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2. Spectroscopic orbits and system parameters

The final orbital elements were found by least-squares fitting with weights inversely proportional to the square of formal velocity errors. The elements and their formal errors are given in Table 3 (click here). For circular orbits I checked that non-zero eccentricity did not result in the significant improvement of the quality of fit. Number of measurements used (primary and secondary lines counted separately) and the unweighted rms residuals are given in the 8th column of Table 3 (click here). Its last column contains mass function for single-lined systems or tex2html_wrap_inline1276 for the components of double-lined systems. Radial velocity curves are given in the Figs. 1-7. Individual observations, their errors and residuals can be found in Table 4 which is available in electronic form only. It contains also the measurements of non-variable components. The CORAVEL measurements are marked as COR in the last column. The measurements rejected in orbit computation are marked by colons.

The reduction of the blended CC dips of double-lined systems ADS 3991 and 8861 was done in two steps. First, the average parameters of component's dips were determined from observations made at the moments of the greatest radial velocity difference. Then the width and contrast of individual dips were fixed and only velocities were fitted. This procedure works well even for radial velocity difference of few km/s.

Magnitude difference of the components of double-lined systems was determined by fitting simultaneously the ratio of dip equivalent widths EW and the combined B-V color (Tokovinin 1990):


It is also assumed that for main-sequence components the standard dependence of absolute magnitude tex2html_wrap_inline1286 and mass on B-V color holds. The interpolation formulas


were used. They offer a good approximation of the data given in the table B1 of Gray (1988) for spectral types from F5V to M2V.

Distance to a multiple system is one of the most important parameters in interpretation and modelling of observations. Generally, the distances to multiple systems can be determined with better accuracy than distances to single stars because different data can be combined. Three systems contain visual binaries with known orbits. Masses of their components are estimated from spectral types and dynamical parallaxes are calculated. For the remaining systems less secure photometric distances are adopted.

The models of multiple systems are given in Table 5 (click here). First column contains ADS numbers, parallaxes and distance moduli m-M (d stands for dynamical distances, s for spectroscopic). Second column gives component identification (visual components are marked by upper-case letters, spectroscopic components by second lower-case letters). Then in Cols. 3 to 7 the estimated visual magnitudes, spectral types, absolute magnitudes and masses of components are given. These estimates come from the magnitude differences of double-lined systems and from spectral type assignments that would match absolute magnitude, observed colors and equivalent widths. Thus the data in the left half of Table 5 (click here) represent an ``educated guess" based on the available observational data, rather than directly measured quantities. Lower limits of secondary mass are given for single-lined systems.

Each hierarchical multiple system can be decomposed into a number of binary systems. The last four columns of Table 5 (click here) summarize the parameters of these ``elementary" binaries. Column ``type" has obvious coding: CPM for common proper motion pairs, VB for visual binaries with known orbit, SB1 and SB2 for single- and double-lined spectroscopic binaries. The periods of CPM pairs are estimated by the third Kepler law from separation a (given in the last column), parallax tex2html_wrap_inline1298 and total mass in solar mass units:

where P is in years, a and tex2html_wrap_inline1304 in arcseconds. The same formula is inverted to calculate apparent semimajor axis of a spectroscopic binary from its period. The radial velocity difference tex2html_wrap_inline1306 in km/s between the components of a visual binary is estimated by the formula

where P is in years. When estimating the expected radial velocity difference between CPM components the terms containing inclination i and eccentricity e are omitted from Eq. (5) because they are not known.

Discussion of individual systems is given in the Appendix.

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