Acceleration of cosmic rays in presence of magnetohydrodynamic fluctuations at small scales

Sayan Kundu, Nishant K Singh, Bhargav Vaidya

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Abstract

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 quasi-linear 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.
Original languageEnglish
Pages (from-to)4950-4972
Number of pages23
JournalMonthly Notices of the Royal Astronomical Society
Volume524
Issue number4
Early online date12 Jul 2023
DOIs
Publication statusPublished - 1 Oct 2023

Bibliographical note

Funding Information:
We would like to thank the anonymous referees for the helpful comments, and constructive remarks on this manuscript. SK and BV would like to thank the financial support from the Max Planck partner group award at Indian Institute of Technology, Indore. SK further acknowledges support from STFC through grant ST/X001067/1 and the hospitality provided to him by IUCAA, Pune, where part of this work were performed. Additionally, SK extends appreciation to Suchismita Banerjee for her assistance in typesetting the mathematical formulas presented here.

Keywords

  • (ISM:) cosmic rays
  • (magnetohydrodynamics) MHD
  • acceleration of particles
  • radiation mechanisms: non-thermal
  • turbulence

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

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