Giant outbursts of luminous blue variables and the formation of the Homunculus nebula around eta Carinae

The observed giant outbursts of luminous blue variables (LBVs) may occur wh en these massive stars approach their Eddington limits, When this happens, they must reach a point at which the centrifugal force and the radiative ac celeration cancel out gravity at the equator. We call this the Omega limit. When stars are close to the Omega limit, strong nonspherical mass loss sho uld occur. This suggests a scenario in which a slow and very dense wind, st rongly confined to the equatorial plane, is followed by a fast and almost s pherical wind. We compute two-dimensional hydrodynamic models of the evolut ion of the nebula formed from such interacting winds, using parameters cons istent 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 s tructured circumstellar nebula. Assuming the star was very close to the Ome ga limit during outburst, our models produce gas distributions that strongl y resemble the Homunculus on large and small scales. This supports the gene ral conjecture that giant outbursts in LBVs occur when they approach the Ed dington limit. Our models constrain the average mass-loss rate since the ou tburst to values smaller than the present-day mass-loss rate and suggest th at eta Car is approaching another outburst. Our models imply that the occur rence of giant LBV outbursts depends on the initial stellar rotation rate a nd that the initial angular momentum is as important to the evolution of ve ry massive stars as their initial mass or metallicity.