Numerical Modeling and Physical Interplay of Stochastic Turbulent Acceleration for Nonthermal Emission Processes

Abstract

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.

Modelling X-shaped radio galaxies: Dynamical and emission signatures from the Back-flow model

“…However, one would need to affirm the universality of this model in formation of XRGs using large-scale and long-term simulations (Hodges-Kluck & Reynolds 2011). Additionally, it would be interesting to understand the interplay of turbulence and shock acceleration (Kundu et al 2021) in wings and its impact on the radiative signature. These studies, along with adopting competing formation models, will be discussed in forthcoming papers.…”

A numerical study of the interplay between Fermi acceleration mechanisms in radio lobes of FR-II radio galaxies

“…Eq. ( 12) is solved using a 2 𝑛𝑑 order accurate finite-volume conservative implicit-explicit (IMEX) scheme (Kundu et al 2021). The radiative losses considered include synchrotron, IC-CMB and adiabatic expansion to model the cooling processes of relativistic electrons.…”

“…For cases (d) and (e) (shown in the right plot of the middle panel and left plot of the bottom panel respectively), the spectrum exhibits an ultra-relativistic Maxwellian distribution at later times. This is a consequence of a steady competition between stochastic acceleration and radiative losses resulting in the acceleration of low-energy electrons towards higher energies (Kundu et al 2021). Moreover, the peak of the distribution corresponds to the value of 𝛾 at which acceleration and loss time scales match, i.e., 𝜏 𝑐 = 𝑡 𝐴 .…”

“…In particular, we have employed MHD simulations to produce radio lobes and analyse the emission features caused by particle energization in the presence of shocks and underlying turbulence. We have adopted our recently developed second-order accurate STA framework (Kundu et al 2021) for this purpose. Owing to the increased computational complexity of the developed framework, this paper will focus on a 2D axisymmetric MHD jet model only while leaving the more computationally expensive 3D case to forthcoming works.…”

Extreme blazars: the result of unstable recollimated jets?

“…In particular, since the simulations clearly show that the flow becomes strongly turbulent after the recollimation shock, it is tempting to explore the possibility that particles energized at the shock can be further accelerated by the turbulence, with an effective interplay between DSA and SA (see e.g. Kundu et al 2021).…”