VLT multi-object spectroscopy of 33 eclipsing binaries in the Small Magellanic Cloud - New distance and depth of the SMC, and a record-breaking apsidal motion

P. North; R. Gauderon; F. Barblan; F. Royer

doi:10.1051/0004-6361/200810284

Free Access

This article has an erratum: [erratum]

Issue		A&A Volume 520, September-October 2010


Article Number		A74
Number of page(s)		57
Section		Extragalactic astronomy
DOI		https://doi.org/10.1051/0004-6361/200810284
Published online		05 October 2010

Online Material

Table 11: Orbital parameters.

Table 12: Wilson-Devinney analysis, as obtained on the basis of both photometry and spectroscopy.

Table 13: Astrophysical parameters for the primary components.

Table 14: Astrophysical parameters for the secondary components.

Table 15: Distance determination.

Table 16: Light curves: ratio of the primary minimum to the rms (I-band), rms scatters and minimum chi-squared values from WD/PHOEBE code.

Table 17: Radial velocity curves: rms scatters.

$\begin{figure} \par\includegraphics[width=15cm,clip]{10284fg17.eps} \end{figure}$	Figure 17: I-band light curves with $\rm O{-}C$ residuals. See text for comments on individual stars.
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$\begin{figure} \par\includegraphics[width=15cm,clip]{10284fg18.eps} \end{figure}$	Figure 18: Same as Fig. 17, for 12 more stars.
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$\begin{figure} \par\includegraphics[width=15cm,clip]{10284fg19.eps} \end{figure}$	Figure 19: Same as Fig. 17, for nine more stars.
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$\begin{figure} \par\includegraphics[width=15cm,clip]{10284fg20.eps} \end{figure}$	Figure 20: Radial velocity data and best-fitting RV curves.The $\rm O{-}C$ residuals are shown with a different arbitrary offset for each component. See text for comments on individual stars.
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$\begin{figure} \par\includegraphics[width=15cm,clip]{10284fg21.eps} \end{figure}$	Figure 21: Same as Fig. 20, for 12 more stars.
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$\begin{figure} \par\includegraphics[width=15cm,clip]{10284fg22.eps} \end{figure}$	Figure 22: Same as Fig. 20, for nine more stars.
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$\begin{figure} \par\includegraphics[width=15cm,clip]{10284fg23.eps} \end{figure}$	Figure 23: Mass-surface gravity diagrams: the positions of the primary and the secondary components are indicated by filled and open symboles, respectively. The lines ares isochrones from Charbonnel et al. (1993) at Z = 0.004, with ages of 3, 5, 10, 20, 30, 40, 50 and 100 Myr. See text for comments on individual stars.
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$\begin{figure} \par\includegraphics[width=15cm,clip]{10284fg24.eps} \end{figure}$	Figure 24: Same as Fig. 23, for 12 more stars.
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$\begin{figure} \par\includegraphics[width=15cm,clip]{10284fg25.eps} \end{figure}$	Figure 25: Same as Fig. 23, for nine more stars.
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$\begin{figure} \par\includegraphics[width=15cm,clip]{10284fg26.eps} \end{figure}$

Figure 26:

HR diagrams: the positions of the primary and the secondary components are indicated by filled and open symbols, respectively. The primary is the component with the larger mass. The evolutionary tracks from Charbonnel et al. (1993) at Z = 0.004, corresponding to the observed masses, are indicated by solid (primary) and dashed black lines (secondary). Since these authors adopt a helium content Y=0.24+3 $\times$ $\Delta Z$ , the helium content of these models is Y=0.252. The oblique line corresponds to the ZAMS. The bold segments on the ZAMS, at the departure point of the evolutionary tracks, indicate the ${\pm }1\sigma$ error on the mass. The red tracks and ZAMS correspond to a poorer metalicity Z=0.001 (Schaller et al. 1992) and a helium content Y=0.243. The green tracks are interpolated from the Z=0.004 models of Claret & Gimenez (1998) for a helium content Y=0.28; thus, they show the effect of a helium enhancement $\Delta Y=0.028$ relative to the tracks of Charbonnel et al. (1993). See text for comments on individual stars.

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$\begin{figure} \par\includegraphics[width=15cm,clip]{10284fg27.eps} \end{figure}$	Figure 27: Same as Fig. 26, for 12 more stars.
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$\begin{figure} \par\includegraphics[width=15cm,clip]{10284fg28.eps} \end{figure}$	Figure 28: Same as Fig. 26, for nine more stars.
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Appendix A: The individual binaries

Each system is discussed thoroughly in this section. We give details concerning the light-curve solution, the radial-velocity solution, the temperature and luminosity-ratio determinations and the characteristics of the spectra. Also discussed are the positions of the components in the mass-surface gravity plane and the temperature-luminosity (HR) diagram. A review of the distances and collective properties of the whole sample of 33 binaries is given in Sect. 4. Except where otherwise stated, we mean the I-band light curve when we refer to the light curve of a specific system.

A.1 4 110409

With a difference of 0.04 mag in the brightness level between phase 0.25 and phase 0.75, this semi-detached system displays the most asymmetric light curve among all systems studied here. The light curve is bright ( $I^{{\rm q}} < 16$ mag) and of high quality, with a low rms scatter combined with a deep primary eclipse ( $\Delta I_{{\rm min I}} / \sigma_I$ $\sim$ 65). This EB-type light curve shows a relatively strong depression occurring just before the primary minimum. Actually, this is strong evidence for absorption by a gas stream stemming from the (inner) L1 Lagrangian point and seen in projection against the primary surface (HHH05). As a consequence, the use of a ``simple'' symmetric model for the light-curve fit is not satisfactory, resulting in a rather poor fit despite the intrinsic quality of the observations. Therefore, this solution was subsequently improved by adding a cool spot on the equator of the primary component (see Sect. 3.7). The parameters of the spot are: a colatitude of $\pi/2$ rad (fixed), a longitude of 0.569 rad, an angular radius of 0.3 rad and a temperature factor of 0.6, i.e. the effective temperature of the spot is 0.6 that of the rest of the stellar surface. Although this new synthetic light curve gives a far more satisfactory fit, the $\rm O{-}C$ curve reveals that this system is certainly more complex than this ``one circular cool spot'' model. Actually, there are still some discrepancies at the bottom of the eclipses and just after the secondary minimum. Nevertheless, this model is certainly sufficient to reliably set the inclination, the brightness ratio of the components and the maximum out-of-eclipse flux. On the finding chart, the image of this star is slightly elongated in the EW direction, suggesting a blend with another, fainter star, which would lie $1\hbox{$^{\prime\prime}$ }$ or slightly farther away to the West. Nevertheless, no clear sign of a third light is seen in the lightcurve.

The RV curves are well constrained with 11 out-of-eclipse spectra and notably observations close to phase 0.75. This system was previously studied by HHH05. There are significant differences between their RV parameters and ours. Our RV semi-amplitudes are 135 and 259 km s^-1, to be compared to their values of 160 and 247 km s^-1. Besides a lower S/N and resolving power than us, in this particular case the discrepancy is certainly due to their admitted lack of observations close to the quadratures. Consequently, our value for the mass ratio, q = 0.52, is certainly more secure than theirs (0.65).

We found a spectroscopic B luminosity ratio of 1.45. This is higher than the photometric value (1.29), perhaps because of the large distortion of the Roche lobe filling companion. Interestingly, the brighter, i.e. primary, component has lower monochromatic luminosities than the secondary component: even though the primary has a higher bolometric luminosity, it emits mostly in the UV part of the spectrum, so that its I luminosity, for instance, is lower than for the secondary.

The most interesting parts of the separated spectra of both components are presented in Fig. A.1. As a consequence of the low B luminosity of the primary, the spectrum of the latter is the noisier of the pair. Not surprisingly, in both spectra the most prominent features are the H I and He I lines. It is tempting to identify a number of features in the primary spectrum with the C II 4267, O II 4276-4277, Si III 4553, Si IV 4089 and Si IV 4116 lines. Nevertheless, both the lack of positive identification of the He II 4542 line for a $\sim$ 14 $\mathcal{M}_{\odot}$ star and the noisy profile of the He I lines mean that one must be careful in not over-interpreting a spectrum of rather poor quality. The better secondary spectrum displays cleaner features. The He I 4471 and Mg II 4481 lines allow us to secure the temperature of the secondary.

By fixing the photometric temperature and B luminosity ratios, a least-squares fit of the 11 out-of-eclipse spectra provided a primary temperature very close to 32 500 K, that is to say 7000 K more than what was determined by HHH05.

