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Third-Body Parameters from Whole Light and Velocity Curves

Eclipsing binaries can improve multiple system statistics via the light-time effect and radial velocity shifts. Here an algorithm operates on data of mixed type to exploit these opportunities. Main reasons for enhanced reliability are that (1) combined light and velocity curves give better timewise coverage than either type alone, (2) properly weighted solutions impersonally balance light and velocity information, and (3) the entire theory is within the computer model, so observations are used directly without corrections. A brief history of mixed whole-curve solutions is given and the relative importance of light-time and radial velocity input for third-body parameters is discussed and quantified. Period sifting by power spectral analysis is essentially indispensable in preliminary work. Applications are to the Algol-type system DM Persei and the detached system VV Orionis. An assumption of coplanarity for DM Per's inner and outer orbits is tested and quantified by dynamical experiments. Derived third-body parameters for DM Per are mainly reasonable and self-consistent. For comparison with whole-curve results, we also investigated DM Per's ephemeris in terms of eclipse timings and found whole-curve solutions to give smaller standard errors in reference epoch (T0), binary orbit period (P), and dP/dt, over a similar baseline in time. An astonishing outcome is lack of evidence that can pass reasonable validity tests for VV Ori's well-accepted third star with P ≈ 120 days. Estimates of third light do indicate a third star, but the correct period cannot now be established, so the star cannot be identified as the one heretofore recognized from radial velocity evidence. The much cited 120 day period appears to be an artifact of the window function for VV Ori's historical velocity observations.