Analytical solutions for energy spectra of electrons accelerated by nonrelativistic shock-waves in shell type supernova remnants
By V. Zirakashvili, F. Aharonian. 2006
208 citations recorded by the source corpus.
Context. Recent observations of hard X-rays and very high energy gamma-rays from a number of young shell type supernova remnants indicate the importance of detailed quantitative studies of energy spectra of relativistic electrons formed via diffusive shock acceleration accompanied by intense nonthermal emission through synchrotron radiation and inverse Compton scattering. Aims. The aim of this work was derivation of exact asymptotic solutions of the kinetic equation which describes the energy distribution of shock-accelerated electrons for an arbitrary energy-dependence of the diffusion coefficient. Methods. The asymptotic solutions at low and very high energy domains coupled with numerical calculations in the intermediate energy range allow analytical presentations of energy spectra of electrons for the entire energy region. Results. Under the assumption that the energy losses of electrons are dominated by synchrotron cooling, we derived the exact asymptotic spectra of electrons without any restriction on the diffusion coefficient. We also obtained simple analytical approximations which describe, with accuracy better than ten percent, the energy spectra of nonthermal emission of shock-accelerated electrons due to the synchrotron radiation and inverse Compton scattering. Conclusions. The results can be applied for interpretation of X-ray and gamma-ray observations of shell type supernova remnants, as well as other nonthermal high energy source populations like microquasars and large scale synchrotron jets of active galactic nuclei.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/24a9f7058e8a475fa7970d9eb69748638e4dc06f
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Citations in the corpus
- Observational Signatures of Particle Acceleration in Supernova Remnants (2012, background): “If we take for example the following asymptotic form of the synchrotron spectrum (c.f. Zirakashvili and Aharonian, 2007; Katsuda et al., 2010b; Patnaude et al., 2011): F (hν) = φBΓ0 × (hν)−Γ0 exp ( − √ ν νcut−off ) , (27) with Γ0 the asymptotic spectral index below the cut-off and φ a normalization…”
- On the Momentum Diffusion of Radiating Ultrarelativistic Electrons in a Turbulent Magnetic Field (2008, background): “The relatively complicated function (57) can instead be conveniently approximated by R(x) 1:81(1:33þ x 2/3) 1/2e x (Zirakashvili & Aharonian 2007), allowing for some analytical investigation of the integral (56).”
- NONTHERMAL RADIATION OF YOUNG SUPERNOVA REMNANTS: THE CASE OF RX J1713.7−3946 (2010, methodology): “With an accuracy of several percent R(ω/ωc) can be presented in a simple analytical form (Zirakashvili & Aharonian 2007): R(x) = 1.81 exp(−x)√ x−2/3 + (3.62/π )2 .”
- Teraelectronvolt Astronomy (2010, background): “…energies achievable in supernova shocks of age 1000 t3 yr are of order Emax ∼ u28t3BµGTeV (2) where u8 is the shock speed in units of 1000 km s −1 (e.g. Reynolds (2008)); for electrons, synchrotron losses limit the peak energy to Emax ∼ 100u8B−1/2µG TeV (3) See Zirakashvili & Aharonian (2007).”
- DIFFUSIVE SHOCK ACCELERATION SIMULATIONS OF RADIO RELICS (2012, background): “It is because the width of the spatial distribution of electrons with γe decreases as γ −1 e (Zirakashvili & Aharonian 2007; Kang 2011).”
- Magnetic Fields in Supernova Remnants and Pulsar-Wind Nebulae (2011, background): “(A more careful calculation in the case of synchrotron losses predicts a spectrum with the same exponential factor e− √ ν/νc ; Zirakashvili & Aharonian 2007).”
- Study of Nonthermal Emission from SNR RX J1713.7–3946 with Suzaku (2008, methodology): “The energy spectrum of synchrotron radiation corresponding to the electron spectrum given by equation (8) has a form (Zirakashvili & Aharonian 2007) dN dε ∝ ε−2 [ 1+ 0.46 ( ε ε0 )0.6 ]2.29 exp [ − ( ε ε0 )1/2 ] .”
- Strong evidence for hadron acceleration in Tycho’s supernova remnant (2011, methodology): “The instantaneous electron spectrum at the shock,fe,0(p), is computed as in Morlino, Amato & Blasi (2009), using the expression worked out by Zirakashvili & Aharonian (2007) for a ∝ p−4 proton spectrum: fe,0(p) = Kep fp,0(p) [ 1+ 0.523 ( p/pe,max ) 9 4 ]2 e−p 2/p2e,max , (12) where pe,max is…”