A statistical model to explain the gamma-ray flare and variability of Crab nebula Qiang Yuan Institute of High Energy Physics, Chinese Academy of Sciences Collaborated with Pengfei Yin, Xuefeng Wu, Xiaojun Bi, Siming Liu and Bing Zhang (2011, ApJ, 730, L15) 32nd ICRC, Beijing, 2011

Outline Introduction to observations Model and results Discussion

Multi-wavelength observation of crab nebula Very bright in almost all wavelength in the sky Overall emission seems to be stable in most bands (standard candle), which was used to calibrate the detectors Detailed image shows dynamical structures (arcsec, Hubble & Chandra)

Broadband SED: non-thermal syn-IC emission Broken power-law electron spectra High energies: SSC and IC with background radiation

Variability shown in MeV-GeV gamma-ray band Variable at ~yr timescale in 1-150 MeV by COMPTEL and EGRET (Much et al. 1995, de Jager et al. 1996) AGILE/Fermi detected flares at >100 MeV Tavani et al., 2011, Science, 331, 736

No other counterpart of the flare!

Properties of the gamma-ray flare Event rate: once per year Lasting days to weeks No other wavelength counterpart: hard spectra Fermi data showed: the synchrotron component is highly variable at month timescales, but IC component is stable Synchrotron up to > GeV: challenge the traditional shock acceleration (Doppler boost, or electric field acceleration) Abdo et al., 2011, Science, 331, 739

Energy spectra Tavani et al., 2011, Science, 331, 736 Buehler 2011, Fermi Symposium

Theoretical scenarios Komissarov & Lyutikov (2011): flare emission from “knot 1” with MHD instability induced variability Bednarek & Idec (2011): electrons accelerated by the reconnection of magnetic field compressed by decelerating pulsar wind Uzdensky et al. (2011): reconnection powered linear electric accelerator

Theoretical scenarios Komissarov & Lyutikov (2011): flare emission from “knot 1” with MHD instability induced variability Bednarek & Idec (2011): electrons accelerated by the reconnection of magnetic field compressed by decelerating pulsar wind Uzdensky et al. (2011): reconnection powered linear electric accelerator The phenomenological statistical picture We propose that the electrons are accelerated in a series of “knots”, with size distribution The most high energy electrons (PeV) are produced by large knots whose event rates are rare: large fluctuations Low energy electrons do not suffer from significant fluctuations due to the average of much more events: stability of X-ray and IC gamma-ray To produce synchrotron >~GeV, a mildly Lorentz factor is assumed

Monte-Carlo simulation Simulation parameters:

Simulated skymaps 10 keV 100 MeV

Expected variability (number of knots in the period)

Summary A statistical scenario is proposed to explain the gamma-ray variability and flare of Crab nebula A size distribution of the acceleration sites can naturally explain the fluctuation of the highest end of the electron spectra and the stability of low energy electrons The observed variability and flare can be reproduced statistically However, the extreme April 2011 flare might not be easily recovered with the present model configuration (special model might be needed)

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