Particle Acceleration in Relativistic Shearing Flows: Energy Spectrum

• Published in: The Astrophysical journal Vol. 933; no. 2; pp. 149 - 156
• Main Authors: Rieger, Frank M., Duffy, Peter
• Format: Journal Article
• Language: English
• Published: Philadelphia The American Astronomical Society 01-07-2022; IOP Publishing
• Subjects: Active galactic nuclei; Astrophysics; Charged particle acceleration; Charged particles; Energy spectra; High energy astronomy; High energy astrophysics; Lorentz factor; Non-thermal radiation sources; Particle acceleration; Particle energy; Particle transport; Power law; Radiation; Relativistic effects; Relativistic jets; Relativistic particles; Shear flow; Shearing; Transport equations; Ultra-high-energy cosmic radiation; Velocity distribution
• ISSN: 0004-637X; 1538-4357
• DOI: 10.3847/1538-4357/ac729c

We consider the acceleration of charged particles in relativistic shearing flows, with Lorentz factor up to Γ
0
∼ 20. We present numerical solutions to the particle transport equation and compare these with results from analytical calculations. We show that in the highly relativistic limit the particle energy spectrum that results from acceleration approaches a power law,
N
(
E
)
∝
E
−
q
˜
, with a universal value
q
˜
=
(
1
+
α
)
for the slope of this power law, where
α
parameterizes the power-law momentum dependence of the particle mean free path. At mildly relativistic flow speeds, the energy spectrum becomes softer and sensitive to the underlying flow profile. We explore different flow examples, including Gaussian and power-law-type velocity profiles, showing that the latter yield comparatively harder spectra, producing
q
˜
≃
2
for Γ
0
≃ 3 and Kolmogorov turbulence. We provide a comparison with a simplified leaky-box approach and derive an approximate relation for estimating the spectral index as a function of the maximum shear flow speed. These results are of relevance for jetted, high-energy astrophysical sources such as active galactic nuclei, since shear acceleration is a promising mechanism for the acceleration of charged particles to relativistic energies and is likely to contribute to the high-energy radiation observed.