Context. Powerful methods are available to reconstruct the spectra of stars in orbit around each other, using a time-series of observed, composite spectra. They act either on the Fourier components of the observed spectra, or directly on these spectra in a velocity grid. Aims. We discuss under which conditions spurious patterns can appear in reconstructed spectra, either as a consequence of (quasi)-degeneracy of the equations or as a consequence of bias in the observed spectra. Also we discuss the equivalence of Fourier and direct methods in practice. Methods. We show under which conditions the equations degenerate, and how to evaluate this. We pay special attention to spectra of binary stars and triple systems analysed in Fourier space. We apply the theory to real data sets and to artificial data sets with several types of data-reduction bias constructed to illustrate degeneracies and the transfer of bias to the reconstructed spectra. Results. Quasi-degeneracy of the equations depends on the lack of significant time-variability in the relative light contribution of the stars, on the length of the spectral interval in units of the involved Doppler shifts, on the presence of very faint stellar components, and on the distribution of the observations over the orbital phases. Eclipse spectra, possibly used with different weight in low-and highfrequency Fourier modes, remove quasi-degeneracies. But when the normalisation of the observed spectra is biased in a systematic way with relation to the orbital phase, then the bias amplifies strongly in the reconstructed spectra, particularly for the faintest components. Wavelength-locked bias is transferred more strongly to the spectrum of the star with the lowest velocity amplitude. Unrecognized variations in line strength lead to bias that is larger in spectral regions with high line-density. Most importantly, the bias in all reconstructed spectra is coupled in a unique, predictable way. This coupling allows us to design robust procedures for the removal of bias from the reconstructed spectra. Conclusions. When the spectral features of all stars visible in the observed spectra undergo a significant time-variable dilution effect, then the reconstructed spectra are well-defined. Otherwise, spurious patterns, mostly of low frequency, may be superimposed on the reconstructed spectra. The analysis presented in this paper allows observers to optimise their observing strategy, gives insight in the origin of spurious patterns and indicates ways either to suppress such patterns or to remove them a posteriori from the reconstructed spectra. In this way, a broader range of astrophysical analyses can be applied to the component spectra.

Aims. θ 2 Tau is a detached and single-lined interferometric-spectroscopic binary as well as the most massive binary system of the Hyades cluster. The system revolves in an eccentric orbit with a periodicity of 140.7 days. Its light curve furthermore shows a complex pattern of δ Scuti-type pulsations. The secondary has a similar temperature but is less evolved and fainter than the primary. In addition, it is rotating more rapidly. Since the composite spectra are heavily blended, the direct extraction of radial velocities over the orbit of component B was hitherto unsuccessful. Our aim is to reveal the spectrum of the fainter component and its corresponding Doppler shifts in order to improve the accuracy of the physical properties of this important "calibrator" system. Methods. Using high-resolution spectroscopic data recently obtained with the Elodie (Observatoire de Haute-Provence, France) and Hermes (Roque de Los Muchachos, La Palma, Spain) spectrographs, and applying a spectra disentangling algorithm to three independent data sets including CfA spectra (Oak Ridge Observatory, USA), we derived an improved spectroscopic orbit. We next used a code based on simulated annealing and general least-squares minimization to refine the orbital solution by performing a combined astrometric-spectroscopic analysis based on the new spectroscopy and the long-baseline data from the Mark III optical interferometer. Results. As a result of the performed disentangling, and notwithstanding the high degree of blending, the velocity amplitude of the fainter component is obtained in a direct and objective way. Major progress based on this new determination includes an improved computation of the orbital parallax (still consistent with previous values). Our mass ratio is in good agreement with the older estimates of Peterson et al. (1991Peterson et al. ( , 1993, but the mass of the primary is 15-25% higher than the more recent estimates by Torres et al. (1997) and Armstrong et al. (2006). Conclusions. The evolutionary status of both components is re-evaluated in the light of the revisited properties of θ 2 Tau AB. Due to the strategic position of the components in the turnoff region of the cluster, the new determinations imply stricter constraints for the age and the metallicity of the Hyades cluster. We conclude that the location of component B can be explained by current evolutionary models, but the location (and the status) of the more evolved component A is not trivially explained and requires a detailed abundance analysis of its disentangled spectrum. The improved accuracy (at the 2% level) on the stellar masses provides a useful basis for the comparison of the observed pulsation frequencies with suitable theoretical models.

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