Both mass- $\log g$ and the HR diagrams are typical of a massive Algol-type binary. The brighter and more massive component of the system appears to be close to the zero-age main sequence (ZAMS), while the secondary component is larger and far more luminous than a non-evolved star of the same mass.

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{10284fgA1a.eps}\hspace*{3mm} \includegraphics[width=8.5cm,clip]{10284fgA1b.eps} \end{figure}$

Figure A.1:

Sections of the separated spectra of the primary and secondary components of the binary 4 110409. The scale on the vertical axis is adapted to the size of the features in each section. The red line represents the best-fit synthetic spectrum shifted to the systemic velocity. Besides prominent H I and He I lines, Mg II and Si III lines are visible in the spectrum of the secondary. The spectrum of the primary is far less convincing; nevertheless Si IV lines seem to be present next to H $\delta$ .

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A.2 4 113853

The best fit was obtained with a semi-detached model. Because of a moderate rms scatter (0.017) combined with shallow eclipses ( $\sim$ 0.18 mag) if not purely ellipsoidal variations, the light curve of this binary is one of the poorest of the whole sample. This low amplitude is due to a low inclination ( $\sim$ 60 $\hbox {$^\circ $ }$ ). The $\rm O{-}C$ curve reveals that the profiles of the eclipses are not perfectly symmetrical. The quality of the data is not sufficient, though, to trace the possible astrophysical cause of this asymmetry. On the finding chart, the star seems fairly well isolated.

Despite only seven out-of-eclipse spectra, the RV curves are rather well constrained with observations close to both quadratures.

The S/N of the composite spectra are low (25-65) and there is a sizeable nebular emission in the Balmer lines. Because of the lack of metallic lines and the severe contamination of the Balmer lines by nebular emission, which hinders the ``disentangling'' procedure, the separated spectra of the components were not used. The least-squares fit was performed, letting both temperatures and the B luminosity ratio free to converge. It provided a temperature ratio remarkably close to the photometric one, and a spectroscopic B luminosity ratio of 0.68, which also perfectly agreed with the photometric ratio (0.68). Thus, fixing the temperature and luminosity ratios to the photometric values was unnecessary for determining a reliable temperature of the primary.

Both the mass- $\log g$ and the HR diagrams show an evolved system with a primary component seemingly half-way between the ZAMS and the terminal-age main sequence (TAMS). On the HR diagram the primary lies much higher than the evolutionary track corresponding to its mass. Whether this is due to a temperature overestimate (linked e.g. with an underestimated sky background) or to some evolutionary effect remains to be examined. Besides, the distance modulus perfectly agrees with the currently accepted value for the SMC.

A.3 4 117831

This faint system has a low-to-medium quality light curve of the EA type. There is a slight ellipsoidal variation between the eclipses, and the latter have a similar depth ( $\sim$ 0.4 mag). This is a close detached system with similar components. The finding chart suggests a possible slight blend with a fainter star located some $1\hbox{$^{\prime\prime}$ }$ to the East of the system. No clear sign of a third light is seen in the lightcurves though.

The RV curves are well constrained with 12 out-of-eclipse spectra and observations close to phase 0.25 and phase 0.75. The mass ratio close to one (q = 0.98) is indicative of a binary with ``twin'' components.

The separated spectra have a quality too poor to see any useful metallic line. The Mg II 4481 and C II 4267 are barely visible. The separation of the Balmer lines was hindered by the strong emission. A first least-squares fit provided both temperatures and a poorly constrained spectroscopic B luminosity ratio of 0.97 $\pm$ 0.11. The WD code converged to a higher luminosity ratio (1.17 $\pm$ 0.05), even when we tried to minimize it by fixing the potential of the primary. The temperature of the primary was finally set by a fit where the ratio of temperatures was fixed to the photometric value, and the luminosity ratio assumed equal to one. The small number of photometric data in the minima, especially the primary one, probably makes the photometric luminosity ratio unreliable and explains why the radius of the primary component appears slightly smaller than that of the secondary one.

According to the mass- $\log g$ diagram, the age of the system is about 50 Myr, assuming the standard SMC metalicity Z=0.004. The positions of both components in the HR diagram agree to within the error bars with the evolutionary tracks.

This system was studied by Wyithe et al. 2002 (see Table 6). Their results were not constrained by spectroscopy, thus it is not surprising that they found a very different solution. They considered this system as a semi-detached binary with a photometric mass ratio of 0.157. Our spectroscopic results completely rule out that model.

A.4 4 121084

This system displays deep eclipses (>0.6 mag) of similar depth. A slight ellipsoidal variation is visible. This is clearly a close detached system with slightly distorted twin components. No clear sign of crowding is seen on the finding chart, except possibly with very faint neighbor stars.

The RV curves are well constrained with nine out-of-eclipse observations regularly distributed around the quadratures.

The composite spectra are polluted by strong nebular emission in both H $\gamma$ and H $\delta$ lines. Nevertheless, the widely separated Balmer lines allow a reliable temperature and luminosity ratio determination. The separated spectra are useful to confirm the rather high $V_{{\rm rot}} \sin i$ values of the components. Not surprisingly, no metallic lines are visible because of the moderate S/N combined with fast rotational velocities. The potential of the primary was fixed so that the luminosity ratio given by the WD code matched the spectroscopic one. The temperature of the primary was obtained by fixing the temperature ratio to the photometric one.

Both stars lie on the ZAMS, both in the mass- $\log g$ and HR diagrams. On the HR diagram, however, they are clearly more luminous and hotter than their expected positions for a metalicity Z=0.004. They would better agree with the ZAMS and evolutionary tracks for Z=0.001, as many other systems do. Moving the representative points to the their expected positions for Z=0.004 would require a 2000 K decrease in effective temperature; that seems high, but the residuals between the observed and synthetic composite spectra show only very subtle changes. Only a modest systematic effect might be responsible.

A.5 4 121110

The medium-to-high quality light curve shows a deep ( $\sim$ 0.5 mag) primary eclipse. A slight ellipsoidal variation is visible between the eclipses. This is again a close detached system with slightly distorted components. No star closer than $3\hbox{$^{\prime\prime}$ }$ is seen on the finding chart, except for a very faint one lying about $2\hbox{$^{\prime\prime}$ }$ away to the SW.

The RV curves are well constrained with 11 out-of-eclipse spectra.

There is strong nebular emission in both Balmer lines. The spectroscopic B luminosity ratio (0.415 $\pm$ 0.047) nicely agrees with the photometric one (0.424), without any need for fixing the potential of the primary. The temperature of the primary was fitted after fixing the temperature and luminosity ratios to their photometric values, as ususal. The Si III 4553 line is clearly visible on the separated spectrum of the primary. The lack of Mg II 4481 confirms the relatively high temperature of the primary. The spectrum of the secondary is too noisy for the identification of metallic lines.

On the mass- $\log g$ diagram, the stars match an isochrone corresponding to about 7-8 Myr. In the HR diagram, the positions of both components are above the Z=0.004 evolutionary tracks but are consistent with the lower metalicity ones (Z=0.001). Increasing the helium content would also help to reconcile their positions with the evolutionary tracks, unless a systematic effect raises the apparent effective temperatures.

A.6 4 121461

This is an eccentric system with two (relatively) widely separated components. Both eclipses are very similar in depth and width. With $I^{{\rm q}} \sim 17.9$ mag, this is one of the faintest systems in our sample. Nevertheless, the finding chart indicates no crowding problem whatsoever. No significant apsidal motion was found on the basis of photometry. An analysis with the EBOP code shows that the $\omega_{0}$ value depends critically on the $e\sin\omega_0$ quantity, which is poorly constrained, while the more robust $e\cos\omega_0$ quantity is such that $\cos\omega_0\simeq 0.75$ and thus does not constrain $\omega_{0}$ very tightly. Figure A.2 suggests a marginal decrease of $e\cos\omega_0$ with time which, if real, could only be due to gravitational perturbations from a third body, because $\dot{\omega}< 0$ , while pure tidal effects always result in $\dot{\omega}> 0$ . We have assumed no apsidal motion.

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{10284fgA2.eps} \end{figure}$	Figure A.2: Variation with time of the $e\cos\omega$ quantity of the system 4 121461, determined with the EBOP code on the basis of the I magnitudes grouped in four time intervals. The solid line corresponds to a hardly significant negative apsidal motion, while the dashed horizontal line indicates no apsidal motion, for e=0.185 and $\omega _0=222.8^\circ$ .
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This system is one of the two in our sample with 16 out-of-eclipse spectra, of which 15 were used (the eighth has too poor SNR). There is a sufficient number of observations close to the quadratures.

