3 Results

   
3.1 Eclipse light curve

The new light curves of S 1082 confirm the findings of Goranskij et al. (1992) and fill in the gap in their data between photometric phase 0.53 and 0.74 (with phase 0 corresponding to primary minimum). In Fig. 1 our data are folded on their ephemeris for the primary minimum:

$${\rm Min I} = 2~444~643.253(5) + 1\hbox{$.\!\!^{\rm d}$ }0677978(50)~E.$$ (1)

Two unequal eclipses with an amplitude of about 0.09 and 0.05 mag in V are clearly visible with the deeper, primary eclipses occuring around phase 0 as expected from Eq. (1). Goranskij et al. note that the light curve near second quadrature (phase 0.75) is systematically higher than near first quadrature (phase 0.25) by 0.01 to 0.02 mag in V. This might also be the case in our data, but the scatter between phases 0.1 and 0.3 makes this difficult to see. The scatter is probably related to the bad observing conditions (nearby moon) of the last run.

Figure 1: Light and colour curves for S 1082 folded on the ephemeris of Goranskij et al. (1992). Data from the three runs are indicated with different symbols: open circles for run 1, filled circles for run 2 and triangles for run 3. A typical error bar is shown for each run. Magnitude and colours are plotted relative to the average V(11.25), U-V (0.45), B-V (0.41) and V-I (0.57) values in our measurements.

Figure 2: Series of H$\alpha$ profiles in S 1082. The phase of the light curve is indicated for each spectrum. Note the central depth of the line and the asymmetric wings. The observations during phase 0.54 and 0.58 are noisy due to the bad weather conditions of run 5. The continuum separation between the spectra is 0.5 unit.

Figure 3: H$\beta$, Mg Ib and Ca II IRT lines in S 1082 for a selected set of observations. Light curve phases are indicated. The continuum separation between the spectra is 0.5 unit.

Figure 4: Spectrum of S 1082 compared with synthetic spectra of various effective temperatures; surface gravity and projected rotational velocity are fixed at $\log g=4.5$ and $v_{\rm rot}\sin i=10$ km s-1. The spectra are normalised to the flux at 4050 Å; each spectrum is offset with 1 unit from the previous spectrum. The relative strength of the Ca II K line and the Ca II H+H$\epsilon$ blend (marked with "K'' and "H''), and the contrast in the Balmer jump (flux near 4050 Å relative to flux near 3600 Å) are indicators of temperature.

   
3.2 Spectral line profiles

The spectra of S 1082 are dominated by a narrow-lined component resembling a star of type early-F. In addition, the presence of a broad and shallow component in the spectra is prominent in the H$\alpha$ line (see also van den Berg et al. 1999). When the spectra are arranged in order of light curve phase using Eq. (1), it is clear that the position and strength of the asymmetric absorption in the wings vary regularly (Fig. 2); the spectra that were included in Fig. 8 of van den Berg et al. (1999) correspond to photometric phases 0.092, 0.16 and 0.25. Around first quadrature (phase 0.25) the depth of H$\alpha$ is smallest while the asymmetric absorption in the wings is maximally blue-shifted; for phases between 0.5 and 1 the phase-coverage is sparser, but in the spectra of phases 0.88 and 0.90 it can be seen that the asymmetric absorption has moved to the red wing. The timing of the velocity shift with respect to the eclipses associates the broad-lined feature with the brighter star in the eclipsing binary (the brighter star must approach us after the primary eclipse). Similar variable line profiles are visible in the H$\beta$, Na I D, Mg I b and Ca II infrared lines (Fig. 3).

The temperature of the narrow-lined star in S 1082 can be measured with the low-resolution spectra. We assume that its light is least contaminated by its companion star(s) in the blue and therefore concentrate on the region around the Balmer jump. In Fig. 4 synthetic spectra for various effective temperatures $T_{\rm eff}$ are compared with the IDS spectrum between 3535 Å and 4050 Å. The spectra were computed with model atmospheres for solar metallicity (Kurucz 1979). The observed spectrum was corrected for the reddening towards M 67 ( $E(B-V)=0.032~\pm~0.006$, Nissen et al. 1987) and for a radial-velocity difference with respect to the model spectra. From the relative strength of the Ca II H&K lines, a sensitive temperature indicator in this region (e.g. Gray & Garrison 1989), and the contrast in the Balmer jump it is clear that the observed spectrum is hotter than that of a 6500 K star.

