Dissecting a SN impostors circumstellar medium: MUSEing about the SHAPE of eta Cars outer ejecta

Aims. The structural inhomogeneities and kinematics of massive star nebulae are tracers of their mass-loss history. We conduct a three-dimensional morpho-kinematic analysis of the ejecta of eta Car outside its famous Homunculus nebula. Methods. We carried out the first large-scale integral field unit observations of eta Car in the optical, covering a field of view of 1x1 centered on the star. Observations with the Multi Unit Spectroscopic Explorer (MUSE) at the Very Large Telescope (VLT) reveal the detailed three-dimensional structure of eta Cars outer ejecta. Morpho-kinematic modeling of these ejecta is conducted with the code SHAPE. Results. The largest coherent structure in eta Cars outer ejecta can be described as a bent cylinder with roughly the same symmetry axis as the Homunculus nebula. This large outer shell is interacting with the surrounding medium, creating soft X-ray emission. We establish the shape and extent of the ghost shell in front of the southern Homunculus lobe and confirm that the NN condensation can best be modeled as a bowshock in the orbital/equatorial plane. Conclusions. The SHAPE modeling of the MUSE observations indicates that the kinematics of the outer ejecta measured with MUSE can be described by a spatially coherent structure, and this structure also correlates with the extended soft X-ray emission associated with the outer debris field. The ghost shell just outside the southern Homunculus lobe hints at a sequence of eruptions within the time frame of the Great Eruption from 1837-1858 or possibly a later shock/reverse shock velocity separation. Our 3D morpho-kinematic modeling and the MUSE observations constitute an invaluable dataset to be confronted with future radiation-hydrodynamics simulations. Such a comparison may shed light on the yet elusive physical mechanism responsible for eta Car-like eruptions.