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Orbits of spectroscopic binary systems have been studied for more than a century. Over three thousand orbits of spectroscopic binary systems have been derived. These orbits are based on the radial velocities measured from the spectra recorded by a photographic plate to a high precision spectrum observed from a modern spectrograph. In many cases, the shape of the orbit was assumed to be circular, of hence the eccentricity is zero. This assumption is based on the fact that a small eccentricity (e < 0.1) measured from the observed data might be a result from the error of observations or from the intrinsic variation of a spectroscopic binary system. Sixteen southern spectroscopic binary systems, including twelve single-lined binaries and four double-lined binaries, were selected to study in this research program. These systems were assumed to have circular orbits or have very nearly circular orbits (e < 0.1) from their previous published solutions. The HERCULES spectrograph was used in conjunction with the 1-m McLellan telescope at Mt John University Observatory to collect the spectra of these systems. The observations, taken from October 2004 to August 2007, comprised about 2000 high-resolution spectra of spectroscopic binary systems and standard radial-velocity stars. Radial velocities of spectroscopic binary systems were measured from these spectra and orbital solutions of the systems were derived from these radial velocities. It was found that from HERCULES data, we are able to achieve high-precision orbital solutions of all the systems studied. The best-fit solutions can be improved as much as 70 times from the literature’s orbital solutions. It has been found that the precision of a system depends on the rotational velocities of the components as well as the level of their chromospheric activity. We are able to confirm the eccentricity in the orbit of only one of the selected spectroscopic binary systems, HD194215. Its eccentricity is 0.123 29 ± 0.000 78. The small eccentricities of other systems are not confirmed. There are four systems; HD22905, HD38099, HD85622 and HD197649, that have circular orbital solutions from the large errors in their measured eccentricities. Two systems, HD77258 and HD124425, have too small eccentricities, e = 0.000 85±0.000 19 and 0.002 60 ± 0.000 99 to be acceptable. An intrinsic variation is a presumed cause of the spurious eccentricities derived from the data of the other eight systems. Photometric data from Mt John University Observatory service photometry program, as well as the photometric data from the Hipparcos satellite and information of these systems from the literature, using various methods and instruments, give a wider view on the systems’ behaviour. It is possible that the spurious eccentricities derived for these systems result from the eclipsing behaviour of a system (HD50337), or from the nature of the components, such as, the distortion of their shape (HD352 and HD136905), their chromospheric activity (HD9053, HD3405, HD77137, HD101379 and HD155555), or stellar pulsation (HD30021). Models of the active chromosphere system, HD101379, have been simulated. An analysis of synthetic radial velocity data shows that spots on the star’s photosphere can cause a spurious eccentricity. The values of the spurious eccentricity and the longitude of periastron are dependent on the spot size, the spot temperature, and the position of the spots.

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