  The highly eccentric binary system Eta Carinae 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 mass-loss
rates. The resultant ionization maps constrain the regions where helium is
singly- and doubly-ionized. We find that reducing the primary's mass-loss rate
increases the volume of He+. Lowering the primary mass-loss rate produces large
variations in the volume of He+ in the pre-shock primary 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 the primary's mass-loss rate might explain
the observed increase in HeI absorption in recent decades, although numerous
questions regarding this scenario remain open. We also propose that the absence
of broad HeI lines in the spectra of Eta Car between its 1890's eruption and
1944 might be explained by the companion star's He0+ ionizing photons not being
able to penetrate the wind-wind interaction region, due to a higher primary
mass-loss rate at that time (by a factor >2, compared to the present value).
