3 Results and discussion

The measurements are presented in Table 1. For multiple systems with at least 3 components, the name of each measured couple is given. Ephemeris are computed for double and/or multiple stars with known orbits. Figure 1 displays the residuals in $\rho$ and $\theta$ as a cloud of points with error bars in the $(\Delta\rho/\rho, \Delta\theta)$ plane. This cloud of points centered on (0,0) validates the data reduction and calibration procedure. We also notice a few cases of abnormally large differences between our measurements and the expected values from the previously determined orbits. This is the case for example of Cou 321 ($\Delta\theta\simeq 40^\circ$) or A 2992 ($\frac{\Delta\rho}{\rho}\simeq 60$%). Corresponding points are labelled with star names in Fig. 1. In order to check whether the problem comes from a poor observation or a bad orbit, we looked for other published data (Hartkopf 1998) and plotted residuals as a function of time. This was done for nine stars (BU 524, A 2681, BU 575, A 2477, BU 1077, A 1777, Cou 612, Cou 321, and STF 2556). Examination of these curves led us to recalculate new orbital elements for all these stars but BU 575.

  

Figure 1: Two dimensionnal plot of the residuals in position angle ($\Delta\theta$) and os the relative residuals in separation ($\Delta\rho/\rho$). For couples with known orbit, each measurement corresponds to a point in the graph. Error bars in $\rho$ and $\theta$ have been drawn to scale. For points with large residuals, corresponding star names are given (in the case of BU 524, 1 refers to the orbit of 1980 while 2 refers to our orbit)

The following comments can be made for some individual stars:

• Moaï 1 was discovered as double in December 1995 (Carbillet et al. 1996). An error occurred with the published values of the position angle, the correct values being: date = 1995.947, $\rho=0 \hbox{$.\!\!^{\prime\prime}$}110 \pm 0 \hbox{$.\!\!^{\prime\prime}$}003$, $\theta=167 \pm 1^\circ$ (Carbillet et al. 1998b).
• BU 524 was observed near periastron, close to the limiting resolution of the telescope (0$.\!\!^{\prime\prime}$066 mas at $\lambda=$ 644 nm).
• A 1777 is a quintuple star. AB, AC and AD are expected to be resolved by a 2 m telescope. The couple AC did not fit in our field of view (separation $\simeq 60\hbox{$.\!\!^{\prime\prime}$}$), so we did not measure it. We searched for companions close to star D but nothing was detected (for a separation $\ge 0\hbox{$.\!\!^{\prime\prime}$}05$ and a magnitude difference <5).
• STF 1517 is a double star with a very uncertain orbit (Hopmann 1970), computed period is about 4050 yr. This orbit cannot be used for ephemeris computation.
• $\nu$ Cyg was initially observed as a reference star and discovered double. The first observation (1997.468) being very poor, it has been reobserved in 1997.471 for confirmation and in 1997.561 for three colors relative photometry. Its duplicity was discovered by Hipparcos (The Hipparcos Catalogue, 1997).
• BU 575 has a very uncertain orbit. A possible confusion between stars A and B (small magnitude difference) causes an uncertainty of 180$^\circ$.
• XY Leo is mentioned as a quadruple star in Tokovinin (1997). Spectroscopic observations have revealed that this system is composed of two close pairs (denoted as Aab and Bab), one being a contact binary. The expected separation between the pairs deduced from spectrophotometric measurements is $AB\simeq 0\hbox{$.\!\!^{\prime\prime}$}15$ (Barden 1987). To our knowledge, it has never been resolved by visible speckle interferometry. We also did not detect this companion.