Uncovering the orbital dynamics of stars hidden inside their powerful winds: application to η Carinae and RMC 140

Determining accurate orbits of binary stars with powerful winds is challenging. The dense outflows increase the effective photospheric radius, precluding direct observation of the Keplerian motion; instead, the observables are broad lines emitted over large radii in the stellar wind. Our analysis reveals strong, systematic discrepancies between the radial velocities extracted from different spectral lines: the more extended a line's emission region, the greater the departure from the true orbital motion. To overcome these challenges, we formulate a novel semi-analytical model that encapsulates both the star's orbital motion and the propagation of the wind. The model encodes the integrated velocity field of the out-flowing gas in terms of a convolution of past motion due to the finite flow speed of the wind. We test this model on two binary systems. (1) For the extreme case eta Carinae, in which the effects are most prominent, we are able to fit the model to 10 Balmer lines from H alpha to H kappa concurrently with a single set of orbital parameters: time of periastron T-0 = 2454848 (JD), eccentricity e = 0.91, semi-amplitude k = 69 km s(-1), and longitude of periastron omega = 241 degrees. (2) For a more typical case, the Wolf-Rayet star in RMC 140, we demonstrate that for commonly used lines, such as He II and N III/Iv/v, we expect deviations between the Keplerian orbit and the predicted radial velocities. Our study indicates that corrective modelling, such as presented here, is necessary in order to identify a consistent set of orbital parameters, independent of the emission line used, especially for future high accuracy work.