Non-linear diffusive shock acceleration: A recipe for injection of electrons

Abstract

Prescriptions for electron injection into the diffusive shock acceleration process are required in many practical considerations of cosmic-ray astrophysics, particularly in modeling of the synchrotron emission of astrophysical sources. In particle-in-cell simulations of quasi-parallel magnetized collisionless shocks, we analyse the evolution of particle spectra. We find that in the later stages of shock evolution, the initially strong suprathermal part in the ion spectra fades, thus leaving the spectra composed of a Maxwellian and a power law. Once the electron and ion spectra flatten and become parallel, we find that the amounts of cosmic ray ions and electrons become similar. We make the step towards relating the micro and macro-scale physics by applying this injection rule to Blasi's semi-analytical model of non-linear diffusive shock acceleration, in order to obtain the particle spectra and electron-to-proton ratio $K_{\mathrm{ep}}$ at high energies. By using shock jump conditions that include the electron heating, we find $K_{\mathrm{ep}}$ as a function of Mach number. For Mach number $\sim$ 100, our model finely reproduces the typically observed ratio for Galactic cosmic-rays $K_{\mathrm{ep}}\sim$ 1:100 in the test particle regime.

17 pages, 12 figures

References in corpus (20)

• Simultaneous Acceleration of Protons and Electrons at Nonrelativistic Quasiparallel Collisionless Shocks
• A Physical Relationship Between Electron-Proton Temperature Equilibration and Mach Number in Fast Collisionless Shocks
• A kinetic approach to cosmic ray induced streaming instability at supernova shocks
• Simulations of relativistic collisionless shocks: shock structure and particle acceleration
• Simulations and Theory of Ion Injection at Non-relativistic Collisionless Shocks
• Galactic cosmic rays after the AMS-02 observations
• Dynamical Feedback of Self-generated Magnetic Fields in Cosmic Ray Modified Shocks
• The maximum momentum of particles accelerated at cosmic ray modified shocks
• Electron Shock Surfing Acceleration in Multidimensions: Two-dimensional Particle-In-Cell Simulation of Collisionless Perpendicular Shock
• Dynamical effects of self-generated magnetic fields in cosmic ray modified shocks
• Observational Evidence for Stochastic Shock Drift Acceleration of Electrons at the Earth's Bow Shock
• Theory of Stochastic Shock Drift Acceleration for Electrons in the Shock Transition Region
• Electron Pre-Acceleration at Nonrelativistic High-Mach-Number Perpendicular Shocks
• Radio Evolution of Supernova Remnants Including Non-linear Particle Acceleration: Insights from Hydrodynamic Simulations
• The Acceleration of Electrons at Collisionless Shocks Moving Through a Turbulent Magnetic Field
• Signature of Energy Losses on the Cosmic Ray Electron Spectrum
• On the non-thermal electron-to-proton ratio at cosmic acceleration sites
• Particle acceleration and wave excitation in quasi-parallel high-Mach-number collisionless shocks: Particle-in-cell simulation
• Resonant micro-instabilities at quasi-parallel collisionless shocks: cause or consequence of shock (re)formation
• Particle acceleration in interstellar shocks

Cited by in corpus (4)

• Electron-Ion Temperature Ratio in Astrophysical Shocks
• Cosmic-ray electrons released by supernova remnants
• On the distribution function of suprathermal particles at collisionless shocks
• Non-linear Diffusive Shock Acceleration of Cosmic Rays -- Quasi-thermal and Non-thermal Particle Distributions