The composite spectra are very noisy. The separated spectra are of a very poor quality, with no exploitable metallic lines. There is strong nebular emission. Letting the temperature of both components free to converge (together with the B luminosity ratio) resulted in very uncertain values, so we fixed the temperature ratio to the photometric one to estimate the temperature of the primary. The rotational velocities were fixed to the pseudosynchronized values. A luminosity ratio of 0.95 $\pm$ 0.06 was found on the basis of the spectra, which agrees well with the photometric one (0.91 $\pm$ 0.03) obtained without fixing the potential of the primary. The photometric luminosity ratio was adopted, which results in almost identical radii for the components. This results in a slightly lower surface gravity for the secondary component than for the primary because of the mass ratio, but this difference is not significant.

On the mass- $\log g$ diagram, this system lies close to the ZAMS but might be up to 15-20 Myr old. The positions of the stars in the HR diagram agree within the error bars with the evolutionary tracks, although they tend to lie too high, as is the case of other systems.

$\begin{figure} \par\includegraphics[width=8cm,clip]{10284fgA3a.eps}\hspace*{7mm} \includegraphics[width=8cm,clip]{10284fgA3b.eps} \vspace*{2mm} \end{figure}$

Figure A.3:

Example of observed spectra close to a quadrature. Both spectra are at the same scale. The red line represents the composite synthetic spectrum of the binary system, i.e. the addition of the scaled and velocity-shifted synthetic spectra of the two components for the corresponding orbital phase. Besides a low S/N, the spectrum of 4 121461 shows strong nebular emission in the Balmer lines. From the best fit the B luminosity ratio was found to be $\sim$ 0.95 with a primary temperature of $\sim$ 22 000 K. The spectrum of 5 123390 points to a B luminosity ratio of 0.59 and a primary temperature of 27 000 K.

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A.7 4 159928

This system presents low-to-medium quality light curves of the EW type with eclipses of unequal depth. The rms scatter of the light curve is rather low, but the minima are not very deep ( $\Delta I_{\rm min I} \sim 0.25$ mag). It can be inferred from this that the system comprises close, strongly distorted components of unequal brightness. The best-fitting model corresponds to a semi-detached binary with a low inclination, close to $60\hbox{$^\circ$ }$ . The finding chart shows a well isolated target, except for a quite faint neighbor at about $2\hbox{$^{\prime\prime}$ }$ to the NNE.

There are only eight out-of-eclipse spectra, but they are close to the two quadratures.

A spectroscopic luminosity ratio of 0.45 was found in the B band, which is higher than the photometric value (0.36). The temperature of the primary was determined by fixing the temperature and luminosity ratios to the photometric values, after suppression of the very strong nebular emission lines. The Si III 4553 line is the only metallic line clearly visible in the separated spectrum of the primary. The spectrum of the secondary shows no exploitable metallic line. The Mg II 4481 is barely visible. The synchronized values for $V_{\rm rot} ~ \sin i$ are close to 200 km s^-1 and therefore all but the strongest lines are buried in the noise.

Both the mass- $\log g$ and HR diagrams show positions typical of a semi-detached system with an evolved secondary component. The primary is slightly overluminous relative to the evolutionary track of a single star.

A.8 4 160094

This detached system of moderate eccentricity presents low-to-medium quality light curves with rather shallow eclipses ( $\Delta I_{\rm min I} \sim 0.20$ mag). Except for a few very faint neighbors, the target seems free from crowding on the finding chart.

There are 11 out-of-eclipse spectra. Both quadratures are well covered by the observations.

The $T_{{\rm eff}}$ of the primary was determined together with that of the secondary and with the B luminosity ratio. The temperature of the secondary proved rather ill-defined, so the photometric temperature ratio was used to define it, as usual. The potential of the primary was fixed to a value that implies a luminosity ratio close to the spectroscopic one. No metallic lines are visible in the very noisy separated spectra. The nebular emission is strong in both H I lines.

Despite the moderate quality of the photometric and spectroscopic data, the positions of both stars fall right on the ZAMS in the mass- $\log g$ diagram. In the HR diagram, their position agree well with the evolutionary tracks, though they appear slightly overluminous.

A notable characteristic of this system is its fast apsidal motion $\dot{\omega} = 9.8$ $\pm$ 1.9 $\hbox {$^\circ $ }$ yr^-1. Figure A.4 shows the $e\cos\omega$ product as a function of time, as obtained using the EBOP code. The solid line represents the WD solution, which appears consistent with the EBOP results, even though the latter would be compatible with a faster apsidal motion coupled with a slightly smaller eccentricity. Further discussion of this result is deferred to Sect. 4.

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{10284fgA4.eps} \end{figure}$	Figure A.4: Variation with time of the $e\cos\omega$ quantity of the 4 160094 system, determined with the EBOP code on the basis of the I magnitudes grouped in four time intervals. The solid line corresponds to the parameters listed in Table 11.
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A.9 4 163552

This is one of the five systems with $I^{{\rm q}} < 16$ mag, displaying a high-quality light curve of the EB type. The eclipses have very similar depths ( ${\sim}0.4$ mag), indicating that the temperature ratio is very close to unity. Some faint neighbors are seen on the finding chart about $2\hbox{$^{\prime\prime}$ }$ from the target, and it is difficult to judge whether closer neighbors might lurk within the relatively large spot left by this bright system. According to the light curve, there is a substantial third-light contribution to this system: we find $\ell_{3,I}\sim 0.12$ , while Graczyk (2003, hereafter dG03) found $\ell_{3,I}\sim 0.26$ . A significant ellipsoidal variation is indicative of tidally distorted components, though the system is still in a detached configuration.

There are only nine out-of-eclipse spectra, but the RV curves are well constrained near quadratures.

The observed spectra of this binary were roughly corrected for the presence of a third component, by subtracting a constant from the normalized spectra. The value of the constant was adjusted until the effective temperatures obtained from the least-squares fit to the corrected spectra give a reasonable match to the evolutionary tracks at the metalicity Z=0.004 in the HR diagram. A constant of 0.1 only proved sufficient to this purpose, which is widely different from dG03's photometric estimate of the third light, $\ell_{3,B}\simeq 0.26$ . On the other hand, our WD analysis resulted in $\ell_{3,B}\simeq 0.14$ , which is more consistent with our rough spectroscopic estimate. Actually, a first attempt to analyze this system resulted in highly overluminous components. This was interpreted as a clear sign that the observed spectra were severely contaminated by the object responsible for the photometric third light.

The separated spectrum of the primary shows a faint Mg II 4481 line and a noisy Si III 4553 line. These lines were used to constrain the temperature of the primary. The Si III 4553 line is visible in the spectrum of the secondary too.

This system was studied by HHH05, dG03 (see his Fig. 6) and WW02. Only dG03 took the third-light contribution into account. Not surprisingly, our photometric solution is very close to theirs.

Since we adjusted the amount of third light so that the primary component have a realistic luminosity, the HR diagram shows a primary close to the stellar evolutionary track of a 9.6 $\mathcal{M}_{\odot}$ star, and a secondary close to the evolutionary track of a 9.1 $\mathcal{M}_{\odot}$ star. Their positions are clearly far from the zero-age main sequence. From the mass- $\log g$ diagram, the age of the system is estimated to be 20 Myr. As the position of the primary was inferred from the expected position in the HR diagram, the proposed solution is not entirely reliable and thus is not used for the determination of the mean distance modulus of the SMC (see Sect. 4.6).

A.10 4 175149

The medium-to-high quality light curve of this system is of the EB type; unfortunately, most of the right part of each eclipse is missing. That is due to a period very close to 2 days exactly. The minima are fairly deep ( $\Delta I_{\rm min I} \sim 0.50$ mag), well-defined and of unequal depth. There is a strong ellipsoidal variation. The binary is a semi-detached system, with distorted components of different brightnesses. A slight depression occurring before the primary eclipse is indicative of a gas stream. However, we did not venture into adding a spot on the primary in order to mimick this effect, because we felt that the large gaps in the light curve already limit the reliability of the proposed solution.

This system is close to the edge of the CCD used in the OGLE II survey, so it was also listed under the designation 5 38079 in the OGLE database. Thanks to that circumstance, there are 574 photometric I magnitudes instead of less than 300. An examination of the OGLE finding chart reveals that this binary is clearly blended.

This is the second system with 16 out-of-eclipse spectroscopic observations. Because of the 2-day period, all these observations took place before the quadratures. Nevertheless, the RV curves seem to be sufficiently constrained.

A spectroscopic B luminosity ratio of 1.39 was found, though with a large scatter ( $\sigma\sim 0.14$ ). This is higher than the photometric value (1.18). The separated spectra are fairly good. The spectrum of the hot primary component displays the He II 4200 and 4542 lines. The Si III 4553 and a faint Si IV 4089 lines are equally visible. These lines provide strong constraints for the temperature of the primary. The best-fitting primary temperature was obtained after fixing the temperature and luminosity ratios to the photometric values.

