The first full orbit of

Aims. The binary system η Carinae has completed its first 5.54 y orbit since the beginning of science operation of the Fermi Large Area Telescope (LAT). We are now able to investigate the high-energy γ-ray source at the position of η Carinae over its full orbital period. By this, we can address and confirm earlier predictions for temporal and spectral variability. Methods. Newer versions of the LAT datasets, instrument response functions and background models allow for a more accurate analysis. Therefore it is important to re-evaluate the previously analyzed time period along with the new data to further constrain location, spectral shape, and flux time history of the γ-ray source. Results. We confirm earlier predictions of increasing flux values above 10 GeV toward the next periastron passage. For the most recent part of the data sample, flux values as high as those before the first periastron passage in 2008 are recorded. A comparison of spectral energy distributions around periastron and apastron passages reveals strong variation in the high-energy band. This is due to a second spectral component that is present only around periastron. Conclusions. Improved spatial consistency with the γ-ray source at the position of η Carinae along with the confirmation of temporal variability above 10 GeV in conjunction with the orbital period strengthens the argument for unambiguous source identification. Spectral variability provides additional constraints for future modeling of the particle acceleration and γ-ray emission in colliding-wind binary systems