Synchrotron X-ray diagnostics of cutoff shape of nonthermal electron spectrum at young supernova remnants

Synchrotron X-rays can be a useful tool to investigate electron acceleration at young supernova remnants (SNRs). At present, since the magnetic field configuration around the shocks of SNRs is uncertain, it is not clear whether electron acceleration is limited by SNR age, synchrotron cooling, or even escape from the acceleration region. We study whether the acceleration mechanism can be constrained by the cutoff shape of the electron spectrum around the maximum energy. We derive analytical formulae of the cutoff shape in each case where the maximum electron energy is determined by SNR age, synchrotron cooling and escape from the shock. They are related to the energy dependence of the electron diffusion coefficient. Next, we discuss whether information on the cutoff shape can be provided by observations in the near future which will simply give the photon indices and the flux ratios in the soft and hard X-ray bands. We find that if the power-law index of the electron spectrum is independently determined by other observations, then we can constrain the cutoff shape by comparing theoretical predictions of the photon indices and/or the flux ratios with observed data which will be measured by NuSTAR and/or ASTRO-H . Such study is helpful in understanding the acceleration mechanism. In particular, it will supply another independent constraint on the magnetic field strength around the shocks of SNRs.

[1]  R. Petre,et al.  Study of Nonthermal Emission from SNR RX J1713.7–3946 with Suzaku , 2008, 0806.1490.

[2]  R. Yamazaki,et al.  TOWARD UNDERSTANDING THE COSMIC-RAY ACCELERATION AT YOUNG SUPERNOVA REMNANTS INTERACTING WITH INTERSTELLAR CLOUDS: POSSIBLE APPLICATIONS TO RX J1713.7−3946 , 2011, 1106.3080.

[3]  Aya Bamba,et al.  Small-Scale Structure of the SN 1006 Shock with Chandra Observations , 2003 .

[4]  Y. Ezoe,et al.  Suzaku X -ray im aging and spectroscopy ofC assiopeia A , 2009, 0912.5020.

[5]  Fine Structures of Shock of SN 1006 with the Chandra Observation , 2003, astro-ph/0302174.

[6]  M. Longair,et al.  High Energy Astrophysics: Volume 2, Stars, the Galaxy and the Interstellar Medium , 1994 .

[7]  S. Reynolds,et al.  Maximum Energies of Shock-accelerated Electrons in Young Shell Supernova Remnants , 1999 .

[8]  J. Martin Laming,et al.  On the Magnetic Fields and Particle Acceleration in Cassiopeia A , 2002, astro-ph/0210669.

[9]  R. Yamazaki,et al.  Gamma-rays from molecular clouds illuminated by cosmic rays escaping from interacting supernova remnants , 2010, 1007.4869.

[10]  L. Drury,et al.  Nonlinear theory of diffusive acceleration of particles by shock waves , 2001 .

[11]  T. Sakamoto,et al.  THE 22 MONTH SWIFT-BAT ALL-SKY HARD X-RAY SURVEY , 2009, 0903.3037.

[12]  Malcolm S. Longair,et al.  High energy astrophysics: The contents of the Universe – the grand design , 1981 .

[13]  Jeremiah P. Ostriker,et al.  Particle Acceleration by Astrophysical Shocks , 1978 .

[14]  On the spectrum of high-energy cosmic rays produced by supernova remnants in the presence of strong cosmic-ray streaming instability and wave dissipation , 2004, astro-ph/0408025.

[15]  A. Bell.  The acceleration of cosmic rays in shock fronts – I , 1978 .

[16]  A. Vladimirov.  Modeling Magnetic Field Amplification in Nonlinear Diffusive Shock Acceleration , 2009, 0904.3760.

[17]  A. Strong,et al.  Propagation of Cosmic-Ray Nucleons in the Galaxy , 1998, astro-ph/9807150.

[18]  J. Chiang,et al.  FERMI-LAT DISCOVERY OF GeV GAMMA-RAY EMISSION FROM THE YOUNG SUPERNOVA REMNANT CASSIOPEIA A , 2010, 1001.1419.

[19]  R. Yamazaki,et al.  EVOLUTION OF SYNCHROTRON X-RAYS IN SUPERNOVA REMNANTS , 2011, 1112.0822.

[20]  Felix A. Aharonian,et al.  Extremely fast acceleration of cosmic rays in a supernova remnant , 2007, Nature.

[21]  Roger D. Blandford,et al.  Particle acceleration at astrophysical shocks: A theory of cosmic ray origin , 1987 .

[22]  Yunjin Kim,et al.  Nuclear Spectroscopic Telescope Array (NuSTAR) Mission , 2013, 2013 IEEE Aerospace Conference.

[23]  R. Yamazaki,et al.  A Spatial and Spectral Study of Nonthermal Filaments in Historical Supernova Remnants: Observational Results with Chandra , 2004, astro-ph/0411326.

[24]  D. Ryu,et al.  Self-Similar Evolution of Cosmic-Ray Modified Shocks , 2009, 0901.1702.

[25]  Fermilab,et al.  On the escape of particles from cosmic ray modified shocks , 2008, 0807.4259.

[26]  R. Petre,et al.  Evidence for shock acceleration of high-energy electrons in the supernova remnant SN1006 , 1995, Nature.