The mass- $\log g$ diagram shows the typical oblique orientation of the segment connecting the components of an evolved binary. The HR diagram shows a highly overluminous primary, relative to the evolutionary track of a 11.8 $\mathcal{M}_{\odot}$ star, and an evolved secondary far more luminous than a main-sequence star of 7.8 $\mathcal{M}_{\odot}$ . One may wonder whether the strange position of the primary is due to an unrecognized third light, both in photometry and spectroscopy, or to some evolutionary effect. In any case, there is no obvious third light in the light curve.

A.11 4 175333

This slightly eccentric system presents low-to-medium quality light curves of the EA type. This is one of the few systems with $I^{\rm q} > 17.5$ mag. Consequently, the $\rm O{-}C$ curve shows a relatively high scatter. The minima are of unequal depth. A slight ellipsoidal variation is visible. This is clearly a detached system with components of unequal brightness. The target appears perfectly isolated on the finding chart.

There are 14 out-of-eclipse spectra. The observations well constrain the RV curves.

This system was studied by WW01. That they consider the eclipses as total (while we consider them as partial) and their lack of spectroscopic constraints on their ratio of radii account for the differences between their solution and ours. The evidence for total eclipses does not appear compelling, so additional photometry would be needed to settle the issue. We found a spectroscopic B luminosity ratio of 0.55, slightly lower than that finally adopted taking photometry into account. The separated spectrum of the primary shows a noisy Mg II 4481 line. The spectrum of the secondary is too noisy to detect any metallic line. The temperature of the primary was fitted with the temperature and luminosity ratios fixed to the photometric values. The fit with both temperatures free to converge, together with the luminosity ratio, gave a rather large scatter of about 1600 K and a secondary temperature about 900 K cooler. In spite of the partial eclipses, there was no need to fix the potential of the primary in order to find a B luminosity ratio that matches the spectroscopic value, so the photometric value of the luminosity ratio was adopted.

On the mass- $\log g$ diagram, both stars fall right on the 20 Myr isochrone. On the HR diagram, however, both stars appear significantly overluminous relative to their evolutionary tracks, suggesting that the effective temperatures may be overestimated by at least 2000 K! Strangely enough, the color excess of this system appears to be small ( E(B-V)=0.07) and the distance modulus (18.6) clearly smaller than the accepted value for the SMC ( ${\sim}18.9{-}19.0$ ). If the effective temperatures had indeed been overestimated, this would have implied both an intrinsic color that is too blue and an intrinsic luminosity that is too large (hence a more negative absolute magnitude), so one would rather expect a high color excess and a high distance modulus.

A.12 5 016658

This close detached system presents medium quality light curves with eclipses of equal depths, and is composed of tidally distorted twin components. The finding chart reveals no crowding problem.

There are 11 out-of-eclipse spectra. The RV curves are well constrained by the observations around phase 0.25.

This system was studied by WW01. As for the previous binary, the differences observed between their (photometric) solution and ours is due to their lack of a spectroscopic constraint on the ratio of radii, and because they assume total eclipses. Evidence for the latter is not compelling, however, and awaits further photometric measurements for confirmation. A spectroscopic B luminosity ratio of $\sim$ 0.60 was found, which guided the choice of the potential of the primary component in the WD analysis. The Mg II 4481 line is clearly visible on the separated spectrum of the primary. The spectrum of the secondary is too noisy to show any metallic line. The best-fitting primary temperature was obtained simultaneously with the temperature of the secondary, which appeared quite compatible (within 300 K) with the photometric one (i.e. given the spectroscopic primary temperature and the photometric temperature ratio), and with the luminosity ratio. The photometric temperature ratio was adopted.

On the mass- $\log g$ diagrams, both stars fall on the 30 Myr isochrone within the errors. On the HR diagram, the primary has a position compatible with its evolutionary track within errors, though it appears slightly too luminous. The secondary is slightly hotter than the primary, and is more overluminous; still, it remains compatible with its evolutionary track if the errors on both luminosity and mass are considered.

A.13 5 026631

This system presents a medium-quality light curve of the EW type with minima of unequal depth. This is clearly a semi-detached system with strongly distorted components of unequal brightness. It presents the second-lowest inclination of the sample with $i \approx 61\hbox{$^\circ$ }$ , implied by the rather small amplitude of the light curve. No blend is apparent on the finding chart, except for two or three very faint neighbors at about $2\hbox{$^{\prime\prime}$ }$ .

There are only eight out-of-eclipse spectra, but these are sufficiently constraining to get reliable RV curves.

A spectroscopic B luminosity ratio of 0.74 was found, while the photometric value is 0.50. The separated spectra show no useful metallic lines. This is due notably to the high $V_{\rm rot} ~ \sin i$ values ( $\sim$ 190 km s^-1). The temperature of the primary was obtained by fixing the temperature and luminosity ratios to the photometric values.

The mass- $\log g$ and HR diagrams show the typical positions for the components of a semi-detached system, with the primary near its expected evolutionary track and an overluminous secondary. The primary is slightly overluminous relative to its track, as is often the case in this work, while the secondary is slightly below its track, a rare occurrence.

This binary was studied by HHH05. Their primary temperature (25 500 K) and mass ratio ( $\sim$ 1) differ significantly from our values.

A.14 5 032412

This wide, detached system presents medium-to-high quality light curves with minima of unequal depth, betraying components of unequal brightness. The target appears well isolated on the finding chart.

There are 13 out-of-eclipse spectra. The RV curves are very well constrained and the rms scatters are low. Interestingly, both the light and velocity curves indicate a negligible eccentricity, in spite of the small relative radii of the components, as if circularization had taken place during the protostellar phase. Note that this is the most massive system of our whole sample: its total mass reaches $30~\mathcal{M}_\odot$ .

A spectroscopic B luminosity ratio of 0.55 was found. The separated spectra are of high quality (Fig. A.5), even for the H I lines. Beside the H I and He I lines, the following lines are visible in the spectrum of the primary: He II 4200 and 4542 (strong), Si IV 4089, Si IV 4116, O II 4185, Si IV 4212, O II 4276-7 and Si III 4553. An effective temperature of about 35 000 K was inferred from the best-fitting synthetic spectrum.

The following metallic lines are visible in the separated spectrum of the secondary: Si IV 4089, Si IV 4116, O II 4185, O II 4190, C II 4267, O II 4276-7, O II 4415-7, Mg II 4481 and Si III 4553. He II 4542 is clearly visible too. Comparing the relative depths of Mg II 4481 with He I 4472, He II 4542 with Si III 4553, C II 4267 with O II 4276-7, Si IV 4089 and Si IV 4116 with He I 4121 allows us to estimate an effective temperature close to 31 000 K. Thanks to the good SNR of the spectra, fitting simultaneously the temperatures of the components and the luminosity ratio resulted in a temperature ratio very close to the photometric one. Nevertheless, the adopted temperatures are those obtained by imposing the photometric ratio.

The mass- $\log g$ diagram shows a very young binary with both components on the ZAMS. On the HR diagram, the positions of both components agree fairly well with the stellar evolutionary tracks of 17.1 and 13.1 $\mathcal{M}_{\odot}$ stars. However, the primary appears slightly overluminous relative to its track.

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{10284fgA5a.eps}\hspace*{3mm} \includegraphics[width=8.5cm,clip]{10284fgA5b.eps} \vspace*{5mm} \end{figure}$

Figure A.5:

Sections of the separated spectra of the primary and secondary components of the binary 5 032412. The scale on the vertical axis is adapted to the size of the features in each section. The red line represents a velocity-shifted synthetic spectrum of the star. Beside prominent H I and He I lines, He II, O II, Mg II, Si III and Si IV lines are visible in both spectra. The strong He II 4542, next to a smaller Si III 4553 line, and the He II 4200 line confirm the high temperature of the primary ( $\sim$ 34 900 K). The lower temperature of the secondary is confirmed by the stronger Mg II 4481 line and the fainter He II lines.

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A.15 5 038089

This bright detached system presents medium-quality light curves with eclipses of very similar depth. Therefore, the components are very similar.

This system has abnormal color indices (see Table 3 and Fig. 3), which suggests the presence of a third light. An examination of the OGLE finding chart reveals that this binary is clearly blended, though with much fainter stars.

There are 11 out-of-eclipse spectra. The RV curves are very well constrained and the rms scatter is remarkably low.

