (dashed line) to the models A25-I25 of PS1 and A25-Z25 of PS2 (solid lines). See the text for details.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg02.eps}}} \end{figure}$	Figure 2: Evolution of the orbital periods of selected systems with Z = 0.01, an initial secondary mass of 1.1 $M_\odot$ and initial periods of 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 0.95, 1.00, 1.25, 1.50, 1.55, 1.60, 1.65, 1.70, 1.75, 2.0, 2.25, 2.5 and 2.75 days. See Fig. 1 for more details.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg08.eps}}} \end{figure}$	Figure 8: Probability distribution of the orbital periods for all models with Z = 0.0001. The characteristics of this plot are the same as in Fig. 6.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg09.eps}}} \end{figure}$	Figure 9: Probability distribution of the orbital periods for all models with Z = 0.002. The characteristics of this plot are the same as in Fig. 6.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg10.eps}}} \end{figure}$	Figure 10: Probability distribution of the orbital periods for all models with Z = 0.02. The characteristics of this plot are the same as in Fig. 6.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\rotatebox{-90}{\includegraphics{1777fg12.eps}}} \end{figure}$	Figure 12: Comparison of our models (dashed line) to the models A25-I25 of PS1 and A25-Z25 of PS2 (solid lines). See the text for details.
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