1. 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

2. Outline
Introduction to observations
Model and results
Discussion

3. 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)

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

5. Variability shown in MeV-GeV gamma-ray band
Variable at ~yr timescale in 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

6. No other counterpart of the flare!

7. 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

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

9. 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

10. 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

11. Monte-Carlo simulation
Simulation parameters:

12. Simulated skymaps
10 keV MeV

13. Expected variability (number of knots in the period)

14. 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)

15. Thank you