This paper presents an orbital analysis of six southern single-lined spectroscopic binary systems. The systems selected were shown to have circular or nearly circular orbits (e < 0.1) from earlier published solutions of only moderate precision. The purpose was to obtain high-precision orbital solutions in order to investigate the presence of small non-Keplerian velocity effects in the data and hence the reality of the small eccentricities found for most of the stars.
The Hercules spectrograph and 1-m McLellan telescope at Mt John Observatory, New Zealand, were used to obtain over 450 CCD spectra between 2004 October and 2007 August. Radial velocities were obtained by cross-correlation. These data were used to achieve high-precision orbital solutions for all the systems studied, sometimes with solutions up to about 50 times more precise than those from the earlier literature. However, the precision of the solutions is limited in some cases by the rotational velocity or chromospheric activity of the stars.
The data for the six binaries analysed here are combined with those for six stars analysed earlier by Komonjinda, Hearnshaw and Ramm. We have performed tests using the prescription of Lucy on all 12 binaries, and conclude that, with one exception, none of the small eccentricities found by fitting Keplerian orbits to the radial-velocity data can be supported. Instead we conclude that small non-Keplerian effects, which are clearly detectable for six of our stars, make impossible the precise determination of spectroscopic binary orbital eccentricities for many late-type stars to better than about 0.03 in eccentricity, unless the systematic perturbations are also carefully modelled. The magnitudes of the non-Keplerian velocity variations are given quantitatively.