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We analyze interferometric measurements of the Luminous Blue Variable EtaCarinae with the goal of constraining the rotational velocity of the primarystar and probing the influence of the companion. Using 2-D radiative transfermodels of latitude-dependent stellar winds, we find that prolate wind modelswith a ratio of the rotational velocity (vrot) to the critical velocity (vcrit)of W=0.77-0.92, inclination angle of i=60-90 degrees, and position anglePA=108-142 degrees reproduce simultaneously K-band continuum visibilities fromVLTI/VINCI and closure phase measurements from VLTI/AMBER. Interestingly,oblate models with W=0.73-0.90 and i=80-90 degrees produce similar fits to theinterferometric data, but require PA=210-230 degrees. Therefore, both prolateand oblate models suggest that the rotation axis of the primary star is notaligned with the Homunculus polar axis. We also compute radiative transfermodels of the primary star allowing for the presence of a cavity and densewind-wind interaction region created by the companion star. We find that thewind-wind interaction has a significant effect on the K-band image mainly viafree-free emission from the compressed walls and, for reasonable modelparameters, can reproduce the VLTI/VINCI visibilities taken at phase 0.92-0.93.We conclude that the density structure of the primary wind can be sufficientlydisturbed by the companion, thus mimicking the effects of fast rotation in theinterferometric observables. Therefore, fast rotation may not be the onlyexplanation for the interferometric observations. Intense temporal monitoringand 3-D modeling are needed to resolve these issues.

Is Eta Carinae a fast rotator, and how much does the companion influence the inner wind structure?