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 which 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 ^ { \circ } .
( 2 ) for a more typical case , the Wolf-Rayet star in RMC 140 , we demonstrate that for commonly used lines , such as \ion HeII and \ion NIII/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 .