We analyze interferometric measurements of the Luminous Blue Variable Eta Carinae with the goal of constraining the rotational velocity of the primary star and probing the influence of the companion .
Using 2-D radiative transfer models of latitude-dependent stellar winds , we find that prolate wind models with a ratio of the rotational velocity ( v _ { rot } ) to the critical velocity ( v _ { crit } ) of W = 0.77 - 0.92 , inclination angle of i = 60 \arcdeg - 90 \arcdeg , and position angle PA = 108 \arcdeg - 142 \arcdeg reproduce simultaneously K-band continuum visibilities from VLTI/VINCI and closure phase measurements from VLTI/AMBER .
Interestingly , oblate models with W = 0.73 - 0.90 and i = 80 \arcdeg - 90 \arcdeg produce similar fits to the interferometric data , but require PA = 210 \arcdeg - 230 \arcdeg .
Therefore , both prolate and oblate models suggest that the rotation axis of the primary star is not aligned with the Homunculus polar axis .
We also compute radiative transfer models of the primary star allowing for the presence of a cavity and dense wind-wind interaction region created by the companion star .
We find that the wind-wind interaction has a significant effect on the K -band image mainly via free-free emission from the compressed walls and , for reasonable model parameters , can reproduce the VLTI/VINCI visibilities taken at \phi _ { \mathrm { vb 03 } } = 0.92 - 0.93 .
We conclude that the density structure of the primary wind can be sufficiently disturbed by the companion , thus mimicking the effects of fast rotation in the interferometric observables .
Therefore , fast rotation may not be the only explanation for the interferometric observations .
Intense temporal monitoring and 3-D modeling are needed to resolve these issues .