  We used data from the Fermi Large Area Telescope obtained during the last 7
years and spanning two passages of $\eta$ Carinae at periastron and compared
them with the predictions of particle acceleration in hydrodynamic simulations.
Two emission components can be distinguished. The low-energy component cuts off
below 10 GeV and its flux, modulated by the orbital motion, varies by a factor
less than 2. Short-term variability occurs at periastron. The flux of the high
energy component varies by a factor 3-4 but differently during the two
periastrons. The variabilities observed at low-energy, including some details
of them, and these observed at high-energy during the first half of the
observations, do match the prediction of the simulation, assuming a surface
magnetic field in the range 0.4-1 kG. The high-energy component and the thermal
X-ray emission were weaker than expected around the second periastron
suggesting a modification of the wind density in the inner wind collision zone.
Diffuse shock acceleration in the complex geometry of the wind collision zone
of $\eta$ Carinae provides a convincing match to the observations and new
diagnostic tools to probe the geometry and energetics of the system.
