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Table 1:

Summary of the notations used in this article to denote the various physical quantities and parameters involved in our description of high energy particle yield in supernova remnants (SNR).
 Turbulence parameters  
$\beta$ One D power-law spectral index of the turbulence spectrum (Eq. (6))
  $\eta_{\rm T}$ Level of magnetic fluctuations with respect to the mean ISM magnetic field (Eq. (6))
$\phi$ Logarithm of the ratio of the maximum momentum to the injection momentum (Eq. (4))
  $\lambda_{\rm max}$ Longest wavelength of the magnetic turbulence spectrum (Sect. 2.3)
  $\ell_{\rm coh}$ Coherence length of the magnetic fluctuations (Sect. 2.3)
$\sigma$ Normalisation factor entering the turbulent spectrum (Sect. 2.3)
  $\delta_{\rm u/d}$ Power-law energy dependance index of the relaxation lengths either up-
  or downstream (Sect. 4 and (Eq. (23))
H Ratio of the upstream to the downstream diffusion coefficient at the shock front (Eq. (16))
  $\delta_{\rm B}$ Ratio of the resonant to the non-resonant magnetic field strength at the shock front (Eq. (3))
 Relativistic particle parameters
  $\xi_{\rm CR}$ Ratio of the CR pressure to the shock dynamical pressure (Eq. (3))
$r_{\rm L}$ Larmor radius of a particle (defined using resonant magnetic field)
$\rho$ Ratio of the particle Larmor radius to $\lambda_{\rm max}/2\pi$ (also called reduced rigidity, see Sect. 2.3)
  $E_{\rm CR-max}$ Maximal cosmic ray energy (Sect. 2.3)
  $E_{\rm e-max}$ Maximal electron energy (Sect. 3.1)
  $E_{\rm\gamma-cut}$ Cut-off synchrotron photon energy emitted by electrons at $E_{\rm e-max}$ (Sect. 3.1)
  $E_{\rm CR-min}$ Injection energy of the cosmic rays (Sect. 4.1.4)
  $E_{\rm e-obs}$ Energy of the electrons producing the observed X-ray filaments (Sect. 4.2.4)

 SNRs parameters
  $V_{\rm sh,4}$ Velocity of the SNR shock wave (in 104 km s-1 unit)
  $B_{\rm d/u,-4}$ Magnetic field amplitude at the shock front respectively in the
  down- and upstream medium (in 10-4 Gauss unit)
  $r_{\rm B}, r_{\rm sub}, r_{\rm tot}$ Magnetic, sub-shock, and total shock compression ratios (Sect. 3.1)
  $\Delta R_{\rm X,-2}$ X-ray filament deprojected width (in 10-2 parsec unit, Sect. 4.2.4)

 Equation parameters
y(r) 3 r2/(r-1) (Eq. (19))
  ${K}(r,\beta)$ $q(\beta) \times (H(r,\beta)/r+1)$(Eq. (36))
  ${f}_{\rm sync}$ $H(r,\beta)+r / H(r,\beta)/r_{\rm B}^2 +r$(Eq. (39))
g(r) $3/(r-1) \times (H(r,\beta)/r + 1)$(Eq. (40))
  $C(\delta_{\rm d})$ $(E_{\rm e-max}/E_{\rm e-obs})^{\delta_{\rm d}}$(Eq. (41))


Source LaTeX | All tables | In the text

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