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$\begin{figure} \psfrag{Helium-star mass (MSun)}[t][c][3][0]{{\sf M$_{\sf He}$ /... ...} \resizebox{8.8cm}{!}{\includegraphics[angle=270]{2824fig4.ps}} \end{figure}$ Figure 1: Mass-loss rates of He stars: a) wind mass-loss rate for a homogeneous He star; b) wind mass-loss rate for a He star at He terminal-age main sequence; c) rough estimate of the mass-loss rate of a star that overflows its Roche lobe on a thermal time scale after completion of core He burning.
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics[clip]{2824fig5.eps}} \end{figure}$ Figure 2: Schematic representation of possible system configurations that are consistent with $\dot{P}/P$ and $\dot{M}$ as observed in Cyg X-3. RLOF solutions give a very narrow range of possible combinations of $m_{\rm a}$ and $m_{\rm d}$ (the two narrow strips in the lower left; the gap is due to the presumed gap between the masses of NSs and those of BHs). For wind-accretion solutions, the range of possible combinations of $m_{\rm a}$ and $m_{\rm d}$ is much larger (hatched areas). Population synthesis shows that RLOF systems with NSs are formed in sufficiently large numbers to produce an observable Cyg-X-3 system. On the other hand, Roche-lobe overflowing BH systems are formed so rarely with P similar to the period of Cyg X-3 that the probability of observing them is negligible. See Figs. 5 and 4 and text.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=15cm,clip]{2824fig7.eps} \end{figure}$ Figure 3: $\dot{M}$ and $\dot{P}/P$ as function of $M_{\rm He}$ for systems with Roche-lobe overflowing He-star donors and compact accretors. Masses $(m_{\rm d}, m_{\rm a})$ at the onset of mass transfer are: (3.0, 5.0), (1.46, 1.4), (1.0, 1.4) $M_\odot$ (from top to bottom). Roche-lobe overflow starts at $P \approx 0.2$ day. In all panels thick solid lines show results of computations. In panels for $\dot{P}/P$ thin solid lines show the limits of observed $\dot{P}/P$ in Cyg X-3. Dotted curves show rough estimates for $\dot{M}$ and $\dot{P}/P$ based on Eq. (3), derived with the approximations to R and L at the terminal-age He main-sequence from Hurley et al. (2000).
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.65cm]{2824fig6.ps} \includ... ...fig2.eps} \includegraphics[angle=-270,width=8.65cm]{2824fig3.eps} \end{figure}$ Figure 4: Current population of core-He-burning He+BH binaries in the Galaxy. Upper panel - distribution in $M_{\rm He} - P$ plane; middle panel - distribution in $M_{\rm BH} - P$ plane; lower panel - distribution in $M_{\rm He} - M_{\rm BH}$ plane. The dash-dotted vertical lines in the upper and lower panel show the lower-mass boundary for He stars identified as WR stars. Systems that satisfy the disk-formation criterion for wind-fed objects (Eq. (4)) are marked by open circles; the subset of them with $3.6 \leq P/{\rm hr} \leq 6.0$ is marked by stars.
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In the text

$\begin{figure} {\includegraphics[angle=270,width=8.8cm,clip]{2824fig8.ps} } \end{figure}$ Figure 5: Current population of core-He-burning He+NS binaries in the Galaxy. The dash-dotted vertical line shows the lower-mass boundary for He stars identified with WR stars. The four dashed lines show the critical periods below which according to criterion (5) disk formation through wind accretion is possible, if v₁₀₀₀ = 1, 1.5, 2, and 3 (highest to lowest), respectively.
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In the text

$\begin{figure} \par {\includegraphics[angle=0,width=8.8cm,clip]{2824fig1.ps} } \end{figure}$ Figure 6: Summary of the evolution of the mass of single stars or components of wide binaries ( top panel) and of stars in binaries experiencing RLOF ( bottom panel). As a function of initial mass, the lines give: the mass at the end of the main-sequence ( $M_{\rm tams}$ , solid line), the initial mass of the He-core ( $M_{\rm core, i}$ , dotted line), the mass just before the supernova explosion or the formation of the white dwarf ( $M_{\rm pre-SN}$ , dashed line), and the mass of the final c.o. ( $M_{\rm comp. obj}$ , black-white-black line). The bottom panel shows the masses for a primary that loses its hydrogen envelope soon after the end of the main sequence, before the He-core burning starts.
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In the text

$\begin{figure} \psfrag{Helium-star mass (MSun)}[t][c][3][0]{{\sf M$_{\sf He}$ /... ...} \resizebox{8.8cm}{!}{\includegraphics[angle=270]{2824fig4.ps}} \end{figure}$	Figure 1: Mass-loss rates of He stars: a) wind mass-loss rate for a homogeneous He star; b) wind mass-loss rate for a He star at He terminal-age main sequence; c) rough estimate of the mass-loss rate of a star that overflows its Roche lobe on a thermal time scale after completion of core He burning.
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$\begin{figure} {\includegraphics[angle=270,width=8.8cm,clip]{2824fig8.ps} } \end{figure}$	Figure 5: Current population of core-He-burning He+NS binaries in the Galaxy. The dash-dotted vertical line shows the lower-mass boundary for He stars identified with WR stars. The four dashed lines show the critical periods below which according to criterion (5) disk formation through wind accretion is possible, if v₁₀₀₀ = 1, 1.5, 2, and 3 (highest to lowest), respectively.
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