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3 Velocity reductions and orbit computations

  Radial velocities of the program stars were determined with the IRAF cross-correlation program fxcor (see Fitzpatrick 1993). Several different IAU radial-velocity standard stars were observed during the course of each night at intervals of one to two hours. Their radial velocities were assumed from the work of Scarfe et al. (1990). Other stars used as standards included $\mu$ Her A, assumed velocity of -16.4 kms-1 (Stockton & Fekel 1992) and $\beta$ Aql, assumed velocity of -40.2 kms-1, from extensive unpublished coudé feed results. The velocities of both stars are tied to the Scarfe et al. (1990) system. The small number of ESO velocities were measured relative to $\beta$ Crv = HR 4786, assumed velocity of -7.6 kms-1 (Udry 1998).

Although the velocities of our standards are on a well-defined system, the combination of our various new data sets into a single radial-velocity solution is complicated because of the spectral-type mismatch of the standard and program stars and the different and relatively small wavelength ranges covered by the spectra (from 55 Å to 300 Å), as well as the strong chromospheric activity and large $v\sin i$ of many of the program stars. Unless the spectral type of a standard star is very similar to that of the program star, line strengths, particularly of the weak and moderate strength features, may differ significantly in the program and standard star. Since our program stars are rotationally broadened, such differences in line strength will cause different amounts of blending with nearby strong lines. Different spectrograph setups, resulting in different observed wavelength ranges, exacerbate the line-strength blending problem associated with any spectral-type mismatch. Despite such potential problems, we found that the zero-point velocity shifts between our data sets were not significant, except for the most chromospherically active stars, whose line profiles show obvious variability due to starspots rotating in and out of view.

When the number of observations warranted it, independent orbital solutions were obtained of our various data sets, as well as solutions of data sets in the literature. Often the errors of the older velocities are quite large compared to those of our velocities. In such cases the older velocities were of little use except to improve the period and so were not usually included in the final orbital solution. Furthermore, if the O-C residual of one of our observation exceeded 3.0 sigma it was given zero weight in the final solution but is still listed in the tables in the Appendix.

Several different computer programs, which were used to determine the orbital elements of the various systems, are mentioned in the individual orbital-elements sections. Preliminary elements often were determined with BISP, a computer program that uses a slightly modified version of the Wilsing-Russell method (Wolfe et al. 1967). A differential-corrections program, called SB1, of Barker et al. (1967) has been used to compute eccentric orbits of single-lined systems. For some systems the orbital eccentricity is small enough that a circular-orbit solution may be appropriate. Circular orbits for single- and double-lined binaries have been computed with SB1C and SB2C (Barlow 1998), respectively, both of which use differential corrections to determine the elements. For triple systems a general least-squares (GLS) program (Daniels 1966) has been used to solve simultaneously for the elements of the short- and long-period orbits.


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