We observed the massive binary stellar system of Eta Carinae in the 0.3-10 keV energy range with the X-ray Telescope onboard the Swift satellite during the period 15 December 2008 - 11 March 2009, i.e. 1 month before to 2 months after the X-ray drop from maximum to minimum, thought to be associated with the periastron encounter of the primary star by the hot companion. Beginning a few months before eclipse, the interaction between the winds of the two stars intensifies and the X-ray flux reaches maximum. The flux drops dramatically thereafter, subsiding in about 20 days to a level that is at least a factor 10 lower than the high state, i.e. the X-ray emission state of the system during the largest fraction of its 5.52 yr orbit (~e-11 erg/s/cm2). Unlike in previous cycles, when the low state lasted about 2.5 months, observations with RXTE showed that the X-ray flux started its recovery to normal level about 1.5 months after the minimum. We suggest that this early recovery may be due to the fact that the companion wind reaches terminal velocity before encountering the shock.
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