The highly eccentric binary system Eta Carinae ( \eta Car ) shows numerous time-variable emission and absorption features .
These observational signatures are the result of interactions between the complex three-dimensional ( 3D ) wind–wind collision regions and photoionization by the luminous stars .
Specifically , helium presents several interesting spectral features that provide important clues on the geometry and physical properties of the system and the individual stars .
We use the simplex algorithm to post-process 3D smoothed particle hydrodynamics simulation output of the interacting winds in \eta Car in order to obtain the fractions of ionized helium assuming three different primary star ( \eta _ { \mathrm { A } } ) mass-loss rates .
The resultant ionization maps constrain the regions where helium is singly- and doubly-ionized .
We find that reducing \eta _ { \mathrm { A } } ’ s mass-loss rate ( \dot { M } _ { \eta _ { \mathrm { A } } } ) increases the volume of He ^ { + } .
Lowering \dot { M } _ { \eta _ { \mathrm { A } } } produces large variations in the volume of He ^ { + } in the pre-shock \eta _ { \mathrm { A } } wind on the periastron side of the system .
Our results show that binary orientations in which apastron is on our side of the system are more consistent with available observations .
We suggest that small variations in \dot { M } _ { \eta _ { \mathrm { A } } } might explain the observed increase in He i absorption in recent decades , although numerous questions regarding this scenario remain open .
We also propose that the absence of broad He i lines in the spectra of \eta Car between its 1890 ’ s eruption and \sim 1944 might be explained by \eta _ { \mathrm { B } } ’ s He ^ { 0 + } -ionizing photons not being able to penetrate the wind-wind interaction region , due to a higher \dot { M } _ { \eta _ { \mathrm { A } } } at that time ( by a factor \gtrsim 2 , compared to the present value ) .