[27]  G. Fleishman,et al.  A role of cosmic rays in generation of radio and optical radiation by plasma mechanisms , 1987 .

[28]  V. Golev,et al.  Design concepts for the Cherenkov Telescope Array CTA: an advanced facility for ground-based high-energy gamma-ray astronomy , 2011 .

[29]  R. Yamazaki,et al.  Gamma-ray spectrum of RX J1713.7-3946 in the Fermi era and future detection of neutrinos , 2008, 0806.3303.

[30]  J. Chiang,et al.  OBSERVATIONS OF THE YOUNG SUPERNOVA REMNANT RX J1713.7−3946 WITH THE FERMI LARGE AREA TELESCOPE , 2011, 1103.5727.

[31]  R. Taillet,et al.  A Markov Chain Monte Carlo technique to sample transport and source parameters of Galactic cosmic rays - I. Method and results for the Leaky-Box model , 2008, 0808.2437.

[32]  F. Aharonian,et al.  Analytical solutions for energy spectra of electrons accelerated by nonrelativistic shock-waves in shell type supernova remnants , 2007 .

[33]  K. Schawinski,et al.  The 105-Month Swift-BAT All-sky Hard X-Ray Survey , 2018, 1801.01882.

[34]  B. Reville,et al.  COMPUTATION OF SYNTHETIC SPECTRA FROM SIMULATIONS OF RELATIVISTIC SHOCKS , 2010, 1010.0872.

[35]  John Raymond,et al.  EFFICIENT COSMIC RAY ACCELERATION, HYDRODYNAMICS, AND SELF-CONSISTENT THERMAL X-RAY EMISSION APPLIED TO SUPERNOVA REMNANT RX J1713.7–3946 , 2010, 1001.1932.

[36]  F. Aharonian,et al.  On the plasma temperature in supernova remnants with cosmic-ray modified shocks , 2008, 0811.3566.

[37]  J. Vink.  Non-thermal bremsstrahlung from supernova remnants and the effect of Coulomb losses , 2008, 0806.4393.

[38]  R. Yamazaki,et al.  Chandra observations of galactic supernova remnant Vela Jr. : A new sample of thin filaments emitting synchrotron X-rays , 2005, astro-ph/0506331.

[39]  J. Laming,et al.  Accelerated Electrons in Cassiopeia A: An Explanation for the Hard X-Ray Tail , 2000, astro-ph/0008426.

[40]  Aya Bamba,et al.  TeV γ-rays from old supernova remnants , 2006 .

[41]  R. Taillet,et al.  A Markov Chain Monte Carlo technique to sample transport and source parameters of Galactic cosmic rays - I. Method and results for the Leaky-Box model , 2009 .

[42]  M. Medvedev.  Theory of “Jitter” Radiation from Small-Scale Random Magnetic Fields and Prompt Emission from Gamma-Ray Burst Shocks , 2000, astro-ph/0001314.

[43]  S. Reynolds.  Models of Synchrotron X-Rays from Shell Supernova Remnants , 1998 .

[44]  Probabilistic description of the first-order Fermi acceleration in shock waves: time-dependent solution by the single-particle approach , 2003, astro-ph/0303024.

[45]  D. Ellison,et al.  Dots, Clumps, and Filaments: The Intermittent Images of Synchrotron Emission in Random Magnetic Fields of Young Supernova Remnants , 2008, 0811.2498.

[46]  S. Reynolds,et al.  Magnetic Fields in Supernova Remnants and Pulsar-Wind Nebulae , 2011, 1104.4047.

[47]  B. Reville,et al.  STEADY-STATE SOLUTIONS IN NONLINEAR DIFFUSIVE SHOCK ACCELERATION , 2008, 0812.3993.

[48]  K. Ioka,et al.  ESCAPE OF COSMIC-RAY ELECTRONS FROM SUPERNOVA REMNANTS , 2011, 1106.1810.

[49]  D. Ellison,et al.  A GENERALIZED MODEL OF NONLINEAR DIFFUSIVE SHOCK ACCELERATION COUPLED TO AN EVOLVING SUPERNOVA REMNANT , 2012, 1203.3614.

[50]  D. Ellison,et al.  GAMMA-RAY EMISSION OF ACCELERATED PARTICLES ESCAPING A SUPERNOVA REMNANT IN A MOLECULAR CLOUD , 2011, 1102.3885.

[51]  R. Chevalier,et al.  Nonthermal Emission from a Supernova Remnant in a Molecular Cloud , 2000 .

[52]  R. Yamazaki,et al.  Escape-limited model of cosmic-ray acceleration revisited , 2009, 0910.3449.

[53]  F. Aharonian,et al.  Fast Variability of Nonthermal X-Ray Emission in Cassiopeia A: Probing Electron Acceleration in Reverse-Shocked Ejecta , 2008, 0803.3410.

[54]  F. Takahara,et al.  A NOVEL EMISSION SPECTRUM FROM A RELATIVISTIC ELECTRON MOVING IN A RANDOM MAGNETIC FIELD , 2011, 1106.2216.

[55]  E. Waxman,et al.  In which shell-type SNRs should we look for gamma-rays and neutrinos from P–P collisions? , 2007, 0706.3485.