A spectroscopic B luminosity ratio of 0.68 was found. The eclipses are not very deep, so we fixed the potential of the primary to reproduce this luminosity ratio. The separated spectra shown in Fig. A.6 are very similar. Strong He II 4200 and 4552 lines are visible in both spectra. The following metallic lines are equally identifiable (Fig. A.6): O II 4076, Si IV 4089, Si IV 4116, O II 4185, O II 4190, C II 4267, O II 4276, O II 4415-4417, Si III 4553. This wealth of lines allows us to determine the temperatures of both components with a great accuracy. From the best-fitting synthetic spectra, we found 30 400 K and 30 800 K for the effective temperature of the primary and secondary, respectively. This is very close (i.e. within 200 K) to the temperatures estimated from the composite spectra by imposing the photometric temperature and luminosity ratios; thus, one can safely conclude from this example that the two methods are equivalent.

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{10284fgA6a.eps}\hspace*{3mm} \includegraphics[width=8.5cm,clip]{10284fgA6b.eps} \end{figure}$

Figure A.6:

Sections of the separated spectra of the primary and secondary components of the binary 5 038089. The scale on the vertical axis is adapted to the size of the features in each section. The red line represents a velocity-shifted synthetic spectrum of the star. Beside prominent H I and He I lines, He II and a number of fainter metallic lines (C II, O II, Si III, Si IV) are visible. The relative intensities of the He II 4542 and Si III 4553 are very useful to constrain the temperature of the two stars.

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The high quality of the spectroscopic observations allowed us to estimate the astrophysical parameters with a greater accuracy than for most systems in our sample. On the mass- $\log g$ diagram, both components lie just above the 10 Myr isochrone; their respective positions suggest that the ratio of radii may be slightly underestimated. The HR diagram shows that both stars are significantly overluminous with respect to the evolutionary tracks of 13.0 and 11.7 $\mathcal{M}_{\odot}$ stars. Invoking the blending of the binary with a third-light contributor does not seem to help much. No clear sign of a third light can be seen in the lightcurve; this is admittedly a weak argument, since the light curve of a detached system with weak proximity effects cannot constrain a third light well. But, in addition, a third light will not much change the relative radii of the components, and the effective temperatures seem well constrained by the relative intensities of several lines, so that the luminosities should remain unaffected. Furthermore, the quality of the radial velocity curves is so good, that it is difficult to imagine how the masses could be biased otherwise than through the inclination angle i. A third light would make the photometric minima less deep and so it would mimick a lower i. Since the RV amplitudes give the product $\mathcal{M}\sin^3i$ , underestimating i is equivalent to overestimating $\mathcal{M}$ , while we would need the reverse to explain the HR diagram we see. A test with the EBOP code confirms this qualitative argument: assuming a third light $\ell_{3,I}=0.2$ changes the radius of the primary by -0.26% only (keeping the ratio of radii constant), so that the luminosity decreases by half a percent, while the inclination is increased by more than three degrees, lowering the masses by 3.6%. That would imply evolutionary tracks with a luminosity about 0.05 dex lower (or 11%) in the HR diagram. Finally, the distance modulus of this system is very close to that expected for the SMC. Therefore, for a third light to be the cause of the inconsistency, it can only be via the RV curves, the amplitude of which should be biased to low values by a stationary third spectrum.

This binary was part of the first release of 10 bright SMC systems by HHH03. Comparing our results with theirs, we see that we have similar estimates for the mass ratio and temperatures of the stars, but markedly different values for the masses and radius of the secondary. A photometric solution was proposed by dG03, who do not recommend it for distance determination because its components do not fall into their mass-luminosity relation.

A.16 5 095337

This is a close but detached system, with tidally distorted components of unequal brightness. The $\rm O{-}C$ curve suggests that the primary eclipse is not perfectly reproduced by the synthetic light curve, but there is no obvious third-light contribution. The finding chart shows some blends with two or three fainter stars at $1\hbox{$.\!\!^{\prime\prime}$ }5$ or so.

There are 10 out-of-eclipse spectra. The RV curves are well constrained with observations close to both quadratures.

A spectroscopic B luminosity ratio of 0.66 was found. The separated spectra are of poor quality. Because of the low S/N and the high $V_{\rm rot} ~ \sin i$ ( $\sim$ 200 km s^-1), no metallic line can be positively identified. There is some nebular emission in the Balmer lines. The best-fitting synthetic spectra allowed us to simultaneously estimate the temperatures of the primary and the secondary, whose ratio agrees quite well with the photometric one. In addition, the spectroscopic B luminosity ratio perfectly matches the photometric one, so that the potential of both the primary and the secondary were left free to converge.

On the mass- $\log g$ diagram, both components define a segment which is perfectly parallel and very close to the 10 Myr isochrone. On the HR diagram, however, both components appear strongly overluminous compared to the evolutionary tracks of 8.7 and 7.6 $\mathcal{M}_{\odot}$ stars. Decreasing the effective temperatures by about 1300 K would reconcile the luminosities with the tracks. However, this looks difficult. The emission in both Balmer lines was suppressed on a 4 Å range centered on each emission line, and we verified that increasing that range to 8 Å does not change the estimated temperature in a significant way. Thus, either this system suffers from some bias on the RV curves, or its metalicity is closer to Z=0.001 than to Z=0.004.

A.17 5 095557

This is the system with the highest eccentricity, displaying a medium-quality light curve with minima of unequal depths. The target is perfectly isolated on the finding chart.

There are 11 out-of-eclipse spectra. The RV curves are well constrained with observations close to both quadratures, but the fit is not very good and, unfortunately, most spectra are grouped in the phase interval with the smaller amplitude.

A spectroscopic B luminosity ratio of $\sim$ 0.5 was found when limiting the fit to the seven spectra for which the radial velocity difference $\Delta {\rm RV} > 250~{\rm km~s^{-1}}$ . This ratio increases to 0.63 if all eleven spectra are taken into account, so that this quantity is rather poorly constrained. The separated spectra are of very poor quality. This is probably partly due to the low S/N of the observed spectra, and partly to some inaccuracies in the orbital parameters. The temperature of the secondary given by the fits to the composite spectra is about 1000 K higher than the photometric estimate, which was adopted. The pseudosynchronized values of $V_{\rm rot} ~ \sin i$ were adopted.

An apsidal motion is detected at the $5\sigma$ significance level, and the WD result is confirmed by the variation of the $e~\cos\omega$ quantity as given by the EBOP code. The photometric data were divided into four sets and the fits were obtained by fixing the inclination, the ratio of radii and the relative radius of the primary. The result is displayed in Fig. A.7 and suggests that the apsidal motion is real. The adopted apsidal motion seems underestimated in that figure, but the constraint imposed by the RV curves has to be kept in mind. On the mass- $\log g$ diagram, the two components lie right on the 30 Myr isochrone, despite the rather large uncertainty of the masses. In the HR diagram both components appear clearly overluminous with regard to their respective evolutionary tracks, as in many other systems.

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{10284fgA7.eps} \end{figure}$

Figure A.7:

Same as Fig. A.4, but for the system 5 95557. The filled black dots represent independent $e\cos\omega$ determinations made on four successive times series containing about the same number of photometric observations in the I band. The solid line is based on the parameters listed in Table 11, while the dotted line corresponds to the fitted $\dot{\omega}+2\sigma$ . The horizontal dashed line shows the result obtained from the whole time series under the assumption of a constant $\omega$ .

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A.18 5 100485

This is a detached system with ``twin'' components and a circular orbit. The finding chart reveals no crowding problem, because the closest neighbor is found at about $2\hbox{$.\!\!^{\prime\prime}$ }5$ .

There are 13 out-of-eclipse spectra. The RV curves are well constrained, with observations close to both quadratures and small residuals.

A spectroscopic B luminosity ratio of 0.93 was found, which matches the photometric value (0.97) rather well. The separated spectra are very similar. The following metallic lines can positively be identified: C II 4267, Mg II 4481 and Si III 4553. These lines allowed us to estimate a temperature close to $\sim$ 22 000 K for each component. The least-squares fit, performed with both temperatures and the luminosity ratio free to converge, provided a temperature ratio very close to the photometric one.

The two components lie right on the 20 Myr isochrone on the mass- $\log g$ diagram, and they are compatible within the errors with their respective evolutionary tracks in the HR diagram. Here again, however, they are slightly overluminous, unless their metalicity is low.

A.19 5 100731

This system presents low-to-medium quality light curves of the EW type, with the smallest amplitudes among those in our sample. This is another case of a binary seen in an unfavourable inclination ( $\sim$ 60 $\hbox {$^\circ $ }$ ). The finding chart shows a perfectly isolated target.

The most satisfying fit of the light curves was obtained with an overcontact model.

