Particle acceleration is a ubiquitous phenomenon in astrophysical and space plasma. Diffusive shock acceleration (DSA) and stochastic turbulent acceleration (STA) are known to be the possible mechanisms for producing very highly energetic particles, particularly in weakly magnetized regions. An interplay of different acceleration processes along with various radiation losses is typically observed in astrophysical sources. While DSA is a systematic acceleration process that energizes particles in the vicinity of shocks, STA is a random energizing process, where the interaction between cosmic ray particles and electromagnetic fluctuations results in particle acceleration. This process is usually interpreted as a biased random walk in energy space, modeled through a Fokker-Planck equation. In the present work, we describe a novel Eulerian algorithm, adopted to incorporate turbulent acceleration in the presence of DSA and radiative processes like synchrotron and inverse Compton emission. The developed framework extends the hybrid Eulerian−Lagrangian module in a full-fledged relativistic Magneto-hydrodynamic (RMHD) code PLUTO. From our validation tests and case studies, we showcase the competing and complementary nature of both acceleration processes. Axisymmetric simulations of an RMHD jet with this extended hybrid framework clearly demonstrate that emission due to shocks is localized, while that due to turbulent acceleration originates in the backflow and is more diffuse, particularly in the high-energy X-ray band.
Context. Radio-loud AGNs are thought to possess various sites of particle acceleration, which gives rise to the observed non-thermal spectra. Stochastic turbulent acceleration (STA) and diffusive shock acceleration (DSA) are commonly cited as potential sources of high-energy particles in weakly magnetized environments. Together, these acceleration processes and various radiative losses determine the emission characteristics of these extra-galactic radio sources. Aims. The purpose of this research is to investigate the dynamical interplay between the STA and DSA in the radio lobes of FR-II radio galaxies, as well as the manner in which these acceleration mechanisms, along with a variety of radiative losses, collectively shape the emission features seen in these extra-galactic sources. Methods. A phenomenologically motivated model of STA is considered and subsequently employed on a magneto-hydrodynamically simulated radio lobe through a novel hybrid Eulerian-Lagrangian framework.Results. STA gives rise to a curved particle spectrum that is morphologically different from the usual shock-accelerated spectrum. As a consequence of this structural difference in the underlying particle energy spectrum, various multi-wavelength features arise in the spectral energy distribution of the radio lobe. Additionally, we observe enhanced diffuse X-ray emission from radio lobes for cases where STA is taken into account in addition to DSA.
Astrophysical systems possess various sites of particle acceleration, which gives rise to the observed non-thermal spectra. Diffusive shock acceleration (DSA) and stochastic turbulent acceleration (STA) are the candidates for producing very high energy particles in weakly magnetized regions. While DSA is a systematic acceleration process, STA is a random energization process, usually modelled as a biased random walk in energy space with a Fokker-Planck equation. In astrophysical systems, different acceleration processes work in an integrated manner along with various energy losses.Here we study the interplay of both STA and DSA in addition to various energy losses, in a simulated RMHD jet cocoon. Further, we consider a phenomenologically motivated STA timescale and discuss its effect on the emission profile of the RMHD jet. A parametric study on the turbulent acceleration timescale is also conducted to showcase the effect of turbulence damping on the emission structure of the simulated jet.
This work investigates the evolution of the distribution of charged particles (cosmic rays) due to the mechanism of stochastic turbulent acceleration (STA) in presence of small-scale turbulence with a mean magnetic field. STA is usually modelled as a biased random walk process in the momentum space of the non-thermal particles. This results in an advection-diffusion type transport equation for the non-thermal particle distribution function. Under quasilinear approximation, and by assuming turbulent spectra with power being available only in the sub-gyroscale range, we find that the Fokker-Planck diffusion coefficients Dγγ and Dμμ scale with the Lorentz factor γ as: Dγγ∝γ−2/3 and Dμμ∝γ−8/3. We consider Alfvèn and fast waves in our calculations, and find a universal trend for the momentum diffusion coefficient irrespective of the properties of the small-scale turbulence. Such universality has already been reported regarding the spatial diffusion of the cosmic rays, and, here too, we observe a universality in the momentum diffusion coefficient. Furthermore, with the calculated transport coefficients, we numerically solve the advection-diffusion type transport equation for the non-thermal particles. We demonstrate the interplay of various mircophysical processes such as STA, synchrotron loss and particle escape on the particle distribution by systematically varying the parameters of the problem. We observe that the effect of the small-scale turbulence is more impactful for the high energy protons as compared to the electrons and such turbulence is capable of sustaining the energy of the protons from catastrophic radiative loss processes. Such a finding is novel and helps us to enhance our understanding about the hadronic emission processes that are typically considered as a competitor for the leptonic emission for certain astrophysical systems.
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