THE MAXIMUM ENERGY OF ACCELERATED PARTICLES IN RELATIVISTIC COLLISIONLESS SHOCKS

Journal Article · Mon Jul 01 04:00:00 EDT 2013 · Astrophysical Journal

DOI:https://doi.org/10.1088/0004-637X/771/1/54· OSTI ID:22140181

Sironi, Lorenzo ^[1]; Spitkovsky, Anatoly ^[2]; Arons, Jonathan ^[3]

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1. Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)
2. Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544-1001 (United States)
3. Department of Astronomy, Department of Physics, and Theoretical Astrophysics Center, University of California, Berkeley, CA 94720 (United States)

The afterglow emission from gamma-ray bursts (GRBs) is usually interpreted as synchrotron radiation from electrons accelerated at the GRB external shock that propagates with relativistic velocities into the magnetized interstellar medium. By means of multi-dimensional particle-in-cell simulations, we investigate the acceleration performance of weakly magnetized relativistic shocks, in the magnetization range 0 {approx}< {sigma} {approx}< 10{sup -1}. The pre-shock magnetic field is orthogonal to the flow, as generically expected for relativistic shocks. We find that relativistic perpendicular shocks propagating in electron-positron plasmas are efficient particle accelerators if the magnetization is {sigma} {approx}< 10{sup -3}. For electron-ion plasmas, the transition to efficient acceleration occurs for {sigma} {approx}< 3 Multiplication-Sign 10{sup -5}. Here, the acceleration process proceeds similarly for the two species, since the electrons enter the shock nearly in equipartition with the ions, as a result of strong pre-heating in the self-generated upstream turbulence. In both electron-positron and electron-ion shocks, we find that the maximum energy of the accelerated particles scales in time as {epsilon}{sub max}{proportional_to}t {sup 1/2}. This scaling is shallower than the so-called (and commonly assumed) Bohm limit {epsilon}{sub max}{proportional_to}t, and it naturally results from the small-scale nature of the Weibel turbulence generated in the shock layer. In magnetized plasmas, the energy of the accelerated particles increases until it reaches a saturation value {epsilon}{sub sat}/{gamma}{sub 0} m{sub i}c {sup 2} {approx} {sigma}{sup -1/4}, where {gamma}{sub 0} m{sub i}c {sup 2} is the mean energy per particle in the upstream bulk flow. Further energization is prevented by the fact that the self-generated turbulence is confined within a finite region of thickness {proportional_to}{sigma}{sup -1/2} around the shock. Our results can provide physically grounded inputs for models of non-thermal emission from a variety of astrophysical sources, with particular relevance to GRB afterglows.

• OSTI ID: 22140181
• Journal Information: Astrophysical Journal, Journal Name: Astrophysical Journal Journal Issue: 1 Vol. 771; ISSN ASJOAB; ISSN 0004-637X
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
ACCELERATION
ACCELERATORS
AFTERGLOW
ASTROPHYSICS
COSMIC GAMMA BURSTS
EMISSION
IONS
LAYERS
MAGNETIC FIELDS
MAGNETIZATION
PLASMA
PULSARS
RELATIVISTIC RANGE
SATURATION
SCALING
SHOCK WAVES
SIMULATION
TURBULENCE