The evolved, massive highly eccentric binary system, eta Carinae, underwent a periastron passage in the summer of 2014. We obtained two coordinated X-ray observations with XMM-Newton and NuSTAR during the elevated X-ray flux state and just before the X-ray minimum flux state around this passage. These NuSTAR observations clearly detected X-ray emission associated with eta Car extending up to ~50 keV for the first time. The NuSTAR spectrum above 10 keV can be fit with the bremsstrahlung tail from a kT ~6 keV plasma. This temperature is Delta kT ~2 keV higher than those measured from the iron K emission line complex, if the shocked gas is in collisional ionization equilibrium. This result may suggest that the companion stars pre-shock wind velocity is underestimated. The NuSTAR observation near the X-ray minimum state showed a gradual decline in the X-ray emission by 40% at energies above 5 keV in a day, the largest rate of change of the X-ray flux yet observed in individual eta Car observations. The column density to the hardest emission component, NH ~1e24 cm-2, marked one of the highest values ever observed for eta Car, strongly suggesting increased obscuration of the wind-wind colliding X-ray emission by the thick primary stellar wind prior to superior conjunction. Neither observation detected the power-law component in the extremely hard band that INTEGRAL and Suzaku observed prior to 2011. If the non-detection by NuSTAR is caused by absorption, the power-law source must be small and located very near the WWC apex. Alternatively, it may be that the power-law source is not related to either eta Car or the GeV gamma-ray source.
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