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The Crab Nebula super-flare in April 2011: extremely fast particle acceleration and gamma-ray emission

We report on the extremely intense and fast gamma-ray are above 100 MeV detected by AGILE from the Crab Nebula in mid-April 2011. This event is the fourth of a sequence of reported major gamma-ray flares produced by the Crab Nebula in the period 2007/mid-2011. These events are attributed to strong radiative and plasma instabilities in the inner Crab Nebula, and their properties are crucial for theoretical studies of fast and efficient particle acceleration up to 10^15 eV. Here we study the very rapid flux and spectral evolution of the event that reached on April 16, 2011 the record-high peak flux of F = (26 +/- 5) x 10^-6 ph cm^-2 s^-1 with a risetime timescale that we determine to be in the range 6-10 hrs. The peak flaring gamma-ray spectrum reaches a distinct maximum near 500 MeV with no substantial emission above 1 GeV. The very rapid risetime and overall evolution of the Crab Nebula are strongly constrain the acceleration mechanisms and challenge MHD models. We briefly discuss the theoretical implications of our observations.