Particle acceleration by ultrarelativistic shocks: theory and simulations

By A. Achterberg, Y. Gallant, J. Kirk, Axel W. Guthmann Astronomical Institute Utrecht, C. Amsterdam, M. Heidelberg. 2001

467 citations recorded by the source corpus.

We consider the acceleration of charged particles near ultra-relativistic shocks, with Lorentz factor Gamma_s >> 1. We present simulations of the acceleration process and compare these with results from semi-analytical calculations. We show that the spectrum that results from acceleration near ultra-relativistic shocks is a power law, N(E) \propto E^{-s}, with a nearly universal value s \approx 2.2 - 2.3 for the slope of this power law. We confirm that the ultra-relativistic equivalent of Fermi acceleration at a shock differs from its non-relativistic counterpart by the occurence of large anisotropies in the distribution of the accelerated particles near the shock. In the rest frame of the upstream fluid, particles can only outrun the shock when their direction of motion lies within a small loss cone of opening angle theta_c \approx 1/Gamma_s around the shock normal. We also show that all physically plausible deflection or scattering mechanisms can change the upstream flight direction of relativistic particles originating from downstream by only a small amount: Delta theta ~ 1/Gamma_s. This limits the energy change per shock crossing cycle to Delta E ~ E, except for the first cycle where particles originate upstream. In that case the upstream energy is boosted by a factor ~ Gamma_s^2 for those particles that are scattered back across the shock into the upstream region.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/8dfbd8496f5348ecc268b7bf9b7c37db1d080745

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In Astronomy and Astrophysics

1. Bing Zhang
2. B. Metzger
3. E. Berger
4. Pawan Kumar
5. D. Giannios
6. L. Sironi
7. A. Spitkovsky
8. E. Liang

In Nuclear and High Energy Physics

1. Bing Zhang
2. D. Giannios
3. A. Spitkovsky
4. L. Sironi
5. A. Marscher
6. B. Metzger
7. J. Arons
8. Pawan Kumar

Citations in the corpus

• THE AFTERGLOWS OF SWIFT-ERA GAMMA-RAY BURSTS. II. TYPE I GRB VERSUS TYPE II GRB OPTICAL AFTERGLOWS (2008, background): “In the standard fireball model3, if the cooling frequency νc lies blueward of the optical bands, it is β = (p − 1)/2 (e.g., Sari et al. 1998; Zhang & Mészáros 2004; Piran 2005, and references therein), with the canonical value p = 2.2 (Kirk et al. 2000; Achterberg et al. 2001), implying β = 0.6.”
• Neutral Beams from Blazar Jets (2002, result): “This acceleration rate is consistent with the maximum energy of particles accelerated by relativistic shocks (Achterberg et al. 2001).”
• The physics of gamma-ray bursts & relativistic jets (2014, background): “ 785, 29. The histogram shows results for pcalculated from lightcurve decay. A xed n= 1 cm3 and B 0 = 10G were assumed; AF/˘n0:2B 1 0 . shock LF (e.g. Bednarz and Ostrowski, 1998; Kirk et al., 2000; Achterberg et al., 2001; Lemoine and Pelletier, 2003). This expectation is not supported by GRB after”
• PARTICLE ACCELERATION AND PLASMA DYNAMICS DURING MAGNETIC RECONNECTION IN THE MAGNETICALLY DOMINATED REGIME (2015, background): “The power-law spectral index p ∼ 1 from relativistic reconnection is significantly harder than the limit p ∼ 2 predicted by nonrelativistic and relativistic shock acceleration theories (e.g., Blandford & Eichler 1987; Achterberg et al. 2001).”
• Relativistic Shocks: Particle Acceleration and Magnetization (2015, background): “For scattering off waves with a small coherence length λ rL, where rL = (pc/eB) is the Larmor radius, roughly (rL/λ) 2 uncorrelated scattering events are needed in order to produce an appreciable deflection, so D ∼ r2Lc/λ ∝ p2 (Achterberg et al. 2001; Pelletier et al. 2009).”
• Swift observations of the very intense flaring activity of Mrk 421 during 2006. I. Phenomenological picture of electron acceleration and predictions for MeV/GeV emission (2009, background): “…a theoretical point of view, several works study relativistic-shock acceleration models that start from different analytical or numerical approaches and find values of s [2.2− 2.4] (Achterberg et al. 2001; Gallant et al. 1999; Lemoine & Pelletier 2003; Blasi & Vietri 2005; Ellison & Double 2004).”
• Synchrotron Self-Compton Model for Rapid Nonthermal Flares in Blazars with Frequency-dependent Time Lags (2004, background): “Achterberg et al. (2001) performed stochastic simulations of the acceleration process at ultrarelativistic shock fronts and found that a power law spectrum N(E) ∝ E−s is produced with a nearly universal value of the slope, s ≈ 2.2–2.3.”
• The Binary Neutron Star Event LIGO/Virgo GW170817 160 Days after Merger: Synchrotron Emission across the Electromagnetic Spectrum (2018, background): “…shocks will lie in between the value p = 2 expected at non-relativistic shock speeds (Bell 1978; Blandford & Ostriker 1978; Blandford & Eichler 1987) and p ' 2.22 at ultra-relativistic velocities (Kirk et al. 2000; Achterberg et al. 2001; Keshet & Waxman 2005; Sironi et al. 2013).”
• ACCELERATION OF PARTICLES AT THE TERMINATION SHOCK OF A RELATIVISTIC STRIPED WIND (2011, result): “This contrasts with the energy spectrum expected from Fermi acceleration in relativistic shocks, which normally yields slopes p > 2 (e.g., Achterberg et al. 2001; Keshet & Waxman 2005), in which case low-energy particles dominate both by number and by energy.”
• Particle Acceleration in Relativistic Collisionless Shocks: Fermi Process at Last? (2008, methodology): “Most progress in studying shock acceleration has been made using Monte Carlo test particle simulations (e.g., Ostrowski & Bednarz 1998, Ellison & Double 2004) and semi-analytic kinetic theory methods (e.g., Kirk et al. 2000, Achterberg et al. 2001, Keshet & Waxman 2005).”
• Particle Acceleration in Relativistic Jets Due to Weibel Instability (2003, methodology): “Anisotropies in the angular distribution of the accelerated particles are large, and the diffusion approximation for spatial transport does not apply (Achterberg et al. 2001).”
• JET BREAKS AND ENERGETICS OF Swift GAMMA-RAY BURST X-RAY AFTERGLOWS (2008, result): “Numerical modelling of electron acceleration (Achterberg et al. 2001; Eichler & Waxman 2005) is also consistent with p > 2.”
• THE MAXIMUM ENERGY OF ACCELERATED PARTICLES IN RELATIVISTIC COLLISIONLESS SHOCKS (2013, background): “As described by Achterberg et al. (2001) and Kirk & Reville (2010), the fact that the spatial diffusion coefficient scales as the square of the particle energy is simply a consequence of the small-scale nature of the Weibel fluctuations.”
• Short-hard gamma-ray bursts (2007, background): “Theoretical predictions of relativistic diffusive shock acceleration typically suggest p ≈ 2.2 (e.g., Achterberg et al. , 2001; Ellison & Double, 2002; Lemoine & Pelletier, 2003; Keshet & Waxman, 2005), which fits the observations nicely 30 .”