Acceleration of UHE Cosmic Ray Particles at Relativistic Jets in Extragalactic Radio Source.pdfVIP

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Acceleration of UHE Cosmic Ray Particles at Relativistic Jets in Extragalactic Radio Source.pdf

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Acceleration of UHE Cosmic Ray Particles at Relativistic Jets in Extragalactic Radio Source

a r X i v : a s t r o - p h / 9 6 1 0 1 9 0 v 1 2 3 O c t 1 9 9 6 Acceleration of UHE Cosmic Ray Particles at Relativistic Jets in Extragalactic Radio Sources M. Ostrowski Obserwatorium Astronomiczne, Uniwersytet Jagiellon?ski, Krako?w, Poland (E-mail: mio@oa.uj.edu.pl) Abstract A mechanism of ultra-high energy (UHE) cosmic ray acceleration in extragalac- tic radio sources at the interface between the relativistic jet and the ambient medium is discussed as a supplement to the shock acceleration in ‘hot spots’. Particles accelerated at the jet side boundary are expected to dominate at high- est energies. The spectrum formation near the cut-off energy is modeled using the Monte Carlo particle simulations. 1. Acceleration processes in relativistic jets We extend the discussion of particle acceleration at shock waves formed in the terminal points of relativistic jets (Rachen Biermann 1993, Sigl et al. 1995) by including the additional acceleration process acting at the jet boundary layer. For particles with UHE energies both the shock and the transition layer between the jet and the ambient medium can be approximated as surfaces of discontinuous velocity change. The tangential discontinuity considered in the latter case can be an efficient cosmic ray acceleration site if the considered velocity difference U is relativistic and the sufficient amount of turbulence is present on its both sides (Berezhko 1990, Ostrowski 1990). On average, for an individual boundary crossing UHE particle gain energy is ?E /E = ρe (γu ? 1) , where γu is the flow Lorentz factor and the numerical factor ρe depends on particle anisotropy at the discontinuity. In the presence of efficient particle scattering, particle simulations give ρe as a substantial fraction of unity (Ostrowski 1990). Let us also note that in the case of non-relativistic velocity jump, U c, the acceleration process is of the second-order in U/c. Fig. 1 The model applied for the final part of the jet, near the termin