Artificial broadening of the high-energy end of electron spectrum in supernova remnants

The observed spectrum of a supernova remnant (SNR) is a superposition of many ``local'' spectra emitted by regions of SNRs that are under different physical conditions. The question remains as to whether the broadening of the high-energy end of the observed nonthermal spectrum of SNRs, like in G347.3-0.5 and SN 1006, can be an artifact of observations or it is a consequence of the microphysics involved in the acceleration process. In this note we study the influence of parameters variations (inside the volume and over the surface of SNR) on the shape of the high-energy end of the synchrotron (and also inverse Compton) spectrum. We consider three possibilities for these parameter variations: i) gradients downstream of the shock with constant maximum energy of the accelerated electrons and the potential variation in time of the injection efficiency, ii) then we add the possibility of the maximum energy depending on time, and finally iii) the possible obliquity dependences of maximum energy and injection efficiency. It is shown that gradients of density and magnetic field strength downstream of the shock are ineffective in modifying the shape of the synchrotron spectrum, even if an SNR evolves in the nonuniform interstellar medium and/or the injection efficiency varies in time. The time dependence of the maximum energy of the electrons accelerated by the shock is also not able to make the observed spectrum much broader. The only possibility of producing considerable broadening in the spectrum is the variation in the maximum energy of electrons over the surface of SNR. In such a case, the obliquity dependence of the injection efficiency also affects the shape of the spectrum, but its role is less significant