Eccentricity e₂ of the hypothetical companion of HD 209458b with e₁ = 0.01 assuming that the eigenmode with the shortest dissipation timescale is damped (black curves in panel a) and b)). a) The mass of the companion is fixed to m₂ = 0.2   M_J. Negative values of e₂ correspond to Δϖ = 180deg while positive ones mean Δϖ = 0deg. The dotted line is the eccentricity that the companion would have had 5.5 Gyr ago assuming a dissipation factor computed with (29). b) Same as a) for different masses m₂ while the semi-major axis is fixed and set to a₂ = 0.4 AU. c) Stellar reflex velocity due to the companion at periastron with the eccentricity of a). d) Idem for the eccentricity of b). In grey regions, the eccentricity of the companion should have been larger than 1 in the past. The configuration appearing in all panels with the same orbital parameters is marked by a fill circle.