Crab Nebula Gamma-ray Flares as Relativistic Reconnection Minijets

We present an analytic statistical model of relativistic magnetic reconnection outflows (``minijets") that can describe the Crab Nebula gamma-ray light curve, including the multiple ∼ week-long flares observed by the AGILE and Fermi/LAT satellites. We argue that the flares' unusually short duration, high luminosity, and high photon energies suggest the flare emission regions are moving toward Earth at bulk relativistic speeds, consistent with reconnection minijets. We show that electrostatic acceleration in the reconnecting region can efficiently accelerate particles up to the radiation reaction limit to produce a mono-energetic synchrotron spectral energy distribution. The statistics of observed minijet high energy fluxes and timescales are assumed to be strongly influenced by their Doppler factors. For statistically independent minijets, we find analytical expressions for all of the moments of the high energy nebular light curve (time average, variance, skewness, etc.). The short timescale variability of the nebula displays a power spectrum with index -2. In the limit of a low reconnection event rate, the observed flare high energy flux distribution follows a power-law of index $\sim -1$, implying that the flare high energy flux average is dominated by bright rare flares. Thus, we provide a simple minijet statistical model of the Crab Nebula light curve that can be directly compared with gamma-ray observations.