This part of the spectrum was fitted to model spectra with surface gravity $\log g$ ranging from 0.5 to 5.0 in steps of 0.5, $T_{\rm eff}$ from 6000 to 8000 K in steps of 250 K and a fixed projected rotational velocity $v_{\rm rot}\sin i$ of 10 km s^-1. A free parameter is a wavelength-independent scale factor ranging from 0.025 to 1 in increments of 0.025 that is a measure of the relative contribution of the narrow-lined star. Observed and model spectra were normalised to the flux at 4050 Å. A straight line was fitted to the difference between the observed and each scaled model spectrum. The model that produces the smallest residuals to the fit has $T_{\rm eff}=7500$ K, $\log g=4.5$ and scale factor 0.85. If the temperature of the hot star is indeed 7500 K, it is a late A rather than an F star; the value of $\log g$ is close to that of a main-sequence star for which $\log g \approx 4.25$ (Gray 1992). This shows that the narrow-lined component dominates the spectrum in the blue and it implies that one of the individual components of S 1082 remains a blue straggler. A more accurate decomposition of S 1082 is given in Sect. 4.

   
3.3 Radial-velocity curves

Radial velocities were measured via cross correlation of the high-resolution spectra with appropriate template spectra (Table 3). To determine the radial velocities of the narrow-lined star in S 1082 we adopted as templates spectra of F-type radial-velocity standards observed during the same run (Table 2). Velocities were derived for each order separately. Only orders without strong telluric lines were selected, and included 4890-6820 Å for the 1996-spectra and 4435-6820 Å for the 2000-spectra. The radial velocities listed in the third column of Table 3 are the averages of the values from the individual orders; the errors represent the spread around the average. Note that systematic errors can still be included, e.g. due to the wavelength calibration. We expect the latter not to exceed 0.75 km s^-1 (see Sect. 2.2.1). Our measurements confirm that the narrow-lined component in S 1082 shows radial-velocity variations of only a few km s^-1.

Figure 5: Cross correlation function resulting from the residual spectrum taken at photometric phase 0.2535 after the contribution of the hot star is removed. The left peak corresponds to the primary star Aa in the eclipsing binary. The width of peak corresponding to the secondary Ab is broader which indicates that its spectral lines are more broadened by rotation. For this particular cross correlation the spectrum between 5160 and 5240 Å was used. The radial velocity is given with respect to the hot star B in S 1082.

The radial-velocity curves of the stars in the eclipsing binary were measured after the contribution of the hot, narrow-lined star to the total spectrum was removed. To that end, all spectra were first brought to the rest frame of the hot star. Then, a hot-star template spectrum was constructed by taking the median of the spectra obtained at phases 0.95, 0.97, 0.0035, 0.019 and 0.048; these particular phases were chosen in order to let the spectral line profiles of the template be as symmetric as possible. For the 1996-spectra, taken with a different instrumental setup, the spectrum obtained at phase 0.092 was chosen as a template. The relative contribution of the hot-star template to the remaining spectra was derived with the same fitting procedure as described in Sect. 3.2: the template multiplied with scaling factors ranging from 0.025 to 1 was subtracted from each individual spectrum, and the scaling that produces the smallest residuals around a fit to a straight line was chosen as the appropriate scaling for that particular spectrum. The scaled template was then subtracted from the total spectrum to obtain the spectrum of the binary at various phases.

Next, these residual spectra were correlated against a synthetic spectrum of $T_{\rm eff}=5250$ K and $\log g=3.5$. For this model spectrum we chose $v_{\rm rot}\sin i=50$ km s^-1 to roughly match the apparently broader lines in the spectrum of the binary. This procedure was repeated for every order between 4380 and 6435 Å, excluding the order that contains the broad H$\beta$ line and the region between 5690 and 6090 Å  for which the cross correlation functions are very noisy with no clear peaks. A cross correlation peak is sometimes visible at $v_{\rm rad}=0$ km s^-1 and represents features of the hot star that were not corrected for (or introduced into the spectrum) by subtraction of the template. The cross correlation functions of most spectra clearly show two peaks with a variable separation (see Fig. 5). One peak is smaller and broader than the other, and is redshifted with respect to the template for phases smaller than 0.5; therefore, this peak is identified with the secondary star in the eclipsing binary. This is the first spectroscopic evidence for the third star in S 1082. The measurements of the velocity of the primary near phase 0.1 are probably distorted due to its eclipse by the secondary star. In the following we will refer to the components of the eclipsing binary as Aa and Ab, and to the outer companion as B.