There are only eight out-of-eclipse spectra. Nevertheless, these observations are sufficiently constraining to get reliable RV curves.

Spectroscopy gives a B luminosity ratio of ${\sim}0.44$ , while the photometric ratio amounts to ${\sim}0.51$ . As usual, the latter was preferred, especially because of the strong constraints provided by a Roche-lobe-filling pair. The separated spectra have a low S/N, and a least-squares fit to the composite spectra with both temperatures free provided two temperatures close to 23 000 K. However, the scatter of the secondary temperature was high, so the photometric temperature ratio was adopted and fixed.

The mass- $\log g$ diagram shows a secondary component more evolved than the primary, as expected. On the HR diagram, both components appear to be underluminous with respect to their evolutionary tracks, though only by a little amount. This is an exceptional occurrence.

A.20 5 106039

This system is a typical semi-detached one. There is a small depression occurring just before the eclipse of the primary, which is strong evidence for a gas stream. We did not attempt to model that stream with a cool spot on the primary, because the distortion of the light curve remains relatively mild. The target appears perfectly isolated on the finding chart.

There are nine out-of-eclipse spectra. The RV curves are well constrained with observations close to both quadratures.

A spectroscopic B luminosity ratio of 1.03 was found, which excellently agrees with the photometric value (1.01). The following metallic lines are visible in the separated spectrum of the primary: C II 4267, Mg II 4481 (faint) and Si III 4553. A stronger Mg II 4481 line is equally visible in the spectrum of the secondary. From these lines, the primary temperature was estimated to be close to 25 500 K. The least-squares fit, performed with temperature and luminosity ratios fixed to the photometric values, provided a primary temperature ${\sim}800$ K higher.

The position of the primary component in the HR diagram is in fair agreement with the theoretical evolutionary track of a 8.6 $\mathcal{M}_{\odot}$ star, though it is slightly overluminous. The evolved secondary component is overluminous with respect to the track of a single star of the same mass.

A.21 5 111649

This is a detached system with very slightly distorted twin components. There is a group of bright stars close to the target in the finding chart, but they are remote enough ( $3.5{-}4\hbox{$^{\prime\prime}$ }$ ) that no third light should be expected from them.

There are 10 out-of-eclipse spectra. The RV curves are not well sampled because the period of 2.95955 days is very close to an integer number of days, but the scatter is small, thanks to the slow projected rotational velocities induced by the relatively long period.

A spectroscopic B luminosity ratio of 0.89 was found, which was imposed (via the potential of the primary) to define the ratio of radii. Indeed, the small amplitude of the light curve prevents a purely photometric ratio to be well constrained. Noisy C II 4267 and Mg II 4481 lines are visible in the separated spectrum of the secondary. The temperature of the primary was determined from a fit with fixed temperature and luminosity ratios. According to both spectroscopy and photometry, the secondary appears marginally hotter than the primary, the temperature difference being about $2\sigma$ .

Both components have a very similar mass ( $\sim$ 5.4 $\mathcal{M}_{\odot}$ ), and according to the mass- $\log g$ diagram, the empirical mass contrast appears a bit too high to match the ${\sim}80$ Myr isochrone. Interestingly, both components lie right on the Terminal Age Main Sequence (TAMS), where evolution is so fast that a theoretical lower limit to the mass ratio can be settled. Starting from the purely empirical surface gravities, and increasing their difference by two sigma (so that $\log g_{\rm P}-1\sigma=3.72$ and $\log g_{\rm S}+1\sigma=3.80$ ), one can read the corresponding masses along the $\log t=7.9$ isochrone. Assuming that both stars have not yet passed the ``hook'' that marks the end of the main sequence, the resulting mass ratio is q=0.98. But it is quite possible that the primary has just passed the hook while the secondary has not, in which case q=0.966. In both cases, the mass ratio is closer to one than the value directly obtained from the RV curves by 0.03 to 0.04. Therefore, this system can be considered as hosting real twins.

The position of the primary in the HR diagram agrees almost perfectly with the theoretical evolutionary track, especially if the star has just evolved beyond the ``hook''. That of the secondary, however, is a bit too high, as if its mass were underestimated.

A.22 5 123390

This slightly eccentric system (e = 0.042) presents low-to-medium quality light curves with a small amplitude. This is clearly a detached system with components of unequal brightness. The finding chart shows a neighbor at about $1\hbox{$.\!\!^{\prime\prime}$ }5$ to the SW of the binary, which might have polluted the spectra slightly.

There are 14 out-of-eclipse spectra. The RV curves have a small rms scatter and are very well constrained by the observations.

A spectroscopic B luminosity ratio of 0.58 was found. The separated spectra are of fairly good quality. The following metallic lines are visible in both spectra: O II 4076, C II 4267, O II 4276, O II 4415-4417, Mg II 4481 and Si III 4553. For the primary, the best-fitting temperature for these lines is $\sim$ 26 000 K. The least-squares fit of the composite spectra gave temperatures of 28 400 and 26 260 K for the primary and secondary respectively, but with a large scatter. A plot of the fitted temperatures versus the unnormalized chi-square shows that in some cases the fit switched components, i.e. attributed the high temperature to the secondary and vice versa, which partly explains the large scatter (see Fig. A.8). Strangely enough, the photometric ratio of temperatures is close to one, so that the temperatures become 27 840 and 28 320 K for the primary and secondary component respectively when fitted while keeping this ratio fixed. Taken at face value, however, Fig. A.8 rather suggests 29 000 and 25 000 K.

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{10284fgA8.eps} \end{figure}$	Figure A.8: Temperature of the primary (black dots) and of the secondary (red dots) component of the system 5 123390, obtained by fitting composite synthetic spectra to the observed ones, versus the quality of the fit. The trends are roughly horizontal, at least for good fits, which inspires confidence. In a few cases, the components are exchanged (see text).
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According to the mass- $\log g$ diagram, this binary is $\sim$ 12 Myr old. The position of the primary component in the HR diagram is a bit too high with regard to its evolutionary track. The secondary component is much too luminous, falling on the track of the primary! If the purely spectroscopic temperatures were adopted, the primary would be even more overluminous, but the secondary would fall right on its track.

There is a marginally significant apsidal motion of 4.75 $\pm$ 1.63 $\hbox {$^\circ $ }$ yr^-1. We show in Fig. A.9 the $e\cos\omega$ quantity found with the EBOP code on the basis of the I magnitudes. There is indeed a slight trend corresponding to an increase of $\omega$ with time.

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{10284fgA9.eps} \end{figure}$

Figure A.9:

Same as Fig. A.4, but for the system 5 123390. The filled black dots represent independent $e\cos\omega$ determinations made on four successive times series containing about the same number of photometric observations in the I band. The open red dots refer to $e\cos\omega$ determinations based on only two time series, but which are twice as long. The solid line is based on the parameters listed in Table 11.

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A.23 5 180185

The EA-type light curves of this system are irregularly sampled, because the period is close to 5.5 days, and there are only very few data in the primary minimum. This is a typical well-detached system with twin components and a small eccentricity. The finding chart reveals a slightly fainter neighbor about $2\hbox{$^{\prime\prime}$ }$ away from the target, i.e. far enough that its influence on the spectra may be considered negligible.

This system has unreliable color indices (see Table 3 and Fig. 3).

There are 12 out-of-eclipse spectra. The RV curves are excellent and well constrained by the observations, with the smallest residuals seen in our sample. The formal errors on the resulting amplitudes are smaller than one percent, allowing mass estimates to within 2-3%.

A spectroscopic B luminosity ratio of 0.63 was found, which is close to the value given by the WD analysis and finally adopted (0.71). This is the system with the longest period ( $P\sim5.5$ days) in our sample. The long period is responsible for the low $V_{\rm rot} ~ \sin i$ values ( $\sim$ 40 km s^-1) compatible with synchronous rotation. As a consequence, the separated spectra of this binary show rather sharp lines. The following metallic lines are visible in both spectra: C II 4267, Mg II 4481 and Si III 4553. The temperature of the primary was obtained as usual by fixing the temperature and luminosity ratios to the photometric values, despite the small number of points in the minima. The secondary has a slightly hotter temperature than the primary.

Both components are fairly well aligned on the 50 Myr isochrone in the mass- $\log g$ diagram, although the primary should be slightly more evolved. On the HR diagram, the secondary falls right on its track, while the luminosity of the primary appears too low. This might be due to an unreliable temperature ratio, because of the small number of photometric points in the minima.

A.24 5 180576

This system presents low quality light curves of the EB type. The depths of both minima are rather low and the rms scatter is high. This is a detached system with components of unequal brightness and a circular orbit. The finding chart shows a close neighbor at about $1\hbox{$.\!\!^{\prime\prime}$ }5$ to the NNW, which might have distorted the temperature estimate of the binary components.

