Electron Acceleration in Relativistic Gamma-Ray Burst Shocks

The shock model of gamma-ray bursts (GRBs) has two free parameters: B and e. It has been shown that B should range between few x 10(-3) and few x 10(-4). However, how to calculate the value of e has remained an outstanding theoretical problem for over a decade. Here, we demonstrate that the Weibel theory inevitably predicts that epsilone approximately radical epsilonB. The GRB afterglow data fully agree with this theoretical prediction. Our result explains why the electrons are close to equipartition in GRBs. This e-B relation can potentially be used to reduce the number of free parameters in afterglow models.

[1]  F. A. Harrison,et al.  A Study of the Afterglows of Four GRBs: Constraining the Explosion and Fireball Model , 2003, astro-ph/0307056.

[2]  M. V. Medvedev,et al.  Interpenetrating Plasma Shells: Near-Equipartition Magnetic Field Generation and Nonthermal Particle Acceleration , 2003, astro-ph/0307500.

[3]  J. Frederiksen,et al.  Non-Fermi Power-Law Acceleration in Astrophysical Plasma Shocks , 2004, astro-ph/0408558.

[4]  N. Gehrels,et al.  Analysis of the X‐ray emission of nine Swift afterglows , 2006 .

[5]  Zhi-Yun Li,et al.  Wind Interaction Models for the Afterglows of GRB 991208 and GRB 000301C , 2000, astro-ph/0010288.

[6]  Cluster Magnetic Fields from Large-Scale Structure and Galaxy Cluster Shocks , 2005, astro-ph/0512079.

[7]  R. Fonseca,et al.  Space-charge effects in the current-filamentation or Weibel instability. , 2006, Physical review letters.

[8]  A. Panaitescu,et al.  Prompt γ-ray and early afterglow emission in the external shock model , 2004, astro-ph/0404588.

[9]  S. R. Kulkarni,et al.  The Broadband Afterglow of GRB 980703 , 2003 .

[10]  Å. Nordlund,et al.  Magnetic Field Generation in Collisionless Shocks: Pattern Growth and Transport , 2003, astro-ph/0308104.

[11]  A. Panaitescu,et al.  Properties of Relativistic Jets in Gamma-Ray Burst Afterglows , 2001, astro-ph/0109124.

[12]  USA,et al.  Cosmic Ray Acceleration at Ultrarelativistic Shock Waves: Effects of a “Realistic” Magnetic Field Structure , 2005, astro-ph/0510811.

[13]  A. Panaitescu,et al.  Jet Energy and Other Parameters for the Afterglows of GRB 980703, GRB 990123, GRB 990510, and GRB 991216 Determined from Modeling of Multifrequency Data , 2001 .

[14]  M. Medvedev.  The Theory of Spectral Evolution of the Gamma-Ray Burst Prompt Emission , 2005, astro-ph/0510472.

[15]  Magnetic field generation in relativistic shocks - An early end of the exponential Weibel instability in electron-proton plasmas , 2004, astro-ph/0408550.

[16]  Zhi-Yun Li,et al.  Wind Interaction Models for Gamma-Ray Burst Afterglows: The Case for Two Types of Progenitors , 1999, astro-ph/9908272.

[17]  Zhi-Yun Li,et al.  Wind-Interaction Models for the Early Afterglows of Gamma-Ray Bursts: The Case of GRB 021004 , 2003, astro-ph/0303650.

[18]  Abraham Loeb,et al.  Generation of Magnetic Fields in the Relativistic Shock of Gamma-Ray Burst Sources , 1999, astro-ph/9904363.

[19]  D. Frail,et al.  The Nonrelativistic Evolution of GRBs 980703 and 970508: Beaming-independent Calorimetry , 2004, astro-ph/0405431.

[20]  A. Panaitescu,et al.  Fundamental Physical Parameters of Collimated Gamma-Ray Burst Afterglows , 2001 .

[21]  Particle Acceleration and Magnetic Field Generation in Electron-Positron Relativistic Shocks , 2004, astro-ph/0409702.

[22]  H. Sol,et al.  Particle Acceleration in Relativistic Jets due to Weibel Instability , 2003 .