Cosmic-ray electrons released by supernova remnants

Abstract

The process that allows cosmic rays (CRs) to escape from their sources and be released into the Galaxy is still largely unknown. The comparison between CR electron and proton spectra measured at Earth suggests that electrons are released with a spectrum steeper than protons by Δ𝑠 ep ∼ 0.3 for energies above ∼ 10 GeV and by Δ𝑠 ep ∼ 1.2 above ∼ 1 TeV. Assuming that both species are accelerated at supernova remnant (SNR) shocks, we here explore two possible scenarios that can in principle justify steeper electron spectra: i) energy losses due to synchrotron radiation in an amplified magnetic field, and ii) time dependent acceleration efficiency. We account for magnetic field amplification (MFA) produced by either CR-induced instabilities or by magneto-hydrodynamics (MHD) instabilities using a parametric description. We show that both mechanisms are required to explain the electron spectrum. In particular synchrotron losses can produce a significant electron steepening only above ∼ 1 TeV, while a time dependent acceleration can explain the spectrum at lower energies if the electron injection into diffusive shock acceleration (DSA) is inversely proportional to the shock speed. We discuss observational and theoretical evidences supporting such a behavior. In addition, we predict two additional spectral features: a spectral break below ∼ few GeV (as required by existing observations) due to the acceleration efficiency drop during the adiabatic phase and a spectral hardening above ∼ 20 TeV (where no data are available yet) resulting from electrons escaping from the shock precursor.

Particle escape from supernova remnant shocks: gamma-ray and cosmic-ray signatures

“…The instantaneous electron spectrum at the shock is assumed proportional to the proton spectrum, with a normalization factor 𝐾 ep that accounts for possibly different injection efficiencies of electrons and protons [9]. Nonetheless, its cutoff is located at the maximum energy which is…”

“…where 𝜎 T is the Thomson cross section and 𝑚 e the mass of the electron, while 𝐵 2 eq = 8𝜋𝑈 rad is the equivalent magnetic field associated to the interstellar radiation field of energy density 𝑈 rad . We refer to [9] for details of the numerical computation: the resulting maximum energy achieved at the shock is shown in Fig. 1, as compared to the proton maximum energy given by Eq.…”

“…Right: CR injection spectrum into the Galaxy, including MHD turbulence amplification with efficiency 𝜉 B with respect to the shock ram pressure and different injection efficiency for protons and electrons. Figure from[9], under the CC BY license.…”

Monte Carlo Study of Electron and Positron Cosmic-Ray Propagation with the CALET Spectrum

“…From radio spectral indices in SNRs, Clark & Caswell (1976) found a dispersion in the non-thermal electron index of σ α ∼ 0.3. The spectral index of electron CRs can be affected by the escape process (Ohira et al 2010(Ohira et al , 2012 and/or radiative cooling (Diesing & Caprioli 2019;Morlino & Celli 2021). The dispersion of the injection index can produce a modulation in the spectral shape.…”

“…However, the implied proton injection index (2.81 ± 0.03 − q = 2.31 ± 0.03) is significantly harder than ᾱ = 2.50. For the IK diffusion, the radiative cooling effect on the escape process of electrons (Diesing & Caprioli 2019;Morlino & Celli 2021) may have to be taken into account.…”