There are 12 out-of-eclipse spectra. The RVs curves are rather good and well constrained by the observations.

A spectroscopic B luminosity ratio of 0.42 was found. This is close to the value reached by the final WD analysis. The observed composite spectra are very noisy ( $25 \leq S/N \leq 64$ ) and are contaminated by nebular emission. The separated spectra are of a rather poor quality. This is partly due to the low reliability of the continuum placement. The C II 4267 and Mg II 4481 lines are visible in the spectrum of the primary. The temperature of the primary, determined from a least-squares fit where the temperature and luminosity ratios were fixed, depends on the quality of the fit, as shown by Fig. A.10. We adopted the temperature of the primary corresponding to the best $\chi^2$ , in view of the roughly linear correlation between $T_{{\rm eff}}$ and $\chi^2$ , but without attempting to extrapolate the relation to $\chi^2=0$ .

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{10284fgA10.eps} \end{figure}$	Figure A.10: Effective temperatures of the system 5 180576 obtained from a fit to the composite spectra, keeping the temperature and luminosity ratios fixed. Black dots are for the primary, red dots for the secondary. Note that the two curves should be considered as one and the same, since their ratio is constant.
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In the mass- $\log g$ diagram, the components are perfectly aligned along the 15 Myr isochrone. The position of the primary component in the HR diagram appears slightly too high relative to the corresponding evolutionary track, while the secondary falls right on its track.

A.25 5 185408

This system presents medium quality light curves of the EA type. The minima are of similar depth and there is some ellipsoidal variation. This is a typical detached system with closely similar components, with medium quality light curves and low amplitude minima of similar depth. The orbit is circular. The I-band light curve was cleaned from five outliers before the PHOEBE/WD analysis. The finding chart shows a well isolated target, the closest neighbor is found at about $3\hbox{$^{\prime\prime}$ }$ to the WNW.

There are 12 out-of-eclipse spectra. The RV curves are excellent, especially in view of the faintness of the object, and well constrained by the observations.

A spectroscopic B luminosity ratio of $\sim$ 0.64 was found. The WD analysis tended to raise this value and the potential of the primary had to be fixed to keep it close to the spectroscopic one. The C II 4267, Mg II 4481 and Si III 4553 lines are visible in both separated spectra. The temperatures were obtained by fixing the temperature and luminosity ratios to the photometric values.

On the mass- $\log g$ diagram, the components are fairly well aligned on the 10 Myr isochrone. On the HR diagram, both components are significantly overluminous with respect to their respective evolutionary tracks, as is often the case.

A.26 5 196565

This detached eccentric system presents medium quality light curves with eclipses of similar depth. The V and B data are missing in the OGLE database. The finding chart shows a neighbor of similar brightness as the target about $2\hbox{$^{\prime\prime}$ }$ to the S, raising some concern regarding possible spectral pollution. The results do not confirm these fears, though.

There are 13 out-of-eclipse spectra. The RV curves are very good and well constrained by the observations, in spite of a lack of observations where the expected amplitude reaches its maximum.

A spectroscopic B luminosity ratio of $\sim$ 0.41 was found, and the potential of the primary was adjusted and fixed in the WD analysis to maintain that value. The C II 4267 and Mg II 4481 lines are visible in both separated spectra. The least-squares fit of composite synthetic spectra to the observed ones provided a temperature ratio higher than that provided by the photometry, and a primary temperature of 20 960 $\pm$ 600 K. Fixing the temperature ratio to the photometric value resulted in the slightly hotter primary temperature that has been adopted.

The mass- $\log g$ diagram suggests that the secondary has a radius too large with regard to the primary, as if the luminosity ratio was overestimated: while the primary lies close to the 40 Myr isochrone, the secondary lies on the 50 Myr one. On the HR diagram, however, each component has a position compatible with its respective evolutionary track within the error bars, though the primary is slightly overluminous while the secondary is slightly underluminous.

This system was studied by WW01. Their relative radius of the primary (0.204) is very close to ours (0.200) but their radius of the secondary (0.116) is smaller than ours (0.150). The difference arises because they consider the eclipses as total, while we consider them as partial. Additional accurate photometry in both minima would be welcome to settle the question.

A.27 5 261267

This is a typical semi-detached system with high-quality light curves and eclipses of unequal depths. The $\rm O{-}C$ curve shows no detectable depression before the primary eclipse. Although the finding chart shows a few neighbors, they all lie beyond $2\hbox{$^{\prime\prime}$ }$ of the target.

This system has peculiar color indices (see Table 3 and Fig. 3). Since it lies near the edge of the CCD in the OGLE-II survey, it is also listed under the name 6 11806 in the corresponding database. Thus, there are more than 600 data points in the I-band light curve, instead of about 300.

There are 10 out-of-eclipse spectra, which constrain the RV curves relatively well.

Both photometric and spectroscopic ratios are very similar ( $\sim$ 0.4). Because of the relatively high $V_{\rm rot} ~ \sin i$ (>150 km s^-1) and moderate S/N of the observations, there are no exploitable metallic lines in the separated spectra. The temperature of the primary was obtained, as usual, by least-squares fit to the composite spectra, after fixing the temperature and luminosity ratios to the values given by a preliminary WD analysis.

The mass- $\log g$ and HR diagrams are typical of a massive Algol-type binary. The primary is overluminous relative to the evolutionary track of an isolated star of the same mass, as are other semi-detached systems like 4 113853 and 5 277080.

A.28 5 265970

This slightly eccentric detached system has medium-to-high quality light curves of the EA type. The sampling of the light-curve is incomplete, due to an orbital period close to 3.5 days. In particular, the depth of the secondary minimum is ill-defined. Therefore, the photometric temperature ratio and inclination are not very reliable. Actually, there is a correlation between these two parameters, in the sense that an increase of inclination implies a decrease of the temperature ratio. The finding chart shows a well defined target, but with an only slightly fainter neighbor about $2\hbox{$.\!\!^{\prime\prime}$ }6$ to the NW.

This system lies near the edge of the OGLE-II CCD, and so was measured also on the adjacent chip under the name 6 17345, so that there are as many as 586 data points in the I band. The two data sets were merged after applying a small magnitude offset to each. With the EBOP code the fitted magnitude at quadrature and its error were defined for each set, then the mean magnitude at quadrature weighted by the inverse of the variance was computed. Finally, the appropriate offset was applied to each of the two sets to adjust it to this mean magnitude.

There are 10 out-of-eclipse spectra. The RV curves are quite good and well constrained by the observations.

Because of the loose constraints on the light curves, the proposed solution for this system heavily relies on the spectroscopic observations. Nevertheless, the proposed solution meets the spectroscopic and photometric constraints very well, so we consider it as close to reality.

A spectroscopic B luminosity ratio of $\sim$ 0.23 was found from the usual least-squares fit, which provides the temperature of the primary with an excellent internal precision. The temperature of the secondary is much less certain, because of the small luminosity ratio. In order to maintain the luminosity ratio to the spectroscopic value in the WD analysis, one has to fix the potential of the primary to an appropriate value, and the temperature ratio converges to a lower value than the spectroscopic one, but still compatible with it given the errors. Thus the photometric temperature ratio was adopted, and the temperature of the primary was determined in the usual way.

A number of metallic lines are identifiable in both separated spectra: C II 4267, O II 4276, O II 4415-17, Mg II 4481 and Si III 4553. There is no emission in the Balmer lines.

The positions of the stars in the mass- $\log g$ diagram are not quite mutually consistent: the ratio of radii should be decreased in order to bring the two components on the same isochrone, which would correspond to about 26 Myr. In the HR diagram, the primary component matches its theoretical evolutionary track surprisingly well, while the secondary has a position consistent with its track within the error bar. The spectroscopic constraints, which are strong, are well fulfilled, but additional photometric data would be useful to improve our solution. This system is especially interesting, because the primary is very close to the TAMS while the secondary is much less evolved.

We applied the EBOP code on four subset of the total time series, after fixing all parameters to their average value, except inclination, $e\cos\omega$ , $e\sin\omega$ , magnitude at quadrature and phase shift. No significant trend can be seen in Fig. A.11, which does not prove, however, that $\omega$ remains constant with time. The less reliable $e\sin\omega$ quantity does not differ significantly from zero according to the EBOP code. In the WD solution, we have arbitrarily imposed a low value $\dot{\omega}=1.8$ $\times$ $10^{-4}~{\rm rad~day^{-1}}$ which roughly corresponds to the theoretical prediction.

