An Investigation of the Small Eccentricity in the Spectroscopic Binary System ζ TrA

Abstract

AbstractThe orbital eccentricity of the SB1 system ζ TrA (S.T. F9V, P ∼ 13 d) was found by Skuljan et al. (2004) to be e = 0.01398 ± 0.00019. Lucy (2005) devised a statistical test of the significance of this result, based on the amplitude and phase of the third harmonic in the Fourier analysis of the radial velocity data, and concluded that the non-zero eccentricity measured does not arise from a slightly eccentric Keplerian orbit, but from proximity effects in the binary. He therefore believes a circular orbit should be assigned to this system. In this paper we investigate one possible proximity effect, namely the tidal distortion of the primary star, such that the measured Doppler shift does not accurately indicate the centre of mass radial velocity of the star as a whole. The code of Wilson & Devinney (2003) was used to model the tidal distortion of the measured radial velocities, assuming a range of possible secondary masses, corresponding to M-dwarf companions. The result is that even for the lowest possible mass secondary of 0.09M⊙ with sin i = 1 (this gives the greatest tidal distortion, as it is closest to the primary) there is no significant effect on the radial velocities (the differences are of order 1 m s−1 as a result of the tidal effects). Similar negligible tidal effects arise using a white dwarf companion. We note that the difference between a circular orbit and the observations amounts to as much as 140 m s−1 at some phases, which is essentially the amplitude of the second harmonic in the data. Our conclusion is that this strong and highly significant second harmonic is most probably the result of a small orbital eccentricity as reported by Skuljan et al (2004). We note that the observed third harmonic according to Lucy (2005) has an amplitude of only 5.2 ± 2.0 m s−1, which is just over twice the error bar of its measurement, and that the predicted third harmonic for an eccentric orbit is only 1.6 m s−1.