2002
DOI: 10.1051/0004-6361:20021173
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Comment on the first-order Fermi acceleration at ultra-relativistic shocks

Abstract: Abstract. The first-order Fermi acceleration process at an ultra-relativistic shock wave is expected to create a particle spectrum with the unique asymptotic spectral index σ γ 1 ≈ 2.2. Below, we discuss this result and differences in its various derivations, which -explicitly or implicitly -always require highly turbulent conditions downstream of the shock. In the presence of medium amplitude turbulence the generated particle spectrum can be much steeper than the above asymptotic one. We also note problems wi… Show more

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Cited by 72 publications
(69 citation statements)
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“…If, indeed, the optical emission is synchrotron emission from a fast-cooling electron distribution, then electrons have been primarily accelerated to a power-law distribution with an injection index of q ¼ p À 1 ¼ 3:5. This is much steeper than the canonical spectral index of q $ 2:2Y2:3 found for acceleration on relativistic, parallel shocks (e.g., Gallant et al 1999;Achterberg et al 2001), and could indicate an oblique magnetic field orientation (e.g., Ostrowski & Bednarz 2002;Niemiec & Ostrowski 2004), which would yield a picture consistent with the predominantly perpendicular magnetic field orientation observed on parsec scales (Jorstad et al 2004;Ojha et al 2004;Lister & Homan 2005). The observed hard lag (B vs. R) may then be the consequence of a gradual spectral hardening of the electron acceleration (injection) spectrum throughout the propagation of a relativistic shock front along the jet.…”
Section: Discussionmentioning
confidence: 71%
“…If, indeed, the optical emission is synchrotron emission from a fast-cooling electron distribution, then electrons have been primarily accelerated to a power-law distribution with an injection index of q ¼ p À 1 ¼ 3:5. This is much steeper than the canonical spectral index of q $ 2:2Y2:3 found for acceleration on relativistic, parallel shocks (e.g., Gallant et al 1999;Achterberg et al 2001), and could indicate an oblique magnetic field orientation (e.g., Ostrowski & Bednarz 2002;Niemiec & Ostrowski 2004), which would yield a picture consistent with the predominantly perpendicular magnetic field orientation observed on parsec scales (Jorstad et al 2004;Ojha et al 2004;Lister & Homan 2005). The observed hard lag (B vs. R) may then be the consequence of a gradual spectral hardening of the electron acceleration (injection) spectrum throughout the propagation of a relativistic shock front along the jet.…”
Section: Discussionmentioning
confidence: 71%
“…Several electron injection/acceleration scenarios have been proposed, e.g. impulsive injection near the base of the jet (e.g., [22,23]; such a scenario might also apply to originally Poyntingflux dominated jets, see [80]), isolated shocks propagating along the jet (e.g., [52,39,78,81]), internal shocks from the collisions of multiple shells of material in the jet [83], stochastic particle acceleration in shear boundary layers of relativistic jets (e.g., [64,73]), magnetic reconnection in Poynting-flux dominated jets (e.g., [80]), or hadronically initiated pair avalanches [37].…”
Section: Blazar Modelsmentioning
confidence: 99%
“…Significant progress has recently been made in our understanding of particle acceleration at relativistic shocks (e.g., [1,64,62,88]) and the conversion of relativistic bulk kinetic energy into relativistic particles and ultimately into radiation [69,76,86,53]. While particle acceleration at relativistic parallel shocks might produce electron injection spectra ofṄ e (γ) ∝ γ −q with 2.2 < ∼ q < ∼ 2.3 (e.g., [1]), oblique shocks tend to produce much softer injection spectral indices (e.g., [64]).…”
Section: Blazar Modelsmentioning
confidence: 99%
“…A different critique was levied (Ostrowski & Bednarz 2002) concerning the spectral slope for particles accelerated at highly relativistic shocks. These authors pointed out that the claims of universality for the spectral index s % 4:2 (Kirk & Schneider 1987;Heavens & Drury 1988;Bednarz & Ostrowski 1998;Kirk et al 2000) possibly overstate their case, because they neglect the fact that, as the regular magnetic field in the downstream region becomes stronger than the field associated with the turbulent component, the spectral slope must increase, the spectrum softens, and the claim to universality evaporates.…”
Section: Accelerationmentioning
confidence: 99%