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{10284fgA11.eps} \end{figure}$	Figure A.11: Same as Fig. A.4, but for the system 5 265970. The horizontal dashed line shows the weighted average of the $e\cos\omega$ values. The solid line corresponds to $\dot{\omega}\simeq 3.8^\circ~{\rm yr^{-1}}$ , the expected theoretical value.
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A.29 5 266015

This system presents high-quality light curves of the EB type with minima of unequal depth. Its bright I-band light curve is perfectly well sampled. The small depression occurring just before the primary eclipse is indicative of a semi-detached system with a secondary component filling its Roche lobe and pouring matter onto the primary component. However, the amplitude of this effect was judged too small to justify an attempt to model it through a spot.

There are 10 out-of-eclipse spectra. The RV curves are well constrained by the observations.

A spectroscopic B luminosity ratio of 0.61 was found, rather remote from the photometric value (0.49), as is often the case in semi-detached systems. The separated spectra of both components have a decent S/N (Fig. A.12). Nevertheless, the $V_{\rm rot} ~ \sin i$ being high (>150 km s^-1), the small metallic lines are not very conspicuous. The He I 4120 and He II 4542 lines are visible in the spectrum of the primary. The Si III line appears in both spectra. This is one of the few systems with apparently no significant nebular emission lines, therefore the separated Balmer lines can be used to find the temperature of the primary. The spectral features of the primary point to a 32 000 K star, which is confirmed by the usual least-squares fit.

The positions of the stars in the mass- $\log g$ and HR diagrams are coherent with an evolved system having undergone mass exchange. The primary component is close to the track corresponding to a 15.6 $\mathcal{M}_{\odot}$ star.

This system was studied by WW02. As with most semi-detached systems they studied, their photometric mass ratio proved to be unreliable.

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{10284fA12a.eps}\hspace*{3mm} \includegraphics[width=8.5cm,clip]{10284fA12b.eps} \vspace*{4mm} \end{figure}$

Figure A.12:

Sections of the separated spectra of the primary and secondary components of the binary 5 266015. The scale on the vertical axis is adapted to the size of the features in each section. The red line represents a velocity-shifted synthetic spectrum of the star. Beside prominent H I and He I lines, He II, O II, Mg II, Si III and Si IV lines are visible in both spectra. The strong He II 4542, next to a smaller Si III 4553 line, and the He II 4200 line confirm the high temperature of the primary ( $\sim$ 32 000 K). Poor continuum placement is responsible for the apparent $\rm O{-}C$ mismatch of the H $\delta$ line.

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A.30 5 266131

The most striking feature of this slightly eccentric detached system ( $e\simeq 0.04$ ) is its huge apsidal motion, which explains the apparently very bad I-band $\rm O{-}C$ curve. An examination of the OGLE finding chart revealed that this binary is slightly blended, but a posteriori, this does not seem to have distorted the results.

This system lying close to the edge of the CCD in the OGLE-II survey, it also exists under the name 6 22883, which doubles the number of data points in the I band. The magnitude at quadrature was determined using the EBOP code for each of the two data sets; the two resulting values agreeing within one thousandth of a magnitude, the two data sets were merged without applying any magnitude offset.

There are 10 out-of-eclipse spectra, which constrain quite well the RV curves.

A spectroscopic B luminosity ratio of $\sim$ 0.65 was found. As usual with the well detached systems, the potential of the primary was fixed at a value which preserves this luminosity ratio through the WD analysis. The S/N of the separated spectra are too low to allow any useful metallic line to be seen. Since the temperature ratio is well constrained by the photometric data, the temperature of the primary was determined by fixing this ratio at its photometric value. There is no nebular emission in the Balmer lines.

The mass- $\log g$ diagram suggests that the ratio of radii has been slightly underestimated, since the secondary has a surface gravity too large compared to the primary. Still, the positions of both components are compatible, within the errors, with an isochrone at 7-8 Myr. The HR diagram shows a good match between the positions of both components and the evolutionary tracks of single 9.0 and 7.7 $\mathcal{M}_{\odot}$ stars. However, both components are slightly overluminous relative to their respective tracks.

The apsidal motion amounts to $\dot{\omega} \simeq 50$ $\hbox {$^\circ $ }$ yr^-1, as shown by the $e\cos\omega$ values obtained with the EBOP code for four successive subsets of the whole time serie in the I band. That value is confirmed by the WD analysis. The run of $e\cos\omega$ versus time is shown in Fig. A.13, together with the best-fit curve provided by the WD code. The reality of a very fast apsidal motion is beyond any doubt. It is further discussed in Sect. 4.

A.31 5 266513

This a close detached system with similar components, according to its medium quality light curves with minima of similar depth. The finding chart shows a slightly fainter star at $1.2{-}1.3\hbox{$^{\prime\prime}$ }$ to the W of the target.

There are 10 out-of-eclipse spectra. The RV curves are well constrained by the observations, though the noise is rather large because this system is the faintest in our sample.

A spectroscopic B luminosity ratio of 0.73 was found, but with a large scatter of 0.09. The potential of the primary was fixed so that the WD analysis preserves a ratio close to that value. The separated spectra have a low S/N and no metallic lines are exploitable. Moreover, the Balmer lines are polluted by nebular emission. The photometric temperature ratio is rather well defined, thanks to the large depth of the minima, and was fixed for the determination of the temperature of the primary, as usual for most detached systems.

The mass- $\log g$ diagram shows the two components fairly well aligned along the ${\sim}15$ Myr isochrone. On the HR diagram, the primary lies almost exactly on its evolutionary track, while the secondary is slightly overluminous, though its position is quite compatible with the evolutionary tracks within the errors. The luminosity ratio (hence the ratio of radii) seems to have been slightly overestimated.

A.32 5 277080

This system is a typical semi-detached binary with high-quality light curves of the EB type. A small depression before the primary eclipse signals the possible presence of a mass-transfer stream. The effect is small enough for us not to deem it worth the effort to model it through a cool spot on the primary.

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{10284fgA13.eps} \end{figure}$	Figure A.13: Same as Fig. A.4, but for the system 5 266131. The solid line is the best fit provided by the WD code.
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This system has peculiar color indices (see Table 3 and Fig. 3). Indeed, an examination of the OGLE finding chart revealed that this binary is strongly blended with a brighter star lying $1\hbox{$.\!\!^{\prime\prime}$ }2$ to the SW of the target.

There are 11 out-of-eclipse spectra. Because of an orbital period close to two days, there are no observations before the quadratures. Yet the RV curves are rather well constrained. This is one of the few systems without nebular emission in the Balmer lines.

A spectroscopic B luminosity ratio of 0.7 was found. This is higher than the photometric ratio (0.57), as seems to be often the case of semi-detached systems. The separated spectra are fairly good. A number of metallic lines are visible in the spectrum of the primary: O II 4185, C II 4267, O II 4276-7, Mg II 4481 and Si III 4553. The Mg II 4481 line is the only metallic line detectable in the spectrum of the secondary. The temperature of the primary was determined after fixing the temperature and luminosity ratios to their photometric values.

The positions of the stars in the mass- $\log g$ and HR diagrams are typical of Algol-type system with a secondary more evolved than the primary. The primary component, however, is much more luminous than expected from the evolutionary track of a single star of the same mass, and we cannot guarantee that its effective temperature has not been overestimated. The peculiar HR diagram might be the result of the blend mentioned above with a nearby bright star.

A.33 5 283079

This is a typical detached system with twin components and a circular orbit. The target appears just isolated on the finding chart, with a companion of similar brightness about $2\hbox{$.\!\!^{\prime\prime}$ }5$ away from it to the SE.

There are 10 out-of-eclipse spectra. The RV curves are well defined and constrained by the observations. There is probably a faint nebular emission in both H $\gamma$ and H $\delta$ lines.

With a spectroscopic B luminosity ratio close to 1.0, a mass ratio of 1.003 and a temperature ratio of 0.997, this is the system with the most similar components in our sample. Thus it is probably a real pair of ``twins'', i.e. it has a mass ratio higher than 0.95. This is why the choice of the primary is undecided in this system: which component is the primary was decided on the basis of an early iteration, and it is only in the last iteration that we obtained q=1.003 > 1. The potential of the primary was fixed in the WD analysis, in order to keep the B luminosity ratio close to 0.99. The separated spectra are noisy and the C II 4267 and Mg II 4481 are barely visible. The temperature of the primary was determined by fixing the temperature ratio to 0.997 and the luminosity ratio to 0.99.

On the mass- $\log g$ diagram, both components lie on the 3 Myr isochrone, so this system is very young. On the HR diagram, they are slightly overluminous with respect to the evolutionary tracks, but still within the error bars. On the other hand, the components lie exactly on the metal-poor tracks (Z=0.001).

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