The observed giant outbursts of Luminous Blue Variables (LBVs) may occur when these massive stars approach their Eddington limits. When this happens, they must reach a point where the centrifugal force and the radiative acceleration cancel out gravity at the equator. We call this the Omega-limit. When stars are close to the Omega-limit, strong non-spherical mass loss should occur. This suggests a scenario where a slow and very dense wind, strongly confined to the equatorial plane, is followed by a fast and almost spherical wind. We compute two-dimensional hydrodynamic models of the evolution of the nebula formed from such interacting winds, using parameters consistent with the outburst of eta Carinae in the last century. This outburst gave birth to the Homunculus, the hourglass-shaped inner part of a highly structured circumstellar nebula. Assuming the star was very close to the Omega-limit during outburst, our models produce gas distributions that strongly resemble the Homunculus on large and small scale. This supports the general conjecture that giant outbursts in LBVs occur when they approach the Eddington limit. Our models constrains the average mass loss rate since the outburst to values smaller than the present-day mass loss rate and suggest that eta Car is approaching another outburst. Our models imply that the occurrence of giant LBV outbursts depends on the initial stellar rotation rate, and that the initial angular momentum is as important to the evolution of very massive stars as their initial mass or metallicity.
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MPI Astronomie theory group