The very massive star system \eta Carinae exhibits regular 5.54-year ( 2024-day ) period disruptive events in wavebands ranging from the radio to X-ray .
There is a growing consensus that these events likely stem from periastron passage of an ( as yet ) unseen companion in a highly eccentric ( \epsilon \sim 0.9 ) orbit .
This paper presents three-dimensional ( 3-D ) Smoothed Particle Hydrodynamics ( SPH ) simulations of the orbital variation of the binary wind-wind collision , and applies these to modeling the X-ray light curve observed by the Rossi X-ray Timing Explorer ( RXTE ) .
By providing a global 3-D model of the phase variation of the density of the interacting winds , the simulations allow computation of the associated variation in X-ray absorption , presumed here to originate from near the apex of the wind-wind interaction cone .
We find that the observed RXTE light curve can be readily fit if the observer ’ s line of sight is within this cone along the general direction of apastron .
Specifically , the data are well fit by an assumed inclination i = 45 ^ { \circ } for the orbit ’ s polar axis , which is thus consistent with orbital angular momentum being along the inferred polar axis of the Homunculus nebula .
The fits also constrain the position angle \phi that an orbital-plane projection makes with the apastron side of the semi-major axis , strongly excluding positions \phi < 9 ^ { \circ } along or to the retrograde side of the axis , with the best fit position given by \phi = 27 ^ { \circ } .
Overall the results demonstrate the utility of a fully 3-D dynamical model for constraining the geometric and physical properties of this complex colliding-wind binary system .