 

 

Table 3: Radial velocities of the three stars in S 1082, the components of the eclipsing binary Aa and Ab, and the outer companion B. From left to right: heliocentric Julian date (-2 450 000) at the midpoint of observation; photometric phase computed with the ephemeris of Goranskij et al. (1992); heliocentric radial velocity for star B; radial velocity of the primary Aa and secondary Ab in the eclipsing binary with respect to star B in km s^-1. The spectra of phases 0.5378 and 0.5609 were taken under bad observing conditions.

HJD-	phot.	$v_{{\rm rad,B}}$	$v_{{\rm rad,Aa}}$	$v_{{\rm rad,Ab}}$
2 450 000	phase	km s-1	km s-1	km s-1
142.5101	.09213	$33.0\pm0.1$	-	-
142.5790	.1567	$33.2\pm0.1$	$-97\pm4$	-
142.6837	.2548	$32.9\pm0.2$	$-108\pm3$	-
1591.3642	.9540	$33.5\pm0.4$	-	-
1591.3822	.9709	$33.7\pm0.3$	-	-
1591.4170	.003451	$34.2\pm0.3$	-	-
1591.4334	.01880	$33.7\pm0.3$	-	-
1591.4640	.04750	$32.4\pm0.3$	-	-
1591.4805	.06294	$32.8\pm0.3$	-	-
1591.4967	.07812	$32.7\pm0.3$	$-73\pm4$	$122\pm7$
1591.5452	.1235	$33.2\pm0.4$	$-96\pm3$	$148\pm4$
1591.5616	.1389	$33.3\pm0.4$	$-95\pm2$	$141\pm4$
1591.5779	.1541	$33.3\pm0.4$	$-100\pm2$	$153\pm5$
1591.5993	.1742	$33.1\pm0.5$	$-104\pm2$	$154\pm5$
1591.6150	.1890	$33.5\pm0.4$	$-108\pm2$	$150\pm12$
1591.6310	.2039	$33.9\pm0.5$	$-107\pm3$	$166\pm5$
1591.6474	.2192	$34.2\pm0.5$	$-109\pm2$	$170\pm8$
1591.6682	.2387	$33.8\pm0.5$	$-113\pm2$	$160\pm7$
1591.6840	.2535	$33.9\pm0.5$	$-113\pm3$	$169\pm14$
1591.7010	.2695	$33.9\pm0.5$	$-115\pm2$	$180\pm5$
1617.4072	.3435	$31.8\pm0.4$	$-104\pm2$	$163\pm5$
1617.4308	.3656	$32.7\pm0.5$	$-96\pm2$	$153\pm5$
1617.6147	.5378	$36.0\pm1.2$	$28\pm5$	-
1617.6394	.5609	$35.2\pm0.8$	-	-
1624.3903	.8832	$35.4\pm0.4$	$91\pm3$	$-130\pm5$
1624.4092	.9009	$34.6\pm0.4$	$85\pm4$	$-132\pm7$
1624.5766	.05765	$32.4\pm0.3$	-	-
1624.5949	.07484	$32.7\pm0.3$	$-80\pm4$	$121\pm6$
1624.6131	.09188	$32.6\pm0.4$	$-90\pm4$	$128\pm5$

We used the spectrum observed near first quadrature (wavelength region 5160 to 5240 Å containing the Mg I b triplet) to derive an estimate for the projected rotational velocities of both components from the widths of their cross correlation peaks. To that end, we cross correlated a synthetic spectrum of a certain temperature ( $\log g=4.0$, $v_{\rm rot}\sin i=30$ km s^-1) with synthetic templates of the same temperature and surface gravity with $v_{\rm rot}\sin i$ranging from 10 to 100 km s^-1, and with the object spectrum. The peak of the cross correlation functions were fitted with Gaussian profiles. This was repeated for synthetic spectra of temperatures 5000 to 6750 K in steps of 250 K. With the results we constructed calibration curves for each temperature that give the width of the cross correlation peak as a function of the projected rotational velocity of the synthetic template. The widths of the cross correlation peaks from the object spectrum then give a rough estimate for the $v_{\rm rot}\sin i$ of both stars. For star Aa we obtain a $v_{\rm rot}\sin i$ of 51 km s^-1 (5750 K) to 58 km s^-1 (6750 K), for star Ab a $v_{\rm rot}\sin i$ of 83 km s^-1 (5500, 5750 K) to 87 km s^-1 (6750 K).

Figure 6: Fit to the light curves in the U, B, V and Gunn i band. The small panels show the residuals to the fit. Only the data from